Trained generative models have shown remarkable performance as priors for inverse problems in imaging -- for example, Generative Adversarial Network priors permit recovery of test images from 5-10x fewer measurements than sparsity priors. Unfortunately, these models may be unable to represent any particular image because of architectural choices, mode collapse, and bias in the training dataset. In this paper, we demonstrate that invertible neural networks, which have zero representation error by design, can be effective natural signal priors at inverse problems such as denoising, compressive sensing, and inpainting. Given a trained generative model, we study the empirical risk formulation of the desired inverse problem under a regularization that promotes high likelihood images, either directly by penalization or algorithmically by initialization. For compressive sensing, invertible priors can yield higher accuracy than sparsity priors across almost all undersampling ratios, and due to their lack of representation error, invertible priors can yield better reconstructions than GAN priors for images that have rare features of variation within the biased training set, including out-of-distribution natural images. We additionally compare performance for compressive sensing to unlearned methods, such as the deep decoder, and we establish theoretical bounds on expected recovery error in the case of a …

The multi-armed bandit (MAB) problem is a classical learning task that exemplifies the exploration-exploitation tradeoff. However, standard formulations do not take into account risk. In online decision making systems, risk is a primary concern. In this regard, the mean-variance risk measure is one of the most common objective functions. Existing algorithms for mean-variance optimization in the context of MAB problems have unrealistic assumptions on the reward distributions. We develop Thompson Sampling-style algorithms for mean-variance MAB and provide comprehensive regret analyses for Gaussian and Bernoulli bandits with fewer assumptions. Our algorithms achieve the best known regret bounds for mean-variance MABs and also attain the information-theoretic bounds in some parameter regimes. Empirical simulations show that our algorithms significantly outperform existing LCB-based algorithms for all risk tolerances.

When machine learning models are deployed on a test distribution different from the training distribution, they can perform poorly, but overestimate their performance. In this work, we aim to better estimate a model's performance under distribution shift, without supervision. To do so, we use a set of domain-invariant predictors as a proxy for the unknown, true target labels. Since the error of the resulting risk estimate depends on the target risk of the proxy model, we study generalization of domain-invariant representations and show that the complexity of the latent representation has a significant influence on the target risk. Empirically, our approach (1) enables self-tuning of domain adaptation models, and (2) accurately estimates the target error of given models under distribution shift. Other applications include model selection, deciding early stopping and error detection.

We propose the Interferometric Graph Transform (IGT), which is a new class of deep unsupervised graph convolutional neural network for building graph representations. Our first contribution is to propose a generic, complex-valued spectral graph architecture obtained from a generalization of the Euclidean Fourier transform. We show that our learned representation consists of both discriminative and invariant features, thanks to a novel greedy concave objective. From our experiments, we conclude that our learning procedure exploits the topology of the spectral domain, which is normally a flaw of spectral methods, and in particular our method can recover an analytic operator for vision tasks. We test our algorithm on various and challenging tasks such as image classification (MNIST, CIFAR-10), community detection (Authorship, Facebook graph) and action recognition from 3D skeletons videos (SBU, NTU), exhibiting a new state-of-the-art in spectral graph unsupervised settings.

Generalization across environments is critical to the successful application of reinforcement learning (RL) algorithms to real-world challenges. In this work we propose a method for learning state abstractions which generalize to novel observation distributions in the multi-environment RL setting. We prove that for certain classes of environments, this approach outputs, with high probability, a state abstraction corresponding to the causal feature set with respect to the return. We give empirical evidence that analogous methods for the nonlinear setting can also attain improved generalization over single- and multi-task baselines. Lastly, we provide bounds on model generalization error in the multi-environment setting, in the process showing a connection between causal variable identification and the state abstraction framework for MDPs.

Speech information can be roughly decomposed into four components: language content, timbre, pitch, and rhythm. Obtaining disentangled representations of these components is useful in many speech analysis and generation applications. Recently, state-of-the-art voice conversion systems have led to speech representations that can disentangle speaker-dependent and independent information. However, these systems can only disentangle timbre, while information about pitch, rhythm and content is still mixed together. Further disentangling the remaining speech components is an under-determined problem in the absence of explicit annotations for each component, which are difficult and expensive to obtain. In this paper, we propose SpeechSplit, which can blindly decompose speech into its four components by introducing three carefully designed information bottlenecks. SpeechSplit is among the first algorithms that can separately perform style transfer on timbre, pitch and rhythm without text labels. Our code is publicly available at https://github.com/auspicious3000/SpeechSplit.

Recovering a signal from its Fourier intensity underlies many important applications, including lensless imaging and imaging through scattering media. Conventional algorithms for retrieving the phase suffer when noise is present but display global convergence when given clean data. Neural networks have been used to improve algorithm robustness, but efforts to date are sensitive to initial conditions and give inconsistent performance. Here, we combine iterative methods from phase retrieval with image statistics from deep denoisers, via regularization-by-denoising. The resulting methods inherit the advantages of each approach and outperform other noise-robust phase retrieval algorithms. Our work paves the way for hybrid imaging methods that integrate machine-learned constraints in conventional algorithms.

The recently proposed Thermodynamic Variational Objective (TVO) leverages thermodynamic integration to provide a family of variational inference objectives, which both tighten and generalize the ubiquitous Evidence Lower Bound (ELBO). However, the tightness of TVO bounds was not previously known, an expensive grid search was used to choose a ``schedule'' of intermediate distributions, and model learning suffered with ostensibly tighter bounds. In this work, we propose an exponential family interpretation of the geometric mixture curve underlying the TVO and various path sampling methods, which allows us to characterize the gap in TVO likelihood bounds as a sum of KL divergences. We propose to choose intermediate distributions using equal spacing in the moment parameters of our exponential family, which matches grid search performance and allows the schedule to adaptively update over the course of training. Finally, we derive a doubly reparameterized gradient estimator which improves model learning and allows the TVO to benefit from more refined bounds. To further contextualize our contributions, we provide a unified framework for understanding thermodynamic integration and the TVO using Taylor series remainders.

This paper presents SimCLR: a simple framework for contrastive learning of visual representations. We simplify recently proposed contrastive self-supervised learning algorithms without requiring specialized architectures or a memory bank. In order to understand what enables the contrastive prediction tasks to learn useful representations, we systematically study the major components of our framework. We show that (1) composition of data augmentations plays a critical role in defining effective predictive tasks, (2) introducing a learnable nonlinear transformation between the representation and the contrastive loss substantially improves the quality of the learned representations, and (3) contrastive learning benefits from larger batch sizes and more training steps compared to supervised learning. By combining these findings, we are able to considerably outperform previous methods for self-supervised and semi-supervised learning on ImageNet. A linear classifier trained on self-supervised representations learned by SimCLR achieves 76.5% top-1 accuracy, which is a 7% relative improvement over previous state-of-the-art, matching the performance of a supervised ResNet-50. When fine-tuned on only 1% of the labels, we achieve 85.8% top-5 accuracy, outperforming AlexNet with 100X fewer labels.

Conditional Value-at-Risk (CVaR) is a widely used risk metric in applications such as finance. We derive concentration bounds for CVaR estimates, considering separately the cases of sub-Gaussian, light-tailed and heavy-tailed distributions. For the sub-Gaussian and light-tailed cases, we use a classical CVaR estimator based on the empirical distribution constructed from the samples. For heavy-tailed random variables, we assume a mild `bounded moment' condition, and derive a concentration bound for a truncation-based estimator. Our concentration bounds exhibit exponential decay in the sample size, and are tighter than those available in the literature for the above distribution classes. To demonstrate the applicability of our concentration results, we consider the CVaR optimization problem in a multi-armed bandit setting. Specifically, we address the best CVaR-arm identification problem under a fixed budget. Using our CVaR concentration results, we derive an upper-bound on the probability of incorrect arm identification.

Parameter estimation, statistical tests and confidence sets are the cornerstones of classical statistics that allow scientists to make inferences about the underlying process that generated the observed data. A key question is whether one can still construct hypothesis tests and confidence sets with proper coverage and high power in a so-called likelihood-free inference (LFI) setting; that is, a setting where the likelihood is not explicitly known but one can forward-simulate observable data according to a stochastic model. In this paper, we present ACORE (Approximate Computation via Odds Ratio Estimation), a frequentist approach to LFI that first formulates the classical likelihood ratio test (LRT) as a parametrized classification problem, and then uses the equivalence of tests and confidence sets to build confidence regions for parameters of interest. We also present a goodness-of-fit procedure for checking whether the constructed tests and confidence regions are valid. ACORE is based on the key observation that the LRT statistic, the rejection probability of the test, and the coverage of the confidence set are conditional distribution functions which often vary smoothly as a function of the parameters of interest. Hence, instead of relying solely on samples simulated at fixed parameter settings (as is the convention in …

Variational Autoencoders (VAE) and their variants have been widely used in a variety of applications, such as dialog generation, image generation and disentangled representation learning. However, the existing VAE models may suffer from KL vanishing in language modeling and low reconstruction quality for disentangling. To address these issues, we propose a novel controllable variational autoencoder framework, ControlVAE, that combines a controller, inspired by automatic control theory, with the basic VAE to improve the performance of resulting generative models. Specifically, we design a new non-linear PI controller, a variant of the proportional-integral-derivative (PID) control, to automatically tune the hyperparameter (weight) added in the VAE objective using the output KL-divergence as feedback during model training. The framework is evaluated using three applications; namely, language modeling, disentangled representation learning, and image generation. The results show that ControlVAE can achieve much better reconstruction quality than the competitive methods for the comparable disentanglement performance. For language modelling, it not only averts the KL-vanishing, but also improves the diversity of generated text. Finally, we also demonstrate that ControlVAE improves the reconstruction quality for image generation compared to the original VAE.

Performance evaluations are critical for quantifying algorithmic advances in reinforcement learning. Recent reproducibility analyses have shown that reported performance results are often inconsistent and difficult to replicate. In this work, we argue that the inconsistency of performance stems from the use of flawed evaluation metrics. Taking a step towards ensuring that reported results are consistent, we propose a new comprehensive evaluation methodology for reinforcement learning algorithms that produces reliable measurements of performance both on a single environment and when aggregated across environments. We demonstrate this method by evaluating a broad class of reinforcement learning algorithms on standard benchmark tasks.

Sensitive attributes such as race are rarely available to learners in real world settings as their collection is often restricted by laws and regulations. We give a scheme that allows individuals to release their sensitive information privately while still allowing any downstream entity to learn non-discriminatory predictors. We show how to adapt non-discriminatory learners to work with privatized protected attributes giving theoretical guarantees on performance. Finally, we highlight how the methodology could apply to learning fair predictors in settings where protected attributes are only available for a subset of the data.

We propose a method for multiple hypothesis testing with familywise error rate (FWER) control, called the i-FWER test. Most testing methods are predefined algorithms that do not allow modifications after observing the data. However, in practice, analysts tend to choose a promising algorithm after observing the data; unfortunately, this violates the validity of the conclusion. The i-FWER test allows much flexibility: a human (or a computer program acting on the human's behalf) may adaptively guide the algorithm in a data-dependent manner. We prove that our test controls FWER if the analysts adhere to a particular protocol of masking and unmasking. We demonstrate via numerical experiments the power of our test under structured non-nulls, and then explore new forms of masking.

We show that on-policy policy gradient (PG) and its variance reduction variants can be derived by taking finite-difference of function evaluations supplied by estimators from the importance sampling (IS) family for off-policy evaluation (OPE). Starting from the doubly robust (DR) estimator (Jiang & Li, 2016), we provide a simple derivation of a very general and flexible form of PG, which subsumes the state-of-the-art variance reduction technique (Cheng et al., 2019) as its special case and immediately hints at further variance reduction opportunities overlooked by existing literature. We analyze the variance of the new DR-PG estimator, compare it to existing methods as well as the Cramer-Rao lower bound of policy gradient, and empirically show its effectiveness.

The remarkable recent advances in object-centric generative world models raise a few questions. First, while many of the recent achievements are indispensable for making a general and versatile world model, it is quite unclear how these ingredients can be integrated into a unified framework. Second, despite using generative objectives, abilities for object detection and tracking are mainly investigated, leaving the crucial ability of temporal imagination largely under question. Third, a few key abilities for more faithful temporal imagination such as multimodal uncertainty and situation-awareness are missing. In this paper, we introduce Generative Structured World Models (G-SWM). The G-SWM achieves the versatile world modeling not only by unifying the key properties of previous models in a principled framework but also by achieving two crucial new abilities, multimodal uncertainty and situation-awareness. Our thorough investigation on the temporal generation ability in comparison to the previous models demonstrates that G-SWM achieves the versatility with the best or comparable performance for all experiment settings including a few complex settings that have not been tested before. https://sites.google.com/view/gswm

We propose a transductive Laplacian-regularized inference for few-shot tasks. Given any feature embedding learned from the base classes, we minimize a quadratic binary-assignment function containing two terms: (1) a unary term assigning query samples to the nearest class prototype, and (2) a pairwise Laplacian term encouraging nearby query samples to have consistent label assignments. Our transductive inference does not re-train the base model, and can be viewed as a graph clustering of the query set, subject to supervision constraints from the support set. We derive a computationally efficient bound optimizer of a relaxation of our function, which computes independent (parallel) updates for each query sample, while guaranteeing convergence. Following a simple cross-entropy training on the base classes, and without complex meta-learning strategies, we conducted comprehensive experiments over five few-shot learning benchmarks. Our LaplacianShot consistently outperforms state-of-the-art methods by significant margins across different models, settings, and data sets. Furthermore, our transductive inference is very fast, with computational times that are close to inductive inference, and can be used for large-scale few-shot tasks.

Irregularly-sampled time series occur in many domains including healthcare. They can be challenging to model because they do not naturally yield a fixed-dimensional representation as required by many standard machine learning models. In this paper, we consider irregular sampling from the perspective of missing data. We model observed irregularly-sampled time series data as a sequence of index-value pairs sampled from a continuous but unobserved function. We introduce an encoder-decoder framework for learning from such generic indexed sequences. We propose learning methods for this framework based on variational autoencoders and generative adversarial networks. For continuous irregularly-sampled time series, we introduce continuous convolutional layers that can efficiently interface with existing neural network architectures. Experiments show that our models are able to achieve competitive or better classification results on irregularly-sampled multivariate time series compared to recent RNN models while offering significantly faster training times.

In the transfer learning problem, the target and the source data domains are typically known. In this article, we study a new paradigm called mutual transfer learning where among many heterogeneous data domains, every data domain could potentially be the target of interest, and it could also be a useful source to help the learning in other data domains. However, it is important to note that given a target not every data domain can be a successful source; only data sets that are similar enough to be thought as from the same population can be useful sources for each other. Under this mutual learnability assumption, a confidence distribution fusion approach is proposed to recover the mutual learnability relation in the transfer learning regime. Our proposed method achieves the same oracle statistical inferential accuracy as if the true learnability structure were known. It can be implemented in an efficient parallel fashion to deal with large-scale data. Simulated and real examples are analyzed to illustrate the usefulness of the proposed method.

The output of a neural network depends on its architecture and weights in a highly nonlinear way, and it is often assumed that a network's parameters cannot be recovered from its output. Here, we prove that, in fact, it is frequently possible to reconstruct the architecture, weights, and biases of a deep ReLU network by observing only its output. We leverage the fact that every ReLU network defines a piecewise linear function, where the boundaries between linear regions correspond to inputs for which some neuron in the network switches between inactive and active ReLU states. By dissecting the set of region boundaries into components associated with particular neurons, we show both theoretically and empirically that it is possible to recover the weights of neurons and their arrangement within the network, up to isomorphism.

Maximizing on k-submodular functions subject to size constraint has received extensive attention recently. In this paper, we investigate a more realistic scenario of this problem that (1) obtaining exact evaluation of an objective function is impractical, instead, its noisy version is acquired; and (2) algorithms are required to take only one single pass over dataset, producing solutions in a timely manner. We propose two novel streaming algorithms, namely DStream and RStream, with their theoretical performance guarantees. We further demonstrate the efficiency of our algorithms in two application, showing that our algorithms can return comparative results to state-of-the-art non-streaming methods while using a much fewer number of queries.

The objective of a reinforcement learning agent is to behave so as to maximise the sum of a suitable scalar function of state: the reward. These rewards are typically given and immutable. In this paper, we instead consider the proposition that the reward function itself can be a good locus of learned knowledge. To investigate this, we propose a scalable meta-gradient framework for learning useful intrinsic reward functions across multiple lifetimes of experience. Through several proof-of-concept experiments, we show that it is feasible to learn and capture knowledge about long-term exploration and exploitation into a reward function. Furthermore, we show that unlike policy transfer methods that capture how'' the agent should behave, the learned reward functions can generalise to other kinds of agents and to changes in the dynamics of the environment by capturingwhat'' the agent should strive to do.

This paper employs a formal connection of machine learning with thermodynamics to characterize the quality of learnt representations for transfer learning. We discuss how information-theoretic functionals such as rate, distortion and classification loss of a model lie on a convex, so-called equilibrium surface. We prescribe dynamical processes to traverse this surface under constraints, e.g., an iso-classification process that trades off rate and distortion to keep the classification loss unchanged. We demonstrate how this process can be used for transferring representations from a source dataset to a target dataset while keeping the classification loss constant. Experimental validation of the theoretical results is provided on standard image-classification datasets.

We develop amortized population Gibbs (APG) samplers, a class of scalable methods that frame structured variational inference as adaptive importance sampling. APG samplers construct high-dimensional proposals by iterating over updates to lower-dimensional blocks of variables. We train each conditional proposal by minimizing the inclusive KL divergence with respect to the conditional posterior. To appropriately account for the size of the input data, we develop a new parameterization in terms of neural sufficient statistics. Experiments show that APG samplers can be used to train highly-structured deep generative models in an unsupervised manner, and achieve substantial improvements in inference accuracy relative to standard autoencoding variational methods.

This paper proposes a new framework for providing approximation guarantees of local search algorithms. Local search is a basic algorithm design technique and is widely used for various combinatorial optimization problems. To analyze local search algorithms for set function maximization, we propose a new notion called \textit{localizability} of set functions, which measures how effective local improvement is. Moreover, we provide approximation guarantees of standard local search algorithms under various combinatorial constraints in terms of localizability. The main application of our framework is sparse optimization, for which we show that restricted strong concavity and restricted smoothness of the objective function imply localizability, and further develop accelerated versions of local search algorithms. We conduct experiments in sparse regression and structure learning of graphical models to confirm the practical efficiency of the proposed local search algorithms.

Coagent policy gradient algorithms (CPGAs) are reinforcement learning algorithms for training a class of stochastic neural networks called coagent networks. In this work, we prove that CPGAs converge to locally optimal policies. Additionally, we extend prior theory to encompass asynchronous and recurrent coagent networks. These extensions facilitate the straightforward design and analysis of hierarchical reinforcement learning algorithms like the option-critic, and eliminate the need for complex derivations of customized learning rules for these algorithms.

The compression of Generative Adversarial Networks (GANs) has lately drawn attention, due to the increasing demand for deploying GANs into mobile devices for numerous applications such as image translation, enhancement and editing. However, compared to the substantial efforts to compressing other deep models, the research on compressing GANs (usually the generators) remains at its infancy stage. Existing GAN compression algorithms are limited to handling specific GAN architectures and losses. Inspired by the recent success of AutoML in deep compression, we introduce AutoML to GAN compression and develop an AutoGAN-Distiller (AGD) framework. Starting with a specifically designed efficient search space, AGD performs an end-to-end discovery for new efficient generators, given the target computational resource constraints. The search is guided by the original GAN model via knowledge distillation, therefore fulfilling the compression. AGD is fully automatic, standalone (i.e., needing no trained discriminators), and generically applicable to various GAN models. We evaluate AGD in two representative GAN tasks: image translation and super resolution. Without bells and whistles, AGD yields remarkably lightweight yet more competitive compressed models, that largely outperform existing alternatives. Our codes and pretrained models are available at: https://github.com/TAMU-VITA/AGD.

Efficient optimisation of black-box problems that comprise both continuous and categorical inputs is important, yet poses significant challenges. Current approaches, like one-hot encoding, severely increase the dimension of the search space, while separate modelling of category-specific data is sample-inefficient. Both frameworks are not scalable to practical applications involving multiple categorical variables, each with multiple possible values. We propose a new approach, Continuous and Categorical Bayesian Optimisation (CoCaBO), which combines the strengths of multi-armed bandits and Bayesian optimisation to select values for both categorical and continuous inputs. We model this mixed-type space using a Gaussian Process kernel, designed to allow sharing of information across multiple categorical variables; this allows CoCaBO to leverage all available data efficiently. We extend our method to the batch setting and propose an efficient selection procedure that dynamically balances exploration and exploitation whilst encouraging batch diversity. We demonstrate empirically that our method outperforms existing approaches on both synthetic and real-world optimisation tasks with continuous and categorical inputs.

In many predictive decision-making scenarios, such as credit scoring and academic testing, a decision-maker must construct a model that accounts for agents' incentives to ``game'' by changing their features to receive better decisions. Whereas the strategic classification literature has previously assumed that agents' outcomes are not causally dependent on their features (and thus strategic behavior is a form of lying), we join concurrent work in modeling agents' outcomes as a function of their changeable attributes. Our work introduces the realizable linear regression setting, and is the first to incorporate a crucial phenomenon: when agents act to change observable features, they may as a side effect perturb hidden features that causally affect their true outcomes. As our main contribution, we provide the efficient algorithms for optimizing three distinct decision-making objectives: accurately predicting agents' post-gaming outcomes (prediction risk minimization), incentivizing agents to improve these outcomes (agent outcome maximization), and estimating the coefficients of the true underlying model (parameter estimation). Our algorithms circumvent the hardness result of Miller et al. (2020) by allowing the decision maker to test a sequence of decision rules and observe agents' responses, in effect performing causal interventions by varying the chosen rule.

Despite the power of deep neural networks for a wide range of tasks, an overconfident prediction issue has limited their practical use in many safety-critical applications. Many recent works have been proposed to mitigate this issue, but most of them require either additional computational costs in training and/or inference phases or customized architectures to output confidence estimates separately. In this paper, we propose a method of training deep neural networks with a novel loss function, named Correctness Ranking Loss, which regularizes class probabilities explicitly to be better confidence estimates in terms of ordinal ranking according to confidence. The proposed method is easy to implement and can be applied to the existing architectures without any modification. Also, it has almost the same computational costs for training as conventional deep classifiers and outputs reliable predictions by a single inference. Extensive experimental results on classification benchmark datasets indicate that the proposed method helps networks to produce well-ranked confidence estimates. We also demonstrate that it is effective for the tasks closely related to confidence estimation, out-of-distribution detection and active learning.

We introduce a self-supervised approach for learning node and graph level representations by contrasting structural views of graphs. We show that unlike visual representation learning, increasing the number of views to more than two or contrasting multi-scale encodings do not improve performance, and the best performance is achieved by contrasting encodings from first-order neighbors and a graph diffusion. We achieve new state-of-the-art results in self-supervised learning on 8 out of 8 node and graph classification benchmarks under the linear evaluation protocol. For example, on Cora (node) and Reddit-Binary (graph) classification benchmarks, we achieve 86.8% and 84.5% accuracy, which are 5.5% and 2.4% relative improvements over previous state-of-the-art. When compared to supervised baselines, our approach outperforms them in 4 out of 8 benchmarks.

Classical linear metric learning methods have recently been extended along two distinct lines: deep metric learning methods for learning embeddings of the data using neural networks, and Bregman divergence learning approaches for extending learning Euclidean distances to more general divergence measures such as divergences over distributions. In this paper, we introduce deep Bregman divergences, which are based on learning and parameterizing functional Bregman divergences using neural networks, and which unify and extend these existing lines of work. We show in particular how deep metric learning formulations, kernel metric learning, Mahalanobis metric learning, and moment-matching functions for comparing distributions arise as special cases of these divergences in the symmetric setting. We then describe a deep learning framework for learning general functional Bregman divergences, and show in experiments that this method yields superior performance on benchmark datasets as compared to existing deep metric learning approaches. We also discuss novel applications, including a semi-supervised distributional clustering problem, and a new loss function for unsupervised data generation.

Machine learning models are not static and may need to be retrained on slightly changed datasets, for instance, with the addition or deletion of a set of data points. This has many applications, including privacy, robustness, bias reduction, and uncertainty quantifcation. However, it is expensive to retrain models from scratch. To address this problem, we propose the DeltaGrad algorithm for rapid retraining machine learning models based on information cached during the training phase. We provide both theoretical and empirical support for the effectiveness of DeltaGrad, and show that it compares favorably to the state of the art.

Recent advances in deep representation learning on Riemannian manifolds extend classical deep learning operations to better capture the geometry of the manifold. One possible extension is the Fréchet mean, the generalization of the Euclidean mean; however, it has been difficult to apply because it lacks a closed form with an easily computable derivative. In this paper, we show how to differentiate through the Fréchet mean for arbitrary Riemannian manifolds. Then, focusing on hyperbolic space, we derive explicit gradient expressions and a fast, accurate, and hyperparameter-free Fréchet mean solver. This fully integrates the Fréchet mean into the hyperbolic neural network pipeline. To demonstrate this integration, we present two case studies. First, we apply our Fréchet mean to the existing Hyperbolic Graph Convolutional Network, replacing its projected aggregation to obtain state-of-the-art results on datasets with high hyperbolicity. Second, to demonstrate the Fréchet mean's capacity to generalize Euclidean neural network operations, we develop a hyperbolic batch normalization method that gives an improvement parallel to the one observed in the Euclidean setting.

In E-commerce, advertising is essential for merchants to reach their target users. The typical objective is to maximize the advertiser's cumulative revenue over a period of time under a budget constraint. In real applications, an advertisement (ad) usually needs to be exposed to the same user multiple times until the user finally contributes revenue (e.g., places an order). However, existing advertising systems mainly focus on the immediate revenue with single ad exposures, ignoring the contribution of each exposure to the final conversion, thus usually falls into suboptimal solutions. In this paper, we formulate the sequential advertising strategy optimization as a dynamic knapsack problem. We propose a theoretically guaranteed bilevel optimization framework, which significantly reduces the solution space of the original optimization space while ensuring the solution quality. To improve the exploration efficiency of reinforcement learning, we also devise an effective action space reduction approach. Extensive offline and online experiments show the superior performance of our approaches over state-of-the-art baselines in terms of cumulative revenue.

The field of deep generative modeling has succeeded in producing astonishingly realistic-seeming images and audio, but quantitative evaluation remains a challenge. Log-likelihood is an appealing metric due to its grounding in statistics and information theory, but it can be challenging to estimate for implicit generative models, and scalar-valued metrics give an incomplete picture of a model's quality. In this work, we propose to use rate distortion (RD) curves to evaluate and compare deep generative models. While estimating RD curves is seemingly even more computationally demanding than log-likelihood estimation, we show that we can approximate the entire RD curve using nearly the same computations as were previously used to achieve a single log-likelihood estimate. We evaluate lossy compression rates of VAEs, GANs, and adversarial autoencoders (AAEs) on the MNIST and CIFAR10 datasets. Measuring the entire RD curve gives a more complete picture than scalar-valued metrics, and we arrive at a number of insights not obtainable from log-likelihoods alone.

A common workflow in data exploration is to learn a low-dimensional representation of the data, identify groups of points in that representation, and examine the differences between the groups to determine what they represent. We treat this workflow as an interpretable machine learning problem by leveraging the model that learned the low-dimensional representation to help identify the key differences between the groups. To solve this problem, we introduce a new type of explanation, a Global Counterfactual Explanation (GCE), and our algorithm, Transitive Global Translations (TGT), for computing GCEs. TGT identifies the differences between each pair of groups using compressed sensing but constrains those pairwise differences to be consistent among all of the groups. Empirically, we demonstrate that TGT is able to identify explanations that accurately explain the model while being relatively sparse, and that these explanations match real patterns in the data.

Graph embeddings are a ubiquitous tool for machine learning tasks, such as node classification and link prediction, on graph-structured data. However, computing the embeddings for large-scale graphs is prohibitively inefficient even if we are interested only in a small subset of relevant vertices. To address this, we present an efficient graph coarsening approach, based on Schur complements, for computing the embedding of the relevant vertices. We prove that these embeddings are preserved exactly by the Schur complement graph that is obtained via Gaussian elimination on the non-relevant vertices. As computing Schur complements is expensive, we give a nearly-linear time algorithm that generates a coarsened graph on the relevant vertices that provably matches the Schur complement in expectation in each iteration. Our experiments involving prediction tasks on graphs demonstrate that computing embeddings on the coarsened graph, rather than the entire graph, leads to significant time savings without sacrificing accuracy.

Although graph neural networks (GNNs) have made great progress recently on learning from graph-structured data in practice, their theoretical guarantee on generalizability remains elusive in the literature. In this paper, we provide a theoretically-grounded generalizability analysis of GNNs with one hidden layer for both regression and binary classification problems. Under the assumption that there exists a ground-truth GNN model (with zero generalization error), the objective of GNN learning is to estimate the ground-truth GNN parameters from the training data. To achieve this objective, we propose a learning algorithm that is built on tensor initialization and accelerated gradient descent. We then show that the proposed learning algorithm converges to the ground-truth GNN model for the regression problem, and to a model sufficiently close to the ground-truth for the binary classification problem. Moreover, for both cases, the convergence rate of the proposed learning algorithm is proven to be linear and faster than the vanilla gradient descent algorithm. We further explore the relationship between the sample complexity of GNNs and their underlying graph properties. Lastly, we provide numerical experiments to demonstrate the validity of our analysis and the effectiveness of the proposed learning algorithm for GNNs.

Communication cost is often a bottleneck in federated learning and other client-based distributed learning scenarios. To overcome this, several gradient compression and model compression algorithms have been proposed. In this work, we propose an alternative approach whereby an ensemble of pre-trained base predictors is trained via federated learning. This method allows for training a model which may otherwise surpass the communication bandwidth and storage capacity of the clients to be learned with on-device data through federated learning. Motivated by language modeling, we prove the optimality of ensemble methods for density estimation for standard empirical risk minimization and agnostic risk minimization. We provide communication-efficient ensemble algorithms for federated learning, where per-round communication cost is independent of the size of the ensemble. Furthermore, unlike works on gradient compression, our proposed approach reduces the communication cost of both server-to-client and client-to-server communication.

Existing approaches to federated learning suffer from a communication bottleneck as well as convergence issues due to sparse client participation. In this paper we introduce a novel algorithm, called FetchSGD, to overcome these challenges. FetchSGD compresses model updates using a Count Sketch, and then takes advantage of the mergeability of sketches to combine model updates from many workers. A key insight in the design of FetchSGD is that, because the Count Sketch is linear, momentum and error accumulation can both be carried out within the sketch. This allows the algorithm to move momentum and error accumulation from clients to the central aggregator, overcoming the challenges of sparse client participation while still achieving high compression rates and good convergence. We prove that FetchSGD has favorable convergence guarantees, and we demonstrate its empirical effectiveness by training two residual networks and a transformer model.

Missing data has the potential to affect analyses conducted in all fields of scientific study including healthcare, economics, and the social sciences. Several approaches to unbiased inference in the presence of non-ignorable missingness rely on the specification of the target distribution and its missingness process as a probability distribution that factorizes with respect to a directed acyclic graph. In this paper, we address the longstanding question of the characterization of models that are identifiable within this class of missing data distributions. We provide the first completeness result in this field of study -- necessary and sufficient graphical conditions under which, the full data distribution can be recovered from the observed data distribution. We then simultaneously address issues that may arise due to the presence of both missing data and unmeasured confounding, by extending these graphical conditions and proofs of completeness, to settings where some variables are not just missing, but completely unobserved.

Incorporating symbolic reasoning into machine learning algorithms is a promising approach to improve performance on learning tasks that require logical reasoning. We study the problem of generating a programmatic variant of referring expressions that we call referring relational programs. In particular, given a symbolic representation of an image and a target object in that image, the goal is to generate a relational program that uniquely identifies the target object in terms of its attributes and its relations to other objects in the image. We propose a neurosymbolic program synthesis algorithm that combines a policy neural network with enumerative search to generate such relational programs. The policy neural network employs a program interpreter that provides immediate feedback on the consequences of the decisions made by the policy, and also takes into account the uncertainty in the symbolic representation of the image. We evaluate our algorithm on challenging benchmarks based on the CLEVR dataset, and demonstrate that our approach significantly outperforms several baselines.

We present a new method for evaluating and training unnormalized density models. Our approach only requires access to the gradient of the unnormalized model’s log-density. We estimate the Stein discrepancy between the data density p(x) and the model density q(x) based on a vector function of the data. We parameterize this function with a neural network and fit its parameters to maximize this discrepancy. This yields a novel goodness-of-fit test which outperforms existing methods on high dimensional data. Furthermore, optimizing q(x) to minimize this discrepancy produces a novel method for training unnormalized models. This training method can fit large unnormalized models faster than existing approaches. The ability to both learn and compare models is a unique feature of the proposed method.

We consider the problem of learning the qualities w1, ... , wn of a collection of items by performing noisy comparisons among them. We assume there is a fixed ``comparison graph'' and every neighboring pair of items is compared k times. We will study the popular Bradley-Terry-Luce model, where the probability that item i wins a comparison against j equals wi/(wi + wj). We are interested in how the expected error in estimating the vector w = (w1, ... , w_n) behaves in the regime when the number of comparisons k is large.

Our contribution is the determination of the minimax rate up to a constant factor. We show that this rate is achieved by a simple algorithm based on weighted least squares, with weights determined from the empirical outcomes of the comparisons. This algorithm can be implemented in nearly linear time in the total number of comparisons.

In this paper, we study the problem of constrained min-max optimization in a black-box setting, where the desired optimizer cannot access the gradients of the objective function but may query its values. We present a principled optimization framework, integrating a zeroth-order (ZO) gradient estimator with an alternating projected stochastic gradient descent-ascent method, where the former only requires a small number of function queries and the later needs just one-step descent/ascent update. We show that the proposed framework, referred to as ZO-Min-Max, has a sublinear convergence rate under mild conditions and scales gracefully with problem size. We also explore a promising connection between black-box min-max optimization and black-box evasion and poisoning attacks in adversarial machine learning (ML). Our empirical evaluations on these use cases demonstrate the effectiveness of our approach and its scalability to dimensions that prohibit using recent black-box solvers.

We introduce a novel approach that endows neural networks with emergent, long-term, large-scale memory. Distinct from strategies that connect neural networks to external memory banks via intricately crafted controllers and hand-designed attentional mechanisms, our memory is internal, distributed, co-located alongside computation, and implicitly addressed, while being drastically simpler than prior efforts. Architecting networks with multigrid structure and connectivity, while distributing memory cells alongside computation throughout this topology, we observe the emergence of coherent memory subsystems. Our hierarchical spatial organization, parameterized convolutionally, permits efficient instantiation of large-capacity memories, while multigrid topology provides short internal routing pathways, allowing convolutional networks to efficiently approximate the behavior of fully connected networks. Such networks have an implicit capacity for internal attention; augmented with memory, they learn to read and write specific memory locations in a dynamic data-dependent manner. We demonstrate these capabilities on synthetic exploration and mapping tasks, where our network is able to self-organize and retain long-term memory for trajectories of thousands of time steps. On tasks decoupled from any notion of spatial geometry: sorting, associative recall, and question answering, our design functions as a truly generic memory and yields excellent results.

The notion of flat minima has gained attention as a key metric of the generalization ability of deep learning models. However, current definitions of flatness are known to be sensitive to parameter rescaling. While some previous studies have proposed to rescale flatness metrics using parameter scales to avoid the scale dependence, the normalized metrics lose the direct theoretical connections between flat minima and generalization. In this paper, we first provide generalization error bounds using existing normalized flatness measures. Using the analysis, we then propose a novel normalized flatness metric. The proposed metric enjoys both direct theoretical connections and better empirical correlation to generalization error.

Data augmentation is a powerful technique to improve performance in applications such as image and text classification tasks. Yet, there is little rigorous understanding of why and how various augmentations work. In this work, we consider a family of linear transformations and study their effects on the ridge estimator in an over-parametrized linear regression setting. First, we show that transformations which preserve the labels of the data can improve estimation by enlarging the span of the training data. Second, we show that transformations which mix data can improve estimation by playing a regularization effect. Finally, we validate our theoretical insights on MNIST. Based on the insights, we propose an augmentation scheme that searches over the space of transformations by how \textit{uncertain} the model is about the transformed data. We validate our proposed scheme on image and text datasets. For example, our method outperforms RandAugment by 1.24\% on CIFAR-100 using Wide-ResNet-28-10. Furthermore, we achieve comparable accuracy to the SoTA Adversarial AutoAugment on CIFAR datasets.

Model-agnostic meta-learning (MAML) formulates meta-learning as a bilevel optimization problem, where the inner level solves each subtask based on a shared prior, while the outer level searches for the optimal shared prior by optimizing its aggregated performance over all the subtasks. Despite its empirical success, MAML remains less understood in theory, especially in terms of its global optimality, due to the nonconvexity of the meta-objective (the outer-level objective). To bridge such a gap between theory and practice, we characterize the optimality gap of the stationary points attained by MAML for both reinforcement learning and supervised learning, where the inner-level and outer-level problems are solved via first-order optimization methods. In particular, our characterization connects the optimality gap of such stationary points with (i) the functional geometry of inner-level objectives and (ii) the representation power of function approximators, including linear models and neural networks. To the best of our knowledge, our analysis establishes the global optimality of MAML with nonconvex meta-objectives for the first time.

The gradient noise of SGD is considered to play a central role in the observed strong generalization abilities of deep learning. While past studies confirm that the magnitude and the covariance structure of gradient noise are critical for regularization, it remains unclear whether or not the class of noise distributions is important. In this work we provide negative results by showing that noises in classes different from the SGD noise can also effectively regularize gradient descent. Our finding is based on a novel observation on the structure of the SGD noise: it is the multiplication of the gradient matrix and a sampling noise that arises from the mini-batch sampling procedure. Moreover, the sampling noises unify two kinds of gradient regularizing noises that belong to the Gaussian class: the one using (scaled) Fisher as covariance and the one using the gradient covariance of SGD as covariance. Finally, thanks to the flexibility of choosing noise class, an algorithm is proposed to perform noisy gradient descent that generalizes well, the variant of which even benefits large batch SGD training without hurting generalization.

Most reinforcement learning methods are based upon the key assumption that the transition dynamics and reward functions are fixed, that is, the underlying Markov decision process is stationary. However, in many real-world applications, this assumption is violated, and using existing algorithms may result in a performance lag. To proactively search for a good future policy, we present a policy gradient algorithm that maximizes a forecast of future performance. This forecast is obtained by fitting a curve to the counter-factual estimates of policy performance over time, without explicitly modeling the underlying non-stationarity. The resulting algorithm amounts to a non-uniform reweighting of past data, and we observe that minimizing performance over some of the data from past episodes can be beneficial when searching for a policy that maximizes future performance. We show that our algorithm, called Prognosticator, is more robust to non-stationarity than two online adaptation techniques, on three simulated problems motivated by real-world applications.

Although state-of-the-art (SOTA) CNNs achieve outstanding performance on various tasks, their high computation demand and massive number of parameters make it difficult to deploy these SOTA CNNs onto resource-constrained devices. Previous works on CNN acceleration utilize low-rank approximation of the original convolution layers to reduce computation cost. However, these methods are very difficult to conduct upon sparse models, which limits execution speedup since redundancies within the CNN model are not fully exploited. We argue that kernel granularity decomposition can be conducted with low-rank assumption while exploiting the redundancy within the remaining compact coefficients. Based on this observation, we propose PENNI, a CNN model compression framework that is able to achieve model compactness and hardware efficiency simultaneously by (1) implementing kernel sharing in convolution layers via a small number of basis kernels and (2) alternately adjusting bases and coefficients with sparse constraints. Experiments show that we can prune 97% parameters and 92% FLOPs on ResNet18 CIFAR10 with no accuracy loss, and achieve a 44% reduction in run-time memory consumption and a 53% reduction in inference latency.

Optimization models with non-convex constraints arise in many tasks in machine learning, e.g., learning with fairness constraints or Neyman-Pearson classification with non-convex loss. Although many efficient methods have been developed with theoretical convergence guarantees for non-convex unconstrained problems, it remains a challenge to design provably efficient algorithms for problems with non-convex functional constraints. This paper proposes a class of subgradient methods for constrained optimization where the objective function and the constraint functions are weakly convex and nonsmooth. Our methods solve a sequence of strongly convex subproblems, where a quadratic regularization term is added to both the objective function and each constraint function. Each subproblem can be solved by various algorithms for strongly convex optimization. Under a uniform Slater’s condition, we establish the computation complexities of our methods for finding a nearly stationary point.

Recently, deep multiagent reinforcement learning (MARL) has become a highly active research area as many real-world problems can be inherently viewed as multiagent systems. A particularly interesting and widely applicable class of problems is the partially observable cooperative multiagent setting, in which a team of agents learns to coordinate their behaviors conditioning on their private observations and commonly shared global reward signals. One natural solution is to resort to the centralized training and decentralized execution paradigm and during centralized training, one key challenge is the multiagent credit assignment: how to allocate the global rewards for individual agent policies for better coordination towards maximizing system-level's benefits. In this paper, we propose a new method called Q-value Path Decomposition (QPD) to decompose the system's global Q-values into individual agents' Q-values. Unlike previous works which restrict the representation relation of the individual Q-values and the global one, we leverage the integrated gradient attribution technique into deep MARL to directly decompose global Q-values along trajectory paths to assign credits for agents. We evaluate QPD on the challenging StarCraft II micromanagement tasks and show that QPD achieves the state-of-the-art performance in both homogeneous and heterogeneous multiagent scenarios compared with existing cooperative MARL algorithms.

The Optimal Transport (a.k.a. Wasserstein) distance is an increasingly popular similarity measure for rich data domains, such as images or text documents. This raises the necessity for fast nearest neighbor search algorithms according to this distance, which poses a substantial computational bottleneck on massive datasets.

In this work we introduce Flowtree, a fast and accurate approximation algorithm for the Wasserstein-1 distance. We formally analyze its approximation factor and running time. We perform extensive experimental evaluation of nearest neighbor search algorithms in the W_1 distance on real-world dataset. Our results show that compared to previous state of the art, Flowtree achieves up to 7.4 times faster running time.

In this paper, we study a family of non-convex and possibly non-smooth inf-projection minimization problems, where the target objective function is equal to minimization of a joint function over another variable. This problem include difference of convex (DC) functions and a family of bi-convex functions as special cases. We develop stochastic algorithms and establish their first-order convergence for finding a (nearly) stationary solution of the target non-convex function under different conditions of the component functions. To the best of our knowledge, this is the first work that comprehensively studies stochastic optimization of non-convex inf-projection minimization problems with provable convergence guarantee. Our algorithms enable efficient stochastic optimization of a family of non-decomposable DC functions and a family of bi-convex functions. To demonstrate the power of the proposed algorithms we consider an important application in variance-based regularization. Experiments verify the effectiveness of our inf-projection based formulation and the proposed stochastic algorithm in comparison with previous stochastic algorithms based on the min-max formulation for achieving the same effect.

Monte-Carlo counterfactual regret minimization (MCCFR) is the state-of-the-art algorithm for solving sequential games that are too large for full tree traversals. It works by using gradient estimates that can be computed via sampling. However, stochastic methods for sequential games have not been investigated extensively beyond MCCFR. In this paper we develop a new framework for developing stochastic regret minimization methods. This framework allows us to use any regret-minimization algorithm, coupled with any gradient estimator. The MCCFR algorithm can be analyzed as a special case of our framework, and this analysis leads to significantly stronger theoretical guarantees on convergence, while simultaneously yielding a simplified proof. Our framework allows us to instantiate several new stochastic methods for solving sequential games. We show extensive experiments on five games, where some variants of our methods outperform MCCFR.

In this work, we investigate the application of Taylor expansions in reinforcement learning. In particular, we propose Taylor Expansion Policy Optimization, a policy optimization formalism that generalizes prior work as a first-order special case. We also show that Taylor expansions intimately relate to off-policy evaluation. Finally, we show that this new formulation entails modifications which improve the performance of several state-of-the-art distributed algorithms.

Higher-order tensors arise frequently in applications such as neuroimaging, recommendation system, and social network analysis. We consider the problem of low-rank tensor estimation from possibly incomplete, ordinal-valued observations. Two related problems are studied, one on tensor denoising and another on tensor completion. We propose a multi-linear cumulative link model, develop a rank-constrained M-estimator, and obtain theoretical accuracy guarantees. Our mean squared error bound enjoys a faster convergence rate than previous results, and we show that the proposed estimator is minimax optimal under the class of low-rank models. Furthermore, the procedure developed serves as an efficient completion method which guarantees consistent recovery of an order-K (d,...,d)-dimensional low-rank tensor using only O(Kd) noisy, quantized observations. We demonstrate the outperformance of our approach over previous methods on the tasks of clustering and collaborative filtering.

We build four new test sets for the Stanford Question Answering Dataset (SQuAD) and evaluate the ability of question-answering systems to generalize to new data. Our first test set is from the original Wikipedia domain and measures the extent to which existing systems overfit the original test set. Despite several years of heavy test set re-use, we find no evidence of adaptive overfitting. The remaining three test sets are constructed from New York Times articles, Reddit posts, and Amazon product reviews and measure robustness to natural distribution shifts. Across a broad range of models, we observe average performance drops of 3.8, 14.0, and 17.4 F1 points, respectively. In contrast, a strong human baseline matches or exceeds the performance of SQuAD models on the original domain and exhibits little to no drop in new domains. Taken together, our results confirm the surprising resilience of the holdout method and emphasize the need to move towards evaluation metrics that incorporate robustness to natural distribution shifts.

An acknowledged weakness of neural networks is their vulnerability to adversarial perturbations to the inputs. To improve the robustness of these models, one of the most popular defense mechanisms is to alternatively maximize the loss over the constrained perturbations (or called adversaries) on the inputs using projected gradient ascent and minimize over weights. In this paper, we analyze the dynamics of the maximization step towards understanding the experimentally observed effectiveness of this defense mechanism. Specifically, we investigate the landscape of the adversaries for a two-layer neural network with a quadratic loss. Our main result proves that projected gradient ascent finds a local maximum of this non-concave problem in a polynomial number of iterations with high probability. To our knowledge, this is the first work that provides a convergence analysis of the first-order adversaries. Moreover, our analysis demonstrates that, in the initial phase of adversarial training, the scale of the inputs matters in the sense that a smaller input scale leads to faster convergence of adversarial training and a ``more regular'' landscape. Finally, we show that these theoretical findings are in excellent agreement with a series of experiments.

We study the distribution and uncertainty of nonconvex optimization for noisy tensor completion --- the problem of estimating a low-rank tensor given incomplete and corrupted observations of its entries. Focusing on a two-stage nonconvex estimation algorithm, we characterize the distribution of this estimator down to fine scales. This distributional theory in turn allows one to construct valid and short confidence intervals for both the unseen tensor entries and its underlying tensor factors. The proposed inferential procedure enjoys several important features: (1) it is fully adaptive to noise heteroscedasticity, and (2) it is data-driven and adapts automatically to unknown noise distributions. Furthermore, our findings unveil the statistical optimality of nonconvex tensor completion: it attains un-improvable estimation accuracy --- including both the rates and the pre-constants --- under i.i.d. Gaussian noise.

We propose a novel algorithm for quantizing continuous latent representations in trained models. Our approach applies to deep probabilistic models, such as variational autoencoders (VAEs), and enables both data and model compression. Unlike current end-to-end neural compression methods that cater the model to a fixed quantization scheme, our algorithm separates model design and training from quantization. Consequently, our algorithm enables ``plug-and-play'' compression at variable rate-distortion trade-off, using a single trained model. Our algorithm can be seen as a novel extension of arithmetic coding to the continuous domain, and uses adaptive quantization accuracy based on estimates of posterior uncertainty. Our experimental results demonstrate the importance of taking into account posterior uncertainties, and show that image compression with the proposed algorithm outperforms JPEG over a wide range of bit rates using only a single standard VAE. Further experiments on Bayesian neural word embeddings demonstrate the versatility of the proposed method.

Minimax optimization has found extensive applications in modern machine learning, in settings such as generative adversarial networks (GANs), adversarial training and multi-agent reinforcement learning. As most of these applications involve continuous nonconvex-nonconcave formulations, a very basic question arises---``what is a proper definition of local optima?''

Most previous work answers this question using classical notions of equilibria from simultaneous games, where the min-player and the max-player act simultaneously. In contrast, most applications in machine learning, including GANs and adversarial training, correspond to sequential games, where the order of which player acts first is crucial (since minimax is in general not equal to maximin due to the nonconvex-nonconcave nature of the problems). The main contribution of this paper is to propose a proper mathematical definition of local optimality for this sequential setting---local minimax, as well as to present its properties and existence results. Finally, we establish a strong connection to a basic local search algorithm---gradient descent ascent (GDA): under mild conditions, all stable limit points of GDA are exactly local minimax points up to some degenerate points.

Adversarial training based on the minimax formulation is necessary for obtaining adversarial robustness of trained models. However, it is conservative or even pessimistic so that it sometimes hurts the natural generalization. In this paper, we raise a fundamental question—do we have to trade off natural generalization for adversarial robustness? We argue that adversarial training is to employ confident adversarial data for updating the current model. We propose a novel formulation of friendly adversarial training (FAT): rather than employing most adversarial data maximizing the loss, we search for least adversarial data (i.e., friendly adversarial data) minimizing the loss, among the adversarial data that are confidently misclassified. Our novel formulation is easy to implement by just stopping the most adversarial data searching algorithms such as PGD (projected gradient descent) early, which we call early-stopped PGD. Theoretically, FAT is justified by an upper bound of the adversarial risk. Empirically, early-stopped PGD allows us to answer the earlier question negatively—adversarial robustness can indeed be achieved without compromising the natural generalization.

Deep reinforcement learning (RL) algorithms have recently achieved remarkable successes in various sequential decision making tasks, leveraging advances in methods for training large deep networks. However, these methods usually require large amounts of training data, which is often a big problem for real-world applications. One natural question to ask is whether learning good representations for states and using larger networks helps in learning better policies. In this paper, we try to study if increasing input dimensionality helps improve performance and sample efficiency of model-free deep RL algorithms. To do so, we propose an online feature extractor network (OFENet) that uses neural nets to produce \textit{good} representations to be used as inputs to an off-policy RL algorithm. Even though the high dimensionality of input is usually thought to make learning of RL agents more difficult, we show that the RL agents in fact learn more efficiently with the high-dimensional representation than with the lower-dimensional state observations. We believe that stronger feature propagation together with larger networks allows RL agents to learn more complex functions of states and thus improves the sample efficiency. Through numerical experiments, we show that the proposed method achieves much higher sample efficiency and better performance. Codes for …

We introduce kernels with random Fourier features in the meta-learning framework for few-shot learning. We propose meta variational random features (MetaVRF) to learn adaptive kernels for the base-learner, which is developed in a latent variable model by treating the random feature basis as the latent variable. We formulate the optimization of MetaVRF as a variational inference problem by deriving an evidence lower bound under the meta-learning framework. To incorporate shared knowledge from related tasks, we propose a context inference of the posterior, which is established by an LSTM architecture. The LSTM-based inference network can effectively integrate the context information of previous tasks with task-specific information, generating informative and adaptive features. The learned MetaVRF can produce kernels of high representational power with a relatively low spectral sampling rate and also enables fast adaptation to new tasks. Experimental results on a variety of few-shot regression and classification tasks demonstrate that MetaVRF delivers much better, or at least competitive, performance compared to existing meta-learning alternatives.

We aim to develop off-policy DRL algorithms that not only exceed state-of-the-art performance but are also simple and minimalistic. For standard continuous control benchmarks, Soft Actor-Critic (SAC), which employs entropy maximization, currently provides state-of-the-art performance. We first demonstrate that the entropy term in SAC addresses action saturation due to the bounded nature of the action spaces, with this insight, we propose a streamlined algorithm with a simple normalization scheme or with inverted gradients. We show that both approaches can match SAC's sample efficiency performance without the need of entropy maximization, we then propose a simple non-uniform sampling method for selecting transitions from the replay buffer during training. Extensive experimental results demonstrate that our proposed sampling scheme leads to state of the art sample efficiency on challenging continuous control tasks. We combine all of our findings into one simple algorithm, which we call Streamlined Off Policy with Emphasizing Recent Experience, for which we provide robust public-domain code.

Plug-and-play (PnP) is a non-convex framework that combines ADMM or other proximal algorithms with advanced denoiser priors. Recently, PnP has achieved great empirical success, especially with the integration of deep learning-based denoisers. However, a key problem of PnP based approaches is that they require manual parameter tweaking. It is necessary to obtain high-quality results across the high discrepancy in terms of imaging conditions and varying scene content. In this work, we present a tuning-free PnP proximal algorithm, which can automatically determine the internal parameters including the penalty parameter, the denoising strength and the terminal time. A key part of our approach is to develop a policy network for automatic search of parameters, which can be effectively learned via mixed model-free and model-based deep reinforcement learning. We demonstrate, through numerical and visual experiments, that the learned policy can customize different parameters for different states, and often more efficient and effective than existing handcrafted criteria. Moreover, we discuss the practical considerations of the plugged denoisers, which together with our learned policy yield state-of-the-art results. This is prevalent on both linear and nonlinear exemplary inverse imaging problems, and in particular, we show promising results on Compressed Sensing MRI and phase retrieval.

Posterior distribution approximation is a central task in Bayesian inference. Stochastic gradient Langevin dynamics (SGLD) and its extensions have been practically used and theoretically studied. While SGLD updates a single particle at a time, ensemble methods that update multiple particles simultaneously have been recently gathering attention. Compared with the naive parallel-chain SGLD that updates multiple particles independently, ensemble methods update particles with their interactions. Thus, these methods are expected to be more particle-efficient than the naive parallel-chain SGLD because particles can be aware of other particles' behavior through their interactions. Although ensemble methods numerically demonstrated their superior performance, no theoretical guarantee exists to assure such particle-efficiency and it is unclear whether those ensemble methods are really superior to the naive parallel-chain SGLD in the non-asymptotic settings. To cope with this problem, we propose a novel ensemble method that uses a non-reversible Markov chain for the interaction, and we present a non-asymptotic theoretical analysis for our method. Our analysis shows that, for the first time, the interaction causes a faster convergence rate than the naive parallel-chain SGLD in the non-asymptotic setting if the discretization error is appropriately controlled. Numerical experiments show that we can control the discretization error by tuning the …

We study the model selection problem in \textit{conditional average treatment effect} (CATE) prediction. Unlike previous works on this topic, we focus on preserving the rank order of the performance of candidate CATE predictors to enable accurate and stable model selection. To this end, we analyze the model performance ranking problem and formulate guidelines to obtain a better evaluation metric. We then propose a novel metric that can identify the ranking of the performance of CATE predictors with high confidence. Empirical evaluations demonstrate that our metric outperforms existing metrics in both model selection and hyperparameter tuning tasks.

Imitation learning in a high-dimensional environment is challenging. Most inverse reinforcement learning (IRL) methods fail to outperform the demonstrator in such a high-dimensional environment, e.g., Atari domain. To address this challenge, we propose a novel reward learning module to generate intrinsic reward signals via a generative model. Our generative method can perform better forward state transition and backward action encoding, which improves the module's dynamics modeling ability in the environment. Thus, our module provides the imitation agent both the intrinsic intention of the demonstrator and a better exploration ability, which is critical for the agent to outperform the demonstrator. Empirical results show that our method outperforms state-of-the-art IRL methods on multiple Atari games, even with one-life demonstration. Remarkably, our method achieves performance that is up to 5 times the performance of the demonstration.

Many machine learning algorithms are trained and evaluated by splitting data from a single source into training and test sets. While such focus on in-distribution learning scenarios has led to interesting advancement, it has not been able to tell if models are relying on dataset biases as shortcuts for successful prediction (e.g., using snow cues for recognising snowmobiles), resulting in biased models that fail to generalise when the bias shifts to a different class. The cross-bias generalisation problem has been addressed by de-biasing training data through augmentation or re-sampling, which are often prohibitive due to the data collection cost (e.g., collecting images of a snowmobile on a desert) and the difficulty of quantifying or expressing biases in the first place. In this work, we propose a novel framework to train a de-biased representation by encouraging it to be different from a set of representations that are biased by design. This tactic is feasible in many scenarios where it is much easier to define a set of biased representations than to define and quantify bias. We demonstrate the efficacy of our method across a variety of synthetic and real-world biases; our experiments show that the method discourages models from taking bias …

In many real-world applications, data are collected in the form of a stream, whose feature space can evolve over time. For instance, in the environmental monitoring task, features can be dynamically vanished or augmented due to the existence of expired old sensors and deployed new sensors. Furthermore, besides the evolvable feature space, the data distribution is usually changing in the streaming scenario. When both feature space and data distribution are evolvable, it is quite challenging to design algorithms with guarantees, particularly theoretical understandings of generalization ability. To address this difficulty, we propose a novel discrepancy measure for data with evolving feature space and data distribution, named the \emph{evolving discrepancy}. Based on that, we present the generalization error analysis, and the theory motivates the design of a learning algorithm which is further implemented by deep neural networks. Empirical studies on synthetic data verify the rationale of our proposed discrepancy measure, and extensive experiments on real-world tasks validate the effectiveness of our algorithm.

This paper studies binary logistic regression for rare events data, or imbalanced data, where the number of events (observations in one class, often called cases) is significantly smaller than the number of nonevents (observations in the other class, often called controls). We first derive the asymptotic distribution of the maximum likelihood estimator (MLE) of the unknown parameter, which shows that the asymptotic variance convergences to zero in a rate of the inverse of the number of the events instead of the inverse of the full data sample size, indicating that the available information in rare events data is at the scale of the number of events instead of the full data sample size. Furthermore, we prove that under-sampling a small proportion of the nonevents, the resulting under-sampled estimator may have identical asymptotic distribution to the full data MLE. This demonstrates the advantage of under-sampling nonevents for rare events data, because this procedure may significantly reduce the computation and/or data collection costs. Another common practice in analyzing rare events data is to over-sample (replicate) the events, which has a higher computational cost. We show that this procedure may even result in efficiency loss in terms of parameter estimation.

In a standard setting of Bayesian optimization (BO), the objective function evaluation is assumed to be highly expensive. Multi-fidelity Bayesian optimization (MFBO) accelerates BO by incorporating lower fidelity observations available with a lower sampling cost. We propose a novel information-theoretic approach to MFBO, called multi-fidelity max-value entropy search (MF-MES), that enables us to obtain a more reliable evaluation of the information gain compared with existing information-based methods for MFBO. Further, we also propose a parallelization of MF-MES mainly for the asynchronous setting because queries typically occur asynchronously in MFBO due to a variety of sampling costs. We show that most of computations in our acquisition functions can be derived analytically, except for at most only two dimensional numerical integration that can be performed efficiently by simple approximations. We demonstrate effectiveness of our approach by using benchmark datasets and a real-world application to materials science data.

The goal of text generation models is to fit the underlying real probability distribution of text. For performance evaluation, quality and diversity metrics are usually applied. However, it is still not clear to what extend can the quality-diversity evaluation reflect the distribution-fitting goal. In this paper, we try to reveal such relation in a theoretical approach. We prove that under certain conditions, a linear combination of quality and diversity constitutes a divergence metric between the generated distribution and the real distribution. We also show that the commonly used BLEU/Self-BLEU metric pair fails to match any divergence metric, thus propose CR/NRR as a substitute for quality/diversity metric pair.

To analyze high-dimensional and complex data in the real world, deep generative models such as variational autoencoder (VAE) embed data in a reduced dimensional latent space and learn the probabilistic model in the latent space. However, they struggle to reproduce the probability distribution function (PDF) in the input space from that of the latent space accurately. If the embedding were isometric, this problem can be solved since PDFs in both spaces become proportional. To achieve isometric property, we propose Rate-Distortion Optimization guided autoencoder inspired by orthonormal transform coding. We show our method has the following properties: (i) the columns of the Jacobian matrix between two spaces is constantly-scaled orthonormal system and enable to embed data in latent space isometrically; (ii) the PDF of the latent space is proportional to that of the data observation space. Furthermore, our method outperforms state-of-the-art methods in unsupervised anomaly detection with four public datasets.

In this paper, we study combinatorial pure exploration for dueling bandits (CPE-DB): we have multiple candidates for multiple positions as modeled by a bipartite graph, and in each round we sample a duel of two candidates on one position and observe who wins in the duel, with the goal of finding the best candidate-position matching with high probability after multiple rounds of samples. CPE-DB is an adaptation of the original combinatorial pure exploration for multi-armed bandit (CPE-MAB) problem to the dueling bandit setting. We consider both the Borda winner and the Condorcet winner cases. For Borda winner, we establish a reduction of the problem to the original CPE-MAB setting and design PAC and exact algorithms that achieve both the sample complexity similar to that in the CPE-MAB setting (which is nearly optimal for a subclass of problems) and polynomial running time per round. For Condorcet winner, we first design a fully polynomial time approximation scheme (FPTAS) for the offline problem of finding the Condorcet winner with known winning probabilities, and then use the FPTAS as an oracle to design a novel pure exploration algorithm CAR-Cond with sample complexity analysis. CAR-Cond is the first algorithm with polynomial running time per round …

Distance metric learning (DML) is to learn a representation space equipped with a metric, such that similar examples are closer than dissimilar examples concerning the metric. The recent success of DNNs motivates many DML losses that encourage the intra-class compactness and inter-class separability. The trade-off between inter-class compactness and inter-class separability shapes the DML representation space by determining how much information of the original inputs to retain. In this paper, we propose a Distance Metric Learning with Joint Representation Diversification (JRD) that allows a better balancing point between intra-class compactness and inter-class separability. Specifically, we propose a Joint Representation Similarity regularizer that captures different abstract levels of invariant features and diversifies the joint distributions of representations across multiple layers. Experiments on three deep DML benchmark datasets demonstrate the effectiveness of the proposed approach.

Domain generalization refers to the task of training a model which generalizes to new domains that are not seen during training. We present CSD (Common Specific Decomposition), for this setting, which jointly learns a common component (which generalizes to new domains) and a domain specific component (which overfits on training domains). The domain specific components are discarded after training and only the common component is retained. The algorithm is extremely simple and involves only modifying the final linear classification layer of any given neural network architecture. We present a principled analysis to understand existing approaches, provide identifiability results of CSD, and study the effect of low-rank on domain generalization. We show that CSD either matches or beats state of the art approaches for domain generalization based on domain erasure, domain perturbed data augmentation, and meta-learning. Further diagnostics on rotated MNIST, where domains are interpretable, confirm the hypothesis that CSD successfully disentangles common and domain specific components and hence leads to better domain generalization; moreover, our code and dataset are publicly available at the following URL: \url{https://github.com/vihari/csd}.

A complementary label (CL) simply indicates an incorrect class of an example, but learning with CLs results in multi-class classifiers that can predict the correct class. Unfortunately, the problem setting only allows a single CL for each example, which notably limits its potential since our labelers may easily identify multiple CLs (MCLs) to one example. In this paper, we propose a novel problem setting to allow MCLs for each example and two ways for learning with MCLs. In the first way, we design two wrappers that decompose MCLs into many single CLs, so that we could use any method for learning with CLs. However, the supervision information that MCLs hold is conceptually diluted after decomposition. Thus, in the second way, we derive an unbiased risk estimator; minimizing it processes each set of MCLs as a whole and possesses an estimation error bound. We further improve the second way into minimizing properly chosen upper bounds. Experiments show that the former way works well for learning with MCLs but the latter is even better.

We introduce a new measure to evaluate the transferability of representations learned by classifiers. Our measure, the Log Expected Empirical Prediction (LEEP), is simple and easy to compute: when given a classifier trained on a source data set, it only requires running the target data set through this classifier once. We analyze the properties of LEEP theoretically and demonstrate its effectiveness empirically. Our analysis shows that LEEP can predict the performance and convergence speed of both transfer and meta-transfer learning methods, even for small or imbalanced data. Moreover, LEEP outperforms recently proposed transferability measures such as negative conditional entropy and H scores. Notably, when transferring from ImageNet to CIFAR100, LEEP can achieve up to 30% improvement compared to the best competing method in terms of the correlations with actual transfer accuracy.

We provide an end-to-end differentially private spectral algorithm for learning LDA, based on matrix/tensor decompositions, and establish theoretical guarantees on utility/consistency of the estimated model parameters. We represent the spectral algorithm as a computational graph. Noise can be injected along the edges of this graph to obtain differential privacy. We identify subsets of edges, named ``configurations'', such that adding noise to all edges in such a subset guarantees differential privacy of the end-to-end spectral algorithm. We characterize the sensitivity of the edges with respect to the input and thus estimate the amount of noise to be added to each edge for any required privacy level. We then characterize the utility loss for each configuration as a function of injected noise. Overall, by combining the sensitivity and utility characterization, we obtain an end-to-end differentially private spectral algorithm for LDA and identify which configurations outperform others under specific regimes. We are the first to achieve utility guarantees under a required level of differential privacy for learning in LDA. We additionally show that our method systematically outperforms differentially private variational inference.

A popular line of recent research incorporates ML advice in the design of online algorithms to improve their performance in typical instances. These papers treat the ML algorithm as a black-box, and redesign online algorithms to take advantage of ML predictions. In this paper, we ask the complementary question: can we redesign ML algorithms to provide better predictions for online algorithms? We explore this question in the context of the classic rent-or-buy problem, and show that incorporating optimization benchmarks in ML loss functions leads to significantly better performance, while maintaining a worst-case adversarial result when the advice is completely wrong. We support this finding both through theoretical bounds and numerical simulations.

We introduce Deep Reasoning Networks (DRNets), an end-to-end framework that combines deep learning with constraint reasoning for solving pattern de-mixing problems, typically in an unsupervised or very-weakly-supervised setting. DRNets exploit problem structure and prior knowledge by tightly combining constraint reasoning with stochastic-gradient-based neural network optimization. Our motivating task is from materials discovery and concerns inferring crystal structures of materials from X-ray diffraction data (Crystal-Structure-Phase-Mapping). Given the complexity of its underlying scientific domain, we start by introducing DRNets on an analogous but much simpler task: de-mixing overlapping hand-written Sudokus (Multi-MNIST-Sudoku). On Multi-MNIST-Sudoku, DRNets almost perfectly recovered the mixed Sudokus' digits, with 100\% digit accuracy, outperforming the supervised state-of-the-art MNIST de-mixing models. On Crystal-Structure-Phase-Mapping, DRNets significantly outperform the state of the art and experts' capabilities, recovering more precise and physically meaningful crystal structures.

We consider a new unsupervised learning task of inferring parameters of a multiobjective decision making model, based on a set of observed decisions from the human expert. This setting is important in applications (such as the task of portfolio management) where it may be difficult to obtain the human expert's intrinsic decision making model. We formulate such a learning problem as an inverse multiobjective optimization problem (IMOP) and propose its first sophisticated model with statistical guarantees. Then, we reveal several fundamental connections between IMOP, K-means clustering, and manifold learning. Leveraging these critical insights and connections, we propose two algorithms to solve IMOP through manifold learning and clustering. Numerical results confirm the effectiveness of our model and the computational efficacy of algorithms.

Gating mechanisms are widely used in neural network models, where they allow gradients to backpropagate easily through depth or time. However, their saturation property introduces problems of its own. For example, in recurrent models these gates need to have outputs near 1 to propagate information over long time-delays, which requires them to operate in their saturation regime and hinders gradient-based learning of the gate mechanism. We address this problem by deriving two synergistic modifications to the standard gating mechanism that are easy to implement, introduce no additional hyperparameters, and improve learnability of the gates when they are close to saturation. We show how these changes are related to and improve on alternative recently proposed gating mechanisms such as chrono-initialization and Ordered Neurons. Empirically, our simple gating mechanisms robustly improve the performance of recurrent models on a range of applications, including synthetic memorization tasks, sequential image classification, language modeling, and reinforcement learning, particularly when long-term dependencies are involved.

Although ordinary differential equations (ODEs) provide insights for designing network architectures, its relationship with the non-residual convolutional neural networks (CNNs) is still unclear. In this paper, we present a novel ODE model by adding a damping term. It can be shown that the proposed model can recover both a ResNet and a CNN by adjusting an interpolation coefficient. Therefore, the damped ODE model provides a unified framework for the interpretation of residual and non-residual networks. The Lyapunov analysis reveals better stability of the proposed model, and thus yields robustness improvement of the learned networks. Experiments on a number of image classification benchmarks show that the proposed model substantially improves the accuracy of ResNet and ResNeXt over the perturbed inputs from both stochastic noise and adversarial attack methods. Moreover, the loss landscape analysis demonstrates the improved robustness of our method along the attack direction.

In face recognition, designing margin-based (\textit{e.g.}, angular, additive, additive angular margins) softmax loss functions plays an important role to learn discriminative features. However, these hand-crafted heuristic methods may be sub-optimal because they require much effort to explore the large design space. Recently, an AutoML for loss function search method AM-LFS has been derived, which leverages reinforcement learning to search loss functions during the training process. But its search space is complex and unstable that hindering its superiority. In this paper, we first analyze that the key to enhance the feature discrimination is actually \textbf{how to reduce the softmax probability}. We then design a unified formulation for the current margin-based softmax losses. Accordingly, we define a novel search space and develop a reward-guided search method to automatically obtain the best candidate. Experimental results on a variety of face recognition benchmarks have demonstrated the effectiveness of our method over the state-of-the-art alternatives.

This work proposes a progressive manifold identification approach for distributed optimization with sound theoretical justifications to greatly reduce both the rounds of communication and the bytes communicated per round for partly-smooth regularized problems such as the L1- and group-LASSO-regularized ones. Our two-stage method first uses an inexact proximal quasi-Newton method to iteratively identify a sequence of low-dimensional manifolds in which the final solution would lie, and restricts the model update within the current manifold to gradually lower the order of the per-round communication cost from the problem dimension to the dimension of the manifold that contains a solution and makes the problem within it smooth. After identifying this manifold, we take superlinear-convergent truncated semismooth Newton steps computed by preconditioned conjugate gradient to largely reduce the communication rounds by improving the convergence rate from the existing linear or sublinear ones to a superlinear rate. Experiments show that our method can be two orders of magnitude better in the communication cost and an order of magnitude faster in the running time than state of the art.

While successful in many fields, deep neural networks (DNNs) still suffer from some open problems such as bad local minima and unsatisfactory generalization performance. In this work, we propose a novel architecture called Maximum-and-Concatenation Networks (MCN) to try eliminating bad local minima and improving generalization ability as well. Remarkably, we prove that MCN has a very nice property; that is, every local minimum of an (l+1)-layer MCN can be better than, at least as good as, the global minima of the network consisting of its first l layers. In other words, by increasing the network depth, MCN can autonomously improve its local minima's goodness, what is more, it is easy to plug MCN into an existing deep model to make it also have this property. Finally, under mild conditions, we show that MCN can approximate certain continuous function arbitrarily well with high efficiency; that is, the covering number of MCN is much smaller than most existing DNNs such as deep ReLU. Based on this, we further provide a tight generalization bound to guarantee the inference ability of MCN when dealing with testing samples.

With the rapid adoption of machine learning systems in sensitive applications, there is an increasing need to make black-box models explainable. Often we want to identify an influential group of training samples in a particular test prediction for a given machine learning model. Existing influence functions tackle this problem by using first-order approximations of the effect of removing a sample from the training set on model parameters. To compute the influence of a group of training samples (rather than an individual point) in model predictions, the change in optimal model parameters after removing that group from the training set can be large. Thus, in such cases, the first-order approximation can be loose. In this paper, we address this issue and propose second-order influence functions for identifying influential groups in test-time predictions. For linear models, across different sizes and types of groups, we show that using the proposed second-order influence function improves the correlation between the computed influence values and the ground truth ones. We also show that second-order influence functions could be used with optimization techniques to improve the selection of the most influential group for a test-sample.

The variational autoencoder (VAE) can learn the manifold of natural images on certain datasets, as evidenced by meaningful interpolating or extrapolating in the continuous latent space. However, on discrete data such as text, it is unclear if unsupervised learning can discover similar latent space that allows controllable manipulation. In this work, we find that sequence VAEs trained on text fail to properly decode when the latent codes are manipulated, because the modified codes often land in holes or vacant regions in the aggregated posterior latent space, where the decoding network fails to generalize. Both as a validation of the explanation and as a fix to the problem, we propose to constrain the posterior mean to a learned probability simplex, and performs manipulation within this simplex. Our proposed method mitigates the latent vacancy problem and achieves the first success in unsupervised learning of controllable representations for text. Empirically, our method outperforms unsupervised baselines and strong supervised approaches on text style transfer. On automatic evaluation metrics used in text style transfer, even with the decoding network trained from scratch, our method achieves comparable results with state-of-the-art supervised approaches leveraging large-scale pre-trained models for generation. Furthermore, it is capable of performing more flexible …

Most recommender systems (RS) research assumes that a user's utility can be maximized independently of the utility of the other agents (e.g., other users, content providers). In realistic settings, this is often not true -- the dynamics of an RS ecosystem couple the long-term utility of all agents. In this work, we explore settings in which content providers cannot remain viable unless they receive a certain level of user engagement. We formulate this problem as one of equilibrium selection in the induced dynamical system, and show that it can be solved as an optimal constrained matching problem. Our model ensures the system reaches an equilibrium with maximal social welfare supported by a sufficiently diverse set of viable providers. We demonstrate that even in a simple, stylized dynamical RS model, the standard myopic approach to recommendation - always matching a user to the best provider - performs poorly. We develop several scalable techniques to solve the matching problem, and also draw connections to various notions of user regret and fairness, arguing that these outcomes are fairer in a utilitarian sense.

Game-theoretic formulations of feature importance have become popular as a way to "explain" machine learning models. These methods define a cooperative game between the features of a model and distribute influence among these input elements using some form of the game's unique Shapley values. Justification for these methods rests on two pillars: their desirable mathematical properties, and their applicability to specific motivations for explanations. We show that mathematical problems arise when Shapley values are used for feature importance and that the solutions to mitigate these necessarily induce further complexity, such as the need for causal reasoning. We also draw on additional literature to argue that Shapley values do not provide explanations which suit human-centric goals of explainability.

Sample selection approaches are popular in robust learning from noisy labels. However, how to properly control the selection process so that deep networks can benefit from the memorization effect is a hard problem. In this paper, motivated by the success of automated machine learning (AutoML), we model this issue as a function approximation problem. Specifically, we design a domain-specific search space based on general patterns of the memorization effect and propose a novel Newton algorithm to solve the bi-level optimization problem efficiently. We further provide a theoretical analysis of the algorithm, which ensures a good approximation to critical points. Experiments are performed on both benchmark and real-world data sets. Results demonstrate that the proposed method is much better than the state-of-the-art noisy-label-learning approaches, and also much more efficient than existing AutoML algorithms.

Graph convolutional networks (GCNs) are a powerful deep learning approach for graph-structured data. Recently, GCNs and subsequent variants have shown superior performance in various application areas on real-world datasets. Despite their success, most of the current GCN models are shallow, due to the {\em over-smoothing} problem. In this paper, we study the problem of designing and analyzing deep graph convolutional networks. We propose the GCNII, an extension of the vanilla GCN model with two simple yet effective techniques: {\em Initial residual} and {\em Identity mapping}. We provide theoretical and empirical evidence that the two techniques effectively relieves the problem of over-smoothing. Our experiments show that the deep GCNII model outperforms the state-of-the-art methods on various semi- and full-supervised tasks.

This paper is concerned with statistical estimation of two preferential attachment models: the Buckley-Osthus model and the block preferential attachment model. We prove that the maximum likelihood estimates for both models are consistent. We perform simulation studies to corroborate our theoretical findings. We also apply both models to study the evolution of a real-world network. A list of open problems are presented.

We propose Zeno++, a new robust asynchronous Stochastic Gradient Descent(SGD) procedure, intended to tolerate Byzantine failures of workers. In contrast to previous work, Zeno++ removes several unrealistic restrictions on worker-server communication, now allowing for fully asynchronous updates from anonymous workers, for arbitrarily stale worker updates, and for the possibility of an unbounded number of Byzantine workers. The key idea is to estimate the descent of the loss value after the candidate gradient is applied, where large descent values indicate that the update results in optimization progress. We prove the convergence of Zeno++ for non-convex problems under Byzantine failures. Experimental results show that Zeno++ outperforms existing Byzantine-tolerant asynchronous SGD algorithms.

In this contribution, we augment the metric learning setting by introducing a parametric pseudo-distance, trained jointly with the encoder. Several interpretations are thus drawn for the learned distance-like model's output. We first show it approximates a likelihood ratio which can be used for hypothesis tests, and that it further induces a large divergence across the joint distributions of pairs of examples from the same and from different classes. Evaluation is performed under the verification setting consisting of determining whether sets of examples belong to the same class, even if such classes are novel and were never presented to the model during training. Empirical evaluation shows such method defines an end-to-end approach for the verification problem, able to attain better performance than simple scorers such as those based on cosine similarity and further outperforming widely used downstream classifiers. We further observe training is much simplified under the proposed approach compared to metric learning with actual distances, requiring no complex scheme to harvest pairs of examples.

Recent convolutional neural networks (CNNs) have led to impressive performance but often suffer from poor calibration. They tend to be overconfident, with the model confidence not always reflecting the underlying true ambiguity and hardness. In this paper, we propose angular visual hardness (AVH), a score given by the normalized angular distance between the sample feature embedding and the target classifier to measure sample hardness. We validate this score with an in-depth and extensive scientific study, and observe that CNN models with the highest accuracy also have the best AVH scores. This agrees with an earlier finding that state-of-art models improve on the classification of harder examples. We observe that the training dynamics of AVH is vastly different compared to the training loss. Specifically, AVH quickly reaches a plateau for all samples even though the training loss keeps improving. This suggests the need for designing better loss functions that can target harder examples more effectively. We also find that AVH has a statistically significant correlation with human visual hardness. Finally, we demonstrate the benefit of AVH to a variety of applications such as self-training for domain adaptation and domain generalization.

We study the problem of estimating the distribution of effect sizes (the mean of the test statistic under the alternate hypothesis) in a multiple testing setting. Knowing this distribution allows us to calculate the power (type II error) of any experimental design. We show that it is possible to estimate this distribution using an inexpensive pilot experiment, which takes significantly fewer samples than would be required by an experiment that identified the discoveries. Our estimator can be used to guarantee the number of discoveries that will be made using a given experimental design in a future experiment. We prove that this simple and computationally efficient estimator enjoys a number of favorable theoretical properties, and demonstrate its effectiveness on data from a gene knockout experiment on influenza inhibition in Drosophila.

This paper presents a framework of successive functional gradient optimization for training nonconvex models such as neural networks, where training is driven by mirror descent in a function space. We provide a theoretical analysis and empirical study of the training method derived from this framework. It is shown that the method leads to better performance than that of standard training techniques.

Autoregressive (AR) models have been the dominating approach to conditional sequence generation, but are suffering from the issue of high inference latency. Non-autoregressive (NAR) models have been recently proposed to reduce the latency by generating all output tokens in parallel but could only achieve inferior accuracy compared to their autoregressive counterparts, primarily due to a difficulty in dealing with the multi-modality in sequence generation. This paper proposes a new approach that jointly optimizes both AR and NAR models in a unified Expectation-Maximization (EM) framework. In the E-step, an AR model learns to approximate the regularized posterior of the NAR model. In the M-step, the NAR model is updated on the new posterior and selects the training examples for the next AR model. This iterative process can effectively guide the system to remove the multi-modality in the output sequences. To our knowledge, this is the first EM approach to NAR sequence generation. We evaluate our method on the task of machine translation. Experimental results on benchmark data sets show that the proposed approach achieves competitive, if not better, performance with existing NAR models and significantly reduces the inference latency.

We consider the batch reinforcement learning problem where the agent needs to learn only from a fixed batch of data, without further interaction with the environment. In such a scenario, we want to prevent the optimized policy from deviating too much from the data collection policy since the estimation becomes highly unstable otherwise due to the off-policy nature of the problem. However, imposing this requirement too strongly will result in a policy that merely follows the data collection policy. Unlike prior work where this trade-off is controlled by hand-tuned hyperparameters, we propose a novel batch reinforcement learning approach, batch optimization of policy and hyperparameter (BOPAH), that uses a gradient-based optimization of the hyperparameter using held-out data. We show that BOPAH outperforms other batch reinforcement learning algorithms in tabular and continuous control tasks, by finding a good balance to the trade-off between adhering to the data collection policy and pursuing the possible policy improvement.

We study the question of how to aggregate controllers for dynamical systems in order to improve their performance. To this end, we propose a framework of boosting for online control. Our main result is an efficient boosting algorithm that combines weak controllers into a provably more accurate one. Empirical evaluation on a host of control settings supports our theoretical findings.

When presented with Out-of-Distribution (OOD) examples, deep neural networks yield confident, incorrect predictions; detecting OOD examples is challenging, and the potential risks are high. In this paper, we propose to detect OOD examples by identifying inconsistencies between activity patterns and predicted class. We find that characterizing activity patterns by Gram matrices and identifying anomalies in Gram matrix values can yield high OOD detection rates. We identify anomalies in the Gram matrices by simply comparing each value with its respective range observed over the training data. Unlike many approaches, this can be used with any pre-trained softmax classifier and neither requires access to OOD data for fine-tuning hyperparameters, nor does it require OOD access for inferring parameters. We empirically demonstrate applicability across a variety of architectures and vision datasets and, for the important and surprisingly hard task of detecting far out-of-distribution examples, it generally performs better than or equal to state-of-the-art OOD detection methods (including those that do assume access to OOD examples).

In distributed online optimization over a computing network with heterogeneous nodes, slow nodes can adversely affect the progress of fast nodes, leading to drastic slowdown of the overall convergence process. To address this issue, we consider a new algorithm termed Distributed Any-Batch Mirror Descent (DABMD), which is based on distributed Mirror Descent but uses a fixed per-round computing time to limit the waiting by fast nodes to receive information updates from slow nodes. DABMD is characterized by varying minibatch sizes across nodes. It is applicable to a broader range of problems compared with existing distributed online optimization methods such as those based on dual averaging, and it accommodates time-varying network topology. We study two versions of DABMD, depending on whether the computing nodes average their primal variables via single or multiple consensus iterations. We show that both versions provide strong theoretical performance guarantee, by deriving upperbounds on their expected dynamic regret, which capture the variability in minibatch sizes. Our experimental results show substantial reduction in cost and acceleration in convergence compared with the known best alternative.

We develop a a new polynomial-time algorithm for identification of structural coefficients in linear causal models that subsumes previous state-of-the-art methods, unifying several disparate approaches to identification in this setting. Building on these results, we develop a procedure for identifying total causal effects in linear systems.

The performance of standard learning procedures has been observed to differ widely across groups. 
Recent studies usually attribute this loss discrepancy to an information deficiency for one group (e.g., one group has less data). 
In this work, we point to a more subtle source of loss discrepancy---feature noise. 
Our main result is that even when there is no information deficiency specific to one group (e.g., both groups have infinite data), adding the same amount of feature noise to all individuals leads to loss discrepancy.
For linear regression, we thoroughly characterize the effect of feature noise on loss discrepancy in terms of the amount of noise, the difference between moments of the two groups, and whether group information is used or not.
We then show this loss discrepancy does not vanish immediately if a shift in distribution causes the groups to have similar moments. 
On three real-world datasets, we show feature noise increases the loss discrepancy if groups have different distributions, while it does not affect the loss discrepancy on datasets that groups have similar distributions.

In this paper, we investigate a Lyapunov-like differential inequality that allows us to establish finite-time stability of a continuous-time state-space dynamical system represented via a multivariate ordinary differential equation or differential inclusion. Equipped with this condition, we successfully synthesize first and second-order dynamical systems that achieve finite-time convergence to the minima of a given sufficiently regular cost function. As a byproduct, we show that the p-rescaled gradient flow (p-RGF) proposed by Wibisono et al. (2016) is indeed finite-time convergent, provided the cost function is gradient dominated of order q in (1,p). Thus, we effectively bridge a gap between the p-RGF and the normalized gradient flow (NGF) (p=\infty) proposed by Cortes (2006) in his seminal paper in the context of multi-agent systems. We discuss strategies to discretize our proposed flows and conclude by conducting some numerical experiments to illustrate our results.

Convolutional Neural Networks (CNNs) are known to rely more on local texture rather than global shape when making decisions. Recent work also indicates a close relationship between CNN's texture-bias and its robustness against distribution shift, adversarial perturbation, random corruption, etc. In this work, we attempt at improving various kinds of robustness universally by alleviating CNN's texture bias. With inspiration from the human visual system, we propose a light-weight model-agnostic method, namely Informative Dropout (InfoDrop), to improve interpretability and reduce texture bias. Specifically, we discriminate texture from shape based on local self-information in an image, and adopt a Dropout-like algorithm to decorrelate the model output from the local texture. Through extensive experiments, we observe enhanced robustness under various scenarios (domain generalization, few-shot classification, image corruption, and adversarial perturbation). To the best of our knowledge, this work is one of the earliest attempts to improve different kinds of robustness in a unified model, shedding new light on the relationship between shape-bias and robustness, also on new approaches to trustworthy machine learning algorithms. Code is available at https://github.com/bfshi/InfoDrop.

The standard risk minimization paradigm of machine learning is brittle when operating in environments whose test distributions are different from the training distribution due to spurious correlations. Training on data from many environments and finding invariant predictors reduces the effect of spurious features by concentrating models on features that have a causal relationship with the outcome. In this work, we pose such invariant risk minimization as finding the Nash equilibrium of an ensemble game among several environments. By doing so, we develop a simple training algorithm that uses best response dynamics and, in our experiments, yields similar or better empirical accuracy with much lower variance than the challenging bi-level optimization problem of Arjovsky et al. (2019). One key theoretical contribution is showing that the set of Nash equilibria for the proposed game are equivalent to the set of invariant predictors for any finite number of environments, even with nonlinear classifiers and transformations. As a result, our method also retains the generalization guarantees to a large set of environments shown in Arjovsky et al. (2019). The proposed algorithm adds to the collection of successful game-theoretic machine learning algorithms such as generative adversarial networks.

We study local SGD (also known as parallel SGD and federated SGD), a natural and frequently used distributed optimization method. Its theoretical foundations are currently lacking and we highlight how all existing error guarantees in the convex setting are dominated by a simple baseline, minibatch SGD. (1) For quadratic objectives we prove that local SGD strictly dominates minibatch SGD and that accelerated local SGD is minmax optimal for quadratics; (2) For general convex objectives we provide the first guarantee that at least \emph{sometimes} improves over minibatch SGD, but our guarantee does not always improve over, nor even match, minibatch SGD; (3) We show that indeed local SGD does \emph{not} dominate minibatch SGD by presenting a lower bound on the performance of local SGD that is worse than the minibatch SGD guarantee.

We consider the task of learning in episodic finite-horizon Markov decision processes with an unknown transition function, bandit feedback, and adversarial losses. We propose an efficient algorithm that achieves O(√L|X|AT ) regret with high probability, where L is the horizon, |X| the number of states, |A| the number of actions, and T the number of episodes. To our knowledge, our algorithm is the first to ensure O(√T) regret in this challenging setting; in fact, it achieves the same regret as (Rosenberg & Mansour, 2019a) who consider the easier setting with full-information. Our key contributions are two-fold: a tighter confidence set for the transition function; and an optimistic loss estimator that is inversely weighted by an "upper occupancy bound".

Machine learning (ML) systems often encounter Out-of-Distribution (OoD) errors when dealing with testing data coming from a distribution different from training data. It becomes important for ML systems in critical applications to accurately quantify its predictive uncertainty and screen out these anomalous inputs. However, existing OoD detection approaches are prone to errors and even sometimes assign higher likelihoods to OoD samples. Unlike standard learning tasks, there is currently no well established guiding principle for designing OoD detection architectures that can accurately quantify uncertainty. To address these problems, we first seek to identify guiding principles for designing uncertainty-aware architectures, by proposing Neural Architecture Distribution Search (NADS). NADS searches for a distribution of architectures that perform well on a given task, allowing us to identify common building blocks among all uncertainty-aware architectures. With this formulation, we are able to optimize a stochastic OoD detection objective and construct an ensemble of models to perform OoD detection. We perform multiple OoD detection experiments and observe that our NADS performs favorably, with up to 57% improvement in accuracy compared to state-of-the-art methods among 15 different testing configurations.

Probabilistic clustering models (or equivalently, mixture models) are basic building blocks in countless statistical models and involve latent random variables over discrete spaces. For these models, posterior inference methods can be inaccurate and/or very slow. In this work we introduce deep network architectures trained with labeled samples from any generative model of clustered datasets. At test time, the networks generate approximate posterior samples of cluster labels for any new dataset of arbitrary size. We develop two complementary approaches to this task, requiring either O(N) or O(K) network forward passes per dataset, where N is the dataset size and K the number of clusters. Unlike previous approaches, our methods sample the labels of all the data points from a well-defined posterior, and can learn nonparametric Bayesian posteriors since they do not limit the number of mixture components. As a scientific application, we present a novel approach to neural spike sorting for high-density multielectrode arrays.

This paper investigates the impact of pre-existing offline data on online learning, in the context of dynamic pricing. We study a single-product dynamic pricing problem over a selling horizon of T periods. The demand in each period is determined by the price of the product according to a linear demand model with unknown parameters. We assume that the seller already has some pre-existing offline data before the start of the selling horizon. The seller wants to utilize both the pre-existing offline data and the sequential online data to minimize the regret of the online learning process. We characterize the joint effect of the size, location and dispersion of the offline data on the optimal regret of the online learning process. Our results reveal surprising transformations of the optimal regret rate with respect to the size of the offline data, which we refer to as phase transitions. In addition, our results demonstrate that the location and dispersion of the offline data also have an intrinsic effect on the optimal regret, and we quantify this effect via the inverse-square law.

It is common practice in deep learning to use overparameterized networks and train for as long as possible; there are numerous studies that show, both theoretically and empirically, that such practices surprisingly do not unduly harm the generalization performance of the classifier. In this paper, we empirically study this phenomenon in the setting of adversarially trained deep networks, which are trained to minimize the loss under worst-case adversarial perturbations. We find that overfitting to the training set does in fact harm robust performance to a very large degree in adversarially robust training across multiple datasets (SVHN, CIFAR-10, CIFAR-100, and ImageNet) and perturbation models (L-infinity and L-2). Based upon this observed effect, we show that the performance gains of virtually all recent algorithmic improvements upon adversarial training can be matched by simply using early stopping. We also show that effects such as the double descent curve do still occur in adversarially trained models, yet fail to explain the observed overfitting. Finally, we study several classical and modern deep learning remedies for overfitting, including regularization and data augmentation, and find that no approach in isolation improves significantly upon the gains achieved by early stopping. All code for reproducing the experiments as well …

The combination of inducing point methods with stochastic variational inference has enabled approximate Gaussian Process (GP) inference on large datasets. Unfortunately, the resulting predictive distributions often exhibit substantially underestimated uncertainties. Notably, in the regression case the predictive variance is typically dominated by observation noise, yielding uncertainty estimates that make little use of the input-dependent function uncertainty that makes GP priors attractive. In this work we propose two simple methods for scalable GP regression that address this issue and thus yield substantially improved predictive uncertainties. The first applies variational inference to FITC (Fully Independent Training Conditional; Snelson et. al. 2006). The second bypasses posterior approximations and instead directly targets the posterior predictive distribution. In an extensive empirical comparison with a number of alternative methods for scalable GP regression, we find that the resulting predictive distributions exhibit significantly better calibrated uncertainties and higher log likelihoods--often by as much as half a nat per datapoint.

Reinforcement learning with function approximation can be unstable and even divergent, especially when combined with off-policy learning and Bellman updates. In deep reinforcement learning, these issues have been dealt with empirically by adapting and regularizing the representation, in particular with auxiliary tasks. This suggests that representation learning may provide a means to guarantee stability. In this paper, we formally show that there are indeed nontrivial state representations under which the canonical SARSA algorithm is stable, even when learning off-policy. We analyze representation learning schemes that are based on the transition matrix of a policy, such as proto-value functions, along three axes: approximation error, stability, and ease of estimation. In the most general case of a defective transition matrix, we show that a Schur basis provides convergence guarantees, but is difficult to estimate from samples. For a fixed reward function, we find that an orthogonal basis of the corresponding Krylov subspace is an even better choice. We conclude by empirically demonstrating that these stable representations can be learned using stochastic gradient descent, opening the door to improved techniques for representation learning with deep networks.

Given n values possessed by n agents, we study the problem of estimating the mean by truthfully eliciting agents' answers to multiple-choice questions about their values. We consider two natural candidates for estimation error: mean squared error (MSE) and mean absolute error (MAE). We design a randomized estimator which is asymptotically optimal for both measures in the worst case. In the case where prior distributions over the agents' values are known, we give an optimal, polynomial-time algorithm for MSE, and show that the task of computing an optimal estimate for MAE is #P-hard. Finally, we demonstrate empirically that knowledge of prior distributions gives a significant edge.

Neural networks and tree ensembles are state-of-the-art learners, each with its unique statistical and computational advantages. We aim to combine these advantages by introducing a new layer for neural networks, composed of an ensemble of differentiable decision trees (a.k.a. soft trees). While differentiable trees demonstrate promising results in the literature, they are typically slow in training and inference as they do not support conditional computation. We mitigate this issue by introducing a new sparse activation function for sample routing, and implement true conditional computation by developing specialized forward and backward propagation algorithms that exploit sparsity. Our efficient algorithms pave the way for jointly training over deep and wide tree ensembles using first-order methods (e.g., SGD). Experiments on 23 classification datasets indicate over 10x speed-ups compared to the differentiable trees used in the literature and over 20x reduction in the number of parameters compared to gradient boosted trees, while maintaining competitive performance. Moreover, experiments on CIFAR, MNIST, and Fashion MNIST indicate that replacing dense layers in CNNs with our tree layer reduces the test loss by 7-53% and the number of parameters by 8x. We provide an open-source TensorFlow implementation with a Keras API.

Current transfer learning methods are mainly based on finetuning a pretrained model with target-domain data. Motivated by the techniques from adversarial machine learning (ML) that are capable of manipulating the model prediction via data perturbations, in this paper we propose a novel approach, black-box adversarial reprogramming (BAR), that repurposes a well-trained black-box ML model (e.g., a prediction API or a proprietary software) for solving different ML tasks, especially in the scenario with scarce data and constrained resources. The rationale lies in exploiting high-performance but unknown ML models to gain learning capability for transfer learning. Using zeroth order optimization and multi-label mapping techniques, BAR can reprogram a black-box ML model solely based on its input-output responses without knowing the model architecture or changing any parameter. More importantly, in the limited medical data setting, on autism spectrum disorder classification, diabetic retinopathy detection, and melanoma detection tasks, BAR outperforms state-of-the-art methods and yields comparable performance to the vanilla adversarial reprogramming method requiring complete knowledge of the target ML model. BAR also outperforms baseline transfer learning approaches by a significant margin, demonstrating cost-effective means and new insights for transfer learning.

Over-parameterization is ubiquitous nowadays in training neural networks to benefit both optimization in seeking global optima and generalization in reducing prediction error. However, compressive networks are desired in many real world ap- plications and direct training of small networks may be trapped in local optima. In this paper, in- stead of pruning or distilling over-parameterized models to compressive ones, we propose a new approach based on differential inclusions of in- verse scale spaces. Specifically, it generates a family of models from simple to complex ones that couples a pair of parameters to simultaneously train over-parameterized deep models and structural sparsity on weights of fully connected and convolutional layers. Such a differential inclusion scheme has a simple discretization, pro- posed as Deep structurally splitting Linearized Bregman Iteration (DessiLBI), whose global convergence analysis in deep learning is established that from any initializations, algorithmic iterations converge to a critical point of empirical risks. Experimental evidence shows that DessiLBI achieve comparable and even better performance than the competitive optimizers in exploring the structural sparsity of several widely used backbones on the benchmark datasets. Remarkably, with early stopping, DessiLBI unveils “winning tickets” in early epochs: the effective sparse structure with comparable test accuracy to fully …

In weakly supervised learning, unbiased risk estimator(URE) is a powerful tool for training classifiers when training and test data are drawn from different distributions. Nevertheless, UREs lead to overfitting in many problem settings when the models are complex like deep networks. In this paper, we investigate reasons for such overfitting by studying a weakly supervised problem called learning with complementary labels. We argue the quality of gradient estimation matters more in risk minimization. Theoretically, we show that a URE gives an unbiased gradient estimator(UGE). Practically, however, UGEs may suffer from huge variance, which causes empirical gradients to be usually far away from true gradients during minimization. To this end, we propose a novel surrogate complementary loss(SCL) framework that trades zero bias with reduced variance and makes empirical gradients more aligned with true gradients in the direction. Thanks to this characteristic, SCL successfully mitigates the overfitting issue and improves URE-based methods.

Motivated by high-stakes decision-making domains like personalized medicine where user information is inherently sensitive, we design privacy preserving exploration policies for episodic reinforcement learning (RL). We first provide a meaningful privacy formulation using the notion of joint differential privacy (JDP)--a strong variant of differential privacy for settings where each user receives their own sets of output (e.g., policy recommendations). We then develop a private optimism-based learning algorithm that simultaneously achieves strong PAC and regret bounds, and enjoys a JDP guarantee. Our algorithm only pays for a moderate privacy cost on exploration: in comparison to the non-private bounds, the privacy parameter only appears in lower-order terms. Finally, we present lower bounds on sample complexity and regret for reinforcement learning subject to JDP.

Projection-free optimization via different variants of the Frank-Wolfe (FW), a.k.a. Conditional Gradient method has become one of the cornerstones in optimization for machine learning since in many cases the linear minimization oracle is much cheaper to implement than projections and some sparsity needs to be preserved. In a number of applications, e.g. Poisson inverse problems or quantum state tomography, the loss is given by a self-concordant (SC) function having unbounded curvature, implying absence of theoretical guarantees for the existing FW methods. We use the theory of SC functions to provide a new adaptive step size for FW methods and prove global convergence rate O(1/k) after k iterations. If the problem admits a stronger local linear minimization oracle, we construct a novel FW method with linear convergence rate for SC functions.

The main approach to defining equivalence among acyclic directed causal graphical models is based on the conditional independence relationships in the distributions that the causal models can generate, in terms of the Markov equivalence. However, it is known that when cycles are allowed in the causal structure, conditional independence may not be a suitable notion for equivalence of two structures, as it does not reflect all the information in the distribution that is useful for identification of the underlying structure. In this paper, we present a general, unified notion of equivalence for linear Gaussian causal directed graphical models, whether they are cyclic or acyclic. In our proposed definition of equivalence, two structures are equivalent if they can generate the same set of data distributions. We also propose a weaker notion of equivalence called quasi-equivalence, which we show is the extent of identifiability from observational data. We propose analytic as well as graphical methods for characterizing the equivalence of two structures. Additionally, we propose a score-based method for learning the structure from observational data, which successfully deals with both acyclic and cyclic structures.

Collaborative machine learning (ML) is an appealing paradigm to build high-quality ML models by training on the aggregated data from many parties. However, these parties are only willing to share their data when given enough incentives, such as a guaranteed fair reward based on their contributions. This motivates the need for measuring a party's contribution and designing an incentive-aware reward scheme accordingly. This paper proposes to value a party's reward based on Shapley value and information gain on model parameters given its data. Subsequently, we give each party a model as a reward. To formally incentivize the collaboration, we define some desirable properties (e.g., fairness and stability) which are inspired by cooperative game theory but adapted for our model reward that is uniquely freely replicable. Then, we propose a novel model reward scheme to satisfy fairness and trade off between the desirable properties via an adjustable parameter. The value of each party's model reward determined by our scheme is attained by injecting Gaussian noise to the aggregated training data with an optimized noise variance. We empirically demonstrate interesting properties of our scheme and evaluate its performance using synthetic and real-world datasets.

Policy learning using historical observational data is an important problem that has found widespread applications. However, existing literature rests on the crucial assumption that the future environment where the learned policy will be deployed is the same as the past environment that has generated the data–an assumption that is often false or too coarse an approximation. In this paper, we lift this assumption and aim to learn a distributionally robust policy with bandit observational data. We propose a novel learning algorithm that is able to learn a robust policy to adversarial perturbations and unknown covariate shifts. We first present a policy evaluation procedure in the ambiguous environment and also give a heuristic algorithm to solve the distributionally robust policy learning problems efficiently. Additionally, we provide extensive simulations to demonstrate the robustness of our policy.

Real-world datasets are often biased with respect to key demographic factors such as race and gender. Due to the latent nature of the underlying factors, detecting and mitigating bias is especially challenging for unsupervised machine learning. We present a weakly supervised algorithm for overcoming dataset bias for deep generative models. Our approach requires access to an additional small, unlabeled reference dataset as the supervision signal, thus sidestepping the need for explicit labels on the underlying bias factors. Using this supplementary dataset, we detect the bias in existing datasets via a density ratio technique and learn generative models which efficiently achieve the twin goals of: 1) data efficiency by using training examples from both biased and reference datasets for learning; and 2) data generation close in distribution to the reference dataset at test time. Empirically, we demonstrate the efficacy of our approach which reduces bias w.r.t. latent factors by an average of up to 34.6% over baselines for comparable image generation using generative adversarial networks.

Generative flows models enjoy the properties of tractable exact likelihood and efficient sampling, which are composed of a sequence of invertible functions. In this paper, we incorporate matrix exponential into generative flows. Matrix exponential is a map from matrices to invertible matrices, this property is suitable for generative flows. Based on matrix exponential, we propose matrix exponential coupling layers that are a general case of affine coupling layers and matrix exponential invertible 1 x 1 convolutions that do not collapse during training. And we modify the networks architecture to make training stable and significantly speed up the training process. Our experiments show that our model achieves great performance on density estimation amongst generative flows models.

Contemporary work on learning in continuous games has commonly overlooked the hierarchical decision-making structure present in machine learning problems formulated as games, instead treating them as simultaneous play games and adopting the Nash equilibrium solution concept. We deviate from this paradigm and provide a comprehensive study of learning in Stackelberg games. This work provides insights into the optimization landscape of zero-sum games by establishing connections between Nash and Stackelberg equilibria along with the limit points of simultaneous gradient descent. We derive novel gradient-based learning dynamics emulating the natural structure of a Stackelberg game using the implicit function theorem and provide convergence analysis for deterministic and stochastic updates for zero-sum and general-sum games. Notably, in zero-sum games using deterministic updates, we show the only critical points the dynamics converge to are Stackelberg equilibria and provide a local convergence rate. Empirically, our learning dynamics mitigate rotational behavior and exhibit benefits for training generative adversarial networks compared to simultaneous gradient descent.

Monocular multi-object detection and localization in 3D space has been proven to be a challenging task. The MoNet3D algorithm is a novel and effective framework that can predict the 3D position of each object in a monocular image, and draw a 3D bounding box on each object. The MoNet3D method incorporates the prior knowledge of spatial geometric correlation of neighboring objects into the deep neural network training process, in order to improve the accuracy of 3D object localization. Experiments over the KITTI data set show that the accuracy of predicting the depth and horizontal coordinate of the object in 3D space can reach 96.25% and 94.74%, respectively. Meanwhile, the method can realize the real-time image processing capability of 27.85 FPS. Our code is publicly available at https://github.com/CQUlearningsystemgroup/YicongPeng

We present Natural Gradient Boosting (NGBoost), an algorithm for generic probabilistic prediction via gradient boosting. Typical regression models return a point estimate, conditional on covariates, but probabilistic regression models output a full probability distribution over the outcome space, conditional on the covariates. This allows for predictive uncertainty estimation - crucial in applications like healthcare and weather forecasting. NGBoost generalizes gradient boosting to probabilistic regression by treating the parameters of the conditional distribution as targets for a multiparameter boosting algorithm. Furthermore, we show how the Natural Gradient is required to correct the training dynamics of our multiparameter boosting approach. NGBoost can be used with any base learner, any family of distributions with continuous parameters, and any scoring rule. NGBoost matches or exceeds the performance of existing methods for probabilistic prediction while offering additional benefits in flexibility, scalability, and usability. An open-source implementation is available at github.com/stanfordmlgroup/ngboost.

To simultaneously capture syntax and global semantics from a text corpus, we propose a new larger-context recurrent neural network (RNN) based language model, which extracts recurrent hierarchical semantic structure via a dynamic deep topic model to guide natural language generation. Moving beyond a conventional RNN-based language model that ignores long-range word dependencies and sentence order, the proposed model captures not only intra-sentence word dependencies, but also temporal transitions between sentences and inter-sentence topic dependencies. For inference, we develop a hybrid of stochastic-gradient Markov chain Monte Carlo and recurrent autoencoding variational Bayes. Experimental results on a variety of real-world text corpora demonstrate that the proposed model not only outperforms larger-context RNN-based language models, but also learns interpretable recurrent multilayer topics and generates diverse sentences and paragraphs that are syntactically correct and semantically coherent.

Graph representation learning is a ubiquitous task in machine learning where the goal is to embed each vertex into a low-dimensional vector space. We consider the bipartite graph and formalize its representation learning problem as a statistical estimation problem of parameters in a semiparametric exponential family distribution: the bipartite graph is assumed to be generated by a semiparametric exponential family distribution, whose parametric component is given by the proximity of outputs of two one-layer neural networks that take high-dimensional features as inputs, while nonparametric (nuisance) component is the base measure. In this setting, the representation learning problem is equivalent to recovering the weight matrices, and the main challenges of estimation arise from the nonlinearity of activation functions and the nonparametric nuisance component of the distribution. To overcome these challenges, we propose a pseudo-likelihood objective based on the rank-order decomposition technique and show that the proposed objective is strongly convex in a neighborhood around the ground truth, so that a gradient descent-based method achieves linear convergence rate. Moreover, we prove that the sample complexity of the problem is linear in dimensions (up to logarithmic factors), which is consistent with parametric Gaussian models. However, our estimator is robust to any model misspecification …

This paper formalizes the binarization operations over neural networks from a learning perspective. In contrast to classical hand crafted rules (\eg hard thresholding) to binarize full-precision neurons, we propose to learn a mapping from full-precision neurons to the target binary ones. Each individual weight entry will not be binarized independently. Instead, they are taken as a whole to accomplish the binarization, just as they work together in generating convolution features. To help the training of the binarization mapping, the full-precision neurons after taking sign operations is regarded as some auxiliary supervision signal, which is noisy but still has valuable guidance. An unbiased estimator is therefore introduced to mitigate the influence of the supervision noise. Experimental results on benchmark datasets indicate that the proposed binarization technique attains consistent improvements over baselines.

The neural plausibility of backpropagation has long been disputed, primarily for its use of non-local weight transport --- the biologically dubious requirement that one neuron instantaneously measure the synaptic weights of another. Until recently, attempts to create local learning rules that avoid weight transport have typically failed in the large-scale learning scenarios where backpropagation shines, e.g. ImageNet categorization with deep convolutional networks. Here, we investigate a recently proposed local learning rule that yields competitive performance with backpropagation and find that it is highly sensitive to metaparameter choices, requiring laborious tuning that does not transfer across network architecture. Our analysis indicates the underlying mathematical reason for this instability, allowing us to identify a more robust local learning rule that better transfers without metaparameter tuning. Nonetheless, we find a performance and stability gap between this local rule and backpropagation that widens with increasing model depth. We then investigate several non-local learning rules that relax the need for instantaneous weight transport into a more biologically-plausible "weight estimation" process, showing that these rules match state-of-the-art performance on deep networks and operate effectively in the presence of noisy updates. Taken together, our results suggest two routes towards the discovery of neural implementations for credit assignment …

Balancing performance and safety is crucial to deploying autonomous vehicles in multi-agent environments. In particular, autonomous racing is a domain that penalizes safe but conservative policies, highlighting the need for robust, adaptive strategies. Current approaches either make simplifying assumptions about other agents or lack robust mechanisms for online adaptation. This work makes algorithmic contributions to both challenges. First, to generate a realistic, diverse set of opponents, we develop a novel method for self-play based on replica-exchange Markov chain Monte Carlo. Second, we propose a distributionally robust bandit optimization procedure that adaptively adjusts risk aversion relative to uncertainty in beliefs about opponents’ behaviors. We rigorously quantify the tradeoffs in performance and robustness when approximating these computations in real-time motion-planning, and we demonstrate our methods experimentally on autonomous vehicles that achieve scaled speeds comparable to Formula One racecars.

On a periodic basis, publicly traded companies report fundamentals, financial data including revenue, earnings, debt, among others. Quantitative finance research has identified several factors, functions of the reported data that historically correlate with stock market performance. In this paper, we first show through simulation that if we could select stocks via factors calculated on future fundamentals (via oracle), that our portfolios would far outperform standard factor models. Motivated by this insight, we train deep nets to forecast future fundamentals from a trailing 5-year history. We propose lookahead factor models which plug these predicted future fundamentals into traditional factors. Finally, we incorporate uncertainty estimates from both neural heteroscedastic regression and a dropout-based heuristic, improving performance by adjusting our portfolios to avert risk. In retrospective analysis, we leverage an industry-grade portfolio simulator (backtester) to show simultaneous improvement in annualized return and Sharpe ratio. Specifically, the simulated annualized return for the uncertainty-aware model is 17.7% (vs 14.0% for a standard factor model) and the Sharpe ratio is 0.84 (vs 0.52).

Generative adversarial imitation learning (GAIL) demonstrates tremendous success in practice, especially when combined with neural networks. Different from reinforcement learning, GAIL learns both policy and reward function from expert (human) demonstration. Despite its empirical success, it remains unclear whether GAIL with neural networks converges to the globally optimal solution. The major difficulty comes from the nonconvex-nonconcave minimax optimization structure. To bridge the gap between practice and theory, we analyze a gradient-based algorithm with alternating updates and establish its sublinear convergence to the globally optimal solution. To the best of our knowledge, our analysis establishes the global optimality and convergence rate of GAIL with neural networks for the first time.

We propose a novel gradient-based tractable approach for the Blahut-Arimoto (BA) algorithm to compute the rate-distortion function where the BA algorithm is fully parameterized. This results in a rich and flexible framework to learn a new class of stochastic encoders, termed PArameterized RAte-DIstortion Stochastic Encoder (PARADISE). The framework can be applied to a wide range of settings from semi-supervised, multi-task to supervised and robust learning. We show that the training objective of PARADISE can be seen as a form of regularization that helps improve generalization. With an emphasis on robust learning we further develop a novel posterior matching objective to encourage smoothness on the loss function and show that PARADISE can significantly improve interpretability as well as robustness to adversarial attacks on the CIFAR-10 and ImageNet datasets. In particular, on the CIFAR-10 dataset, our model reduces standard and adversarial error rates in comparison to the state-of-the-art by 50% and 41%, respectively without the expensive computational cost of adversarial training.

Rank aggregation from pairwise preferences has widespread applications in recommendation systems and information retrieval. Given the enormous economic and societal impact of these applications, and the consequent incentives for malicious players to manipulate ranking outcomes in their favor, an important challenge is to make rank aggregation algorithms robust to adversarial manipulations in data. In this paper, we initiate the study of robustness in rank aggregation under the popular Bradley-Terry-Luce (BTL) model for pairwise comparisons. We consider a setting where pairwise comparisons are initially generated according to a BTL model, but a fraction of these comparisons are corrupted by an adversary prior to being reported to us. We consider a strong contamination model, where an adversary having complete knowledge of the initial truthful data and the underlying true BTL parameters, can subsequently corrupt the truthful data by inserting, deleting, or changing data points. The goal is to estimate the true score/weight of each item under the BTL model, even in the presence of these corruptions. We characterize the extent of adversarial corruption under which the true BTL parameters are uniquely identifiable. We also provide a novel pruning algorithm that provably cleans the data of adversarial corruption under reasonable conditions on data …

Learning graph generative models is a challenging task for deep learning and has wide applicability to a range of domains like chemistry, biology and social science. However current deep neural methods suffer from limited scalability: for a graph with n nodes and m edges, existing deep neural methods require Omega(n^2) complexity by building up the adjacency matrix. On the other hand, many real world graphs are actually sparse in the sense that m << n^2. Based on this, we develop a novel autoregressive model, named BiGG, that utilizes this sparsity to avoid generating the full adjacency matrix, and importantly reduces the graph generation time complexity to O((n + m) log n). Furthermore, during training this autoregressive model can be parallelized with O(log n) synchronization stages, which makes it much more efficient than other autoregressive models that require Omega(n). Experiments on several benchmarks show that the proposed approach not only scales to orders of magnitude larger graphs than previously possible with deep autoregressive graph generative models, but also yields better graph generation quality.

Linear quadratic regulator (LQR) is one of the most popular frameworks to tackle continuous Markov decision process tasks. With its fundamental theory and tractable optimal policy, LQR has been revisited and analyzed in recent years, in terms of reinforcement learning scenarios such as the model-free or model-based setting. In this paper, we introduce the Structured Policy Iteration (S-PI) for LQR, a method capable of deriving a structured linear policy. Such a structured policy with (block) sparsity or low-rank can have significant advantages over the standard LQR policy: more interpretable, memory-efficient, and well-suited for the distributed setting. In order to derive such a policy, we first cast a regularized LQR problem when the model is known. Then, our Structured Policy Iteration (S-PI) algorithm, which takes a policy evaluation step and a policy improvement step in an iterative manner, can solve this regularized LQR efficiently. We further extend the S-PI algorithm to the model-free setting where a smoothing procedure is adopted to estimate the gradient. In both the known-model and model-free setting, we prove convergence analysis under the proper choice of parameters. Finally, the experiments demonstrate the advantages of S-PI in terms of balancing the LQR performance and level of structure by …

We consider an agent that is assigned with a temporal logic task in an environment whose semantic representation is only partially known. We represent the semantics of the environment with a set of state properties, called \textit{atomic propositions} over which, the agent holds a probabilistic belief and updates it as new sensory measurements arrive. The goal is to design a policy for the agent that realizes the task with high probability. We develop a planning strategy that takes the semantic uncertainties into account and by doing so provides probabilistic guarantees on the task success. Furthermore, as new data arrive, the belief over the atomic propositions evolves and, subsequently, the planning strategy adapts accordingly. We evaluate the proposed method on various finite-horizon tasks in planar navigation settings where the empirical results show that the proposed method provides reliable task performance that also improves as the knowledge about the environment enhances.

Deep generative modeling has achieved many successes for continuous data generation, such as producing realistic images and controlling their properties (e.g., styles). However, the development of generative modeling techniques for optimizing discrete data, such as sequences or strings, still lags behind largely due to the challenges in modeling complex and long-range constraints, including both syntax and semantics, in discrete structures. In this paper, we formulate the sequence optimization task as a chance-constrained optimization problem. The key idea is to enforce a high probability of generating valid sequences and also optimize the property of interest. We propose a novel minmax algorithm to simultaneously tighten a bound of the valid chance and optimize the expected property. Extensive experimental results in three domains demonstrate the superiority of our approach over the existing sequence optimization methods.

We study why overparameterization---increasing model size well beyond the point of zero training error---can hurt test error on minority groups despite improving average test error when there are spurious correlations in the data. Through simulations and experiments on two image datasets, we identify two key properties of the training data that drive this behavior: the proportions of majority versus minority groups, and the signal-to-noise ratio of the spurious correlations. We then analyze a linear setting and theoretically show how the inductive bias of models towards ``memorizing'' fewer examples can cause overparameterization to hurt. Our analysis leads to a counterintuitive approach of subsampling the majority group, which empirically achieves low minority error in the overparameterized regime, even though the standard approach of upweighting the minority fails. Overall, our results suggest a tension between using overparameterized models versus using all the training data for achieving low worst-group error.

We propose a unified framework for adaptive connection sampling in graph neural networks (GNNs) that generalizes existing stochastic regularization methods for training GNNs. The proposed framework not only alleviates over-smoothing and over-fitting tendencies of deep GNNs, but also enables learning with uncertainty in graph analytic tasks with GNNs. Instead of using fixed sampling rates or hand-tuning themas model hyperparameters in existing stochastic regularization methods, our adaptive connection sampling can be trained jointly with GNN model parameters in both global and local fashions. GNN training with adaptive connection sampling is shown to be mathematically equivalent to an efficient approximation of training BayesianGNNs. Experimental results with ablation studies on benchmark datasets validate that adaptively learning the sampling rate given graph training data is the key to boost the performance of GNNs in semi-supervised node classification, less prone to over-smoothing and over-fitting with more robust prediction.

A fundamental challenge in contextual bandits is to develop flexible, general-purpose algorithms with computational requirements no worse than classical supervised learning tasks such as classification and regression. Algorithms based on regression have shown promising empirical success, but theoretical guarantees have remained elusive except in special cases. We provide the first universal and optimal reduction from contextual bandits to online regression. We show how to transform any oracle for online regression with a given value function class into an algorithm for contextual bandits with the induced policy class, with no overhead in runtime or memory requirements. We characterize the minimax rates for contextual bandits with general, potentially nonparametric function classes, and show that our algorithm is minimax optimal whenever the oracle obtains the optimal rate for regression. Compared to previous results, our algorithm requires no distributional assumptions beyond realizability, and works even when contexts are chosen adversarially.

We study the problem of learning Granger causality between event types from asynchronous, interdependent, multi-type event sequences. Existing work suffers from either limited model flexibility or poor model explainability and thus fails to uncover Granger causality across a wide variety of event sequences with diverse event interdependency. To address these weaknesses, we propose CAUSE (Causality from AttribUtions on Sequence of Events), a novel framework for the studied task. The key idea of CAUSE is to first implicitly capture the underlying event interdependency by fitting a neural point process, and then extract from the process a Granger causality statistic using an axiomatic attribution method. Across multiple datasets riddled with diverse event interdependency, we demonstrate that CAUSE achieves superior performance on correctly inferring the inter-type Granger causality over a range of state-of-the-art methods.

Machine learning algorithms are known to be susceptible to data poisoning attacks, where an adversary manipulates the training data to degrade performance of the resulting classifier. In this work, we propose a strategy for building linear classifiers that are certifiably robust against a strong variant of label flipping, where each test example is targeted independently. In other words, for each test point, our classifier includes a certification that its prediction would be the same had some number of training labels been changed adversarially. Our approach leverages randomized smoothing, a technique that has previously been used to guarantee---with high probability---test-time robustness to adversarial manipulation of the input to a classifier. We derive a variant which provides a deterministic, analytical bound, sidestepping the probabilistic certificates that traditionally result from the sampling subprocedure. Further, we obtain these certified bounds with minimal additional runtime complexity over standard classification and no assumptions on the train or test distributions. We generalize our results to the multi-class case, providing the first multi-class classification algorithm that is certifiably robust to label-flipping attacks.

A dynamic treatment regime (DTR) consists of a sequence of decision rules, one per stage of intervention, that dictates how to determine the treatment assignment to patients based on evolving treatments and covariates' history. These regimes are particularly effective for managing chronic disorders and is arguably one of the critical ingredients underlying more personalized decision-making systems. All reinforcement learning algorithms for finding the optimal DTR in online settings will suffer O(\sqrt{|D{X, S}|T}) regret on some environments, where T is the number of experiments, and D{X, S} is the domains of treatments X and covariates S. This implies T = O (|D{X, S}|) trials to generate an optimal DTR. In many applications, domains of X and S could be so enormous that the time required to ensure appropriate learning may be unattainable. We show that, if the causal diagram of the underlying environment is provided, one could achieve regret that is exponentially smaller than D{X, S}. In particular, we develop two online algorithms that satisfy such regret bounds by exploiting the causal structure underlying the DTR; one is based on the principle of optimism in the face of uncertainty (OFU-DTR), and the other uses the posterior sampling …

Interpretability is important in text generation for guiding the generation with interpretable attributes. Variational auto-encoder (VAE) with Gaussian distribution as prior has been successfully applied in text generation, but it is hard to interpret the meaning of the latent variable. To enhance the controllability and interpretability, one can replace the Gaussian prior with a mixture of Gaussian distributions (GM-VAE), whose mixture components could be related to some latent attributes of data. Unfortunately, straightforward variational training of GM-VAE leads the mode-collapse problem. In this paper, we find that mode-collapse is a general problem for VAEs with exponential family mixture priors. We propose DEM-VAE, which introduces an extra dispersion term to induce a well-structured latent space. Experimental results show that our approach does obtain a well structured latent space, with which our method outperforms strong baselines in interpretable text generation benchmarks.

Creating open-ended algorithms, which generate their own never-ending stream of novel and appropriately challenging learning opportunities, could help to automate and accelerate progress in machine learning. A recent step in this direction is the Paired Open-Ended Trailblazer (POET), an algorithm that generates and solves its own challenges, and allows solutions to goal-switch between challenges to avoid local optima. However, the original POET was unable to demonstrate its full creative potential because of limitations of the algorithm itself and because of external issues including a limited problem space and lack of a universal progress measure. Importantly, both limitations pose impediments not only for POET, but for the pursuit of open-endedness in general. Here we introduce and empirically validate two new innovations to the original algorithm, as well as two external innovations designed to help elucidate its full potential. Together, these four advances enable the most open-ended algorithmic demonstration to date. The algorithmic innovations are (1) a domain-general measure of how meaningfully novel new challenges are, enabling the system to potentially create and solve interesting challenges endlessly, and (2) an efficient heuristic for determining when agents should goal-switch from one problem to another (helping open-ended search better scale). Outside the algorithm itself, …

Many cooperative multiagent reinforcement learning environments provide agents with a sparse team-based reward, as well as a dense agent-specific reward that incentivizes learning basic skills. Training policies solely on the team-based reward is often difficult due to its sparsity. Also, relying solely on the agent-specific reward is sub-optimal because it usually does not capture the team coordination objective. A common approach is to use reward shaping to construct a proxy reward by combining the individual rewards. However, this requires manual tuning for each environment. We introduce Multiagent Evolutionary Reinforcement Learning (MERL), a split-level training platform that handles the two objectives separately through two optimization processes. An evolutionary algorithm maximizes the sparse team-based objective through neuroevolution on a population of teams. Concurrently, a gradient-based optimizer trains policies to only maximize the dense agent-specific rewards. The gradient-based policies are periodically added to the evolutionary population as a way of information transfer between the two optimization processes. This enables the evolutionary algorithm to use skills learned via the agent-specific rewards toward optimizing the global objective. Results demonstrate that MERL significantly outperforms state-of-the-art methods, such as MADDPG, on a number of difficult coordination benchmarks.

The instability in GANs' training has been a long-standing problem despite remarkable research efforts. We identify that instability issues stem from difficulties of performing feature matching with mini-batch statistics, due to a fragile balance between the fixed target distribution and the progressively generated distribution. In this work, we propose feature quantizatoin (FQ) for the discriminator, to embed both true and fake data samples into a shared discrete space. The quantized values of FQ are constructed as an evolving dictionary, which is consistent with feature statistics of the recent distribution history. Hence, FQ implicitly enables robust feature matching in a compact space. Our method can be easily plugged into existing GAN models, with little computational overhead in training. Extensive experimental results show that the proposed FQ-GAN can improve the FID scores of baseline methods by a large margin on a variety of tasks, including three representative GAN models on 10 benchmarks, achieving new state-of-the-art performance.

Learning long-range behaviors on complex high-dimensional agents is a fundamental problem in robot learning. For such tasks, we argue that transferring learned information from a morphologically simpler agent can massively improve the sample efficiency of a more complex one. To this end, we propose a hierarchical decoupling of policies into two parts: an independently learned low-level policy and a transferable high-level policy. To remedy poor transfer performance due to mismatch in morphologies, we contribute two key ideas. First, we show that incentivizing a complex agent's low-level to imitate a simpler agent's low-level significantly improves zero-shot high-level transfer. Second, we show that KL-regularized training of the high level stabilizes learning and prevents mode-collapse. Finally, on a suite of publicly released navigation and manipulation environments, we demonstrate the applicability of hierarchical transfer on long-range tasks across morphologies.

Training machine learning models that are robust against adversarial inputs poses seemingly insurmountable challenges. To better understand adversarial robustness, we consider the underlying problem of learning robust representations. We develop a notion of representation vulnerability that captures the maximum change of mutual information between the input and output distributions, under the worst-case input perturbation. Then, we prove a theorem that establishes a lower bound on the minimum adversarial risk that can be achieved for any downstream classifier based on its representation vulnerability. We propose an unsupervised learning method for obtaining intrinsically robust representations by maximizing the worst-case mutual information between the input and output distributions. Experiments on downstream classification tasks %and analyses of saliency maps support the robustness of the representations found using unsupervised learning with our training principle.

We study the problem of efficiently estimating the effect of an intervention on a single variable using observational samples. Our goal is to give algorithms with polynomial time and sample complexity in a non-parametric setting. Tian and Pearl (AAAI '02) have exactly characterized the class of causal graphs for which causal effects of atomic interventions can be identified from observational data. We make their result quantitative. Suppose 𝒫 is a causal model on a set V of n observable variables with respect to a given causal graph G, and let do(x) be an identifiable intervention on a variable X. We show that assuming that G has bounded in-degree and bounded c-components (k) and that the observational distribution satisfies a strong positivity condition: (i) [Evaluation] There is an algorithm that outputs with probability 2/3 an evaluator for a distribution P^ that satisfies TV(P(V | do(x)), P^(V)) < eps using m=O~(n/eps^2) samples from P and O(mn) time. The evaluator can return in O(n) time the probability P^(v) for any assignment v to V. (ii) [Sampling] There is an algorithm that outputs with probability 2/3 a sampler for a distribution P^ that satisfies TV(P(V | do(x)), P^(V)) < eps using m=O~(n/eps^2) samples from …

Most real-world tasks are compound tasks that consist of multiple simpler sub-tasks. The main challenge of learning compound tasks is that we have no explicit supervision to learn the hierarchical structure of compound tasks. To address this challenge, previous imitation learning methods exploit task-specific knowledge, e.g., labeling demonstrations manually or specifying termination conditions for each sub-task. However, the need for task-specific knowledge makes it difficult to scale imitation learning to real-world tasks. In this paper, we propose an imitation learning method that can learn compound tasks without task-specific knowledge. The key idea behind our method is to leverage a self-supervised learning framework to learn the hierarchical structure of compound tasks. Our work also proposes a task-agnostic regularization technique to prevent unstable switching between sub-tasks, which has been a common degenerate case in previous works. We evaluate our method against several baselines on compound tasks. The results show that our method achieves state-of-the-art performance on compound tasks, outperforming prior imitation learning methods.

We introduce the lookahead-bounded Q-learning (LBQL) algorithm, a new, provably convergent variant of Q-learning that seeks to improve the performance of standard Q-learning in stochastic environments through the use of “lookahead” upper and lower bounds. To do this, LBQL employs previously collected experience and each iteration’s state-action values as dual feasible penalties to construct a sequence of sampled information relaxation problems. The solutions to these problems provide estimated upper and lower bounds on the optimal value, which we track via stochastic approximation. These quantities are then used to constrain the iterates to stay within the bounds at every iteration. Numerical experiments on benchmark problems show that LBQL exhibits faster convergence and more robustness to hyperparameters when compared to standard Q-learning and several related techniques. Our approach is particularly appealing in problems that require expensive simulations or real-world interactions.

Efficient and interpretable spatial analysis is crucial in many fields such as geology, sports, and climate science. Tensor latent factor models can describe higher-order correlations for spatial data. However, they are computationally expensive to train and are sensitive to initialization, leading to spatially incoherent, uninterpretable results. We develop a novel Multiresolution Tensor Learning (MRTL) algorithm for efficiently learning interpretable spatial patterns. MRTL initializes the latent factors from an approximate full-rank tensor model for improved interpretability and progressively learns from a coarse resolution to the fine resolution for boosted efficiency. We also prove the theoretical convergence and computational complexity of MRTL. When applied to two real-world datasets, MRTL demonstrates 4~5x speedup compared to a fixed resolution approach while yielding accurate and interpretable models.

Regularization for optimization is a crucial technique to avoid overfitting in machine learning. In order to obtain the best performance, we usually train a model by tuning the regularization parameters. It becomes costly, however, when a single round of training takes significant amount of time. Very recently, Neu and Rosasco show that if we run stochastic gradient descent (SGD) on linear regression problems, then by averaging the SGD iterates properly, we obtain a regularized solution. It left open whether the same phenomenon can be achieved for other optimization problems and algorithms. In this paper, we establish an averaging scheme that provably converts the iterates of SGD on an arbitrary strongly convex and smooth objective function to its regularized counterpart with an adjustable regularization parameter. Our approaches can be used for accelerated and preconditioned optimization methods as well. We further show that the same methods work empirically on more general optimization objectives including neural networks. In sum, we obtain adjustable regularization for free for a large class of optimization problems and resolve an open question raised by Neu and Rosasco.

Language model pre-training has been shown to capture a surprising amount of world knowledge, crucial for NLP tasks such as question answering. However, this knowledge is stored implicitly in the parameters of a neural network, requiring ever-larger networks to cover more facts. To capture knowledge in a more modular and interpretable way, we augment language model pre-training with a latent knowledge retriever, which allows the model to retrieve and attend over documents from a large corpus such as Wikipedia, used during pre-training, fine-tuning and inference. For the first time, we show how to pre-train such a knowledge retriever in an unsupervised manner, using masked language modeling as the learning signal and backpropagating through a retrieval step that considers millions of documents. We demonstrate the effectiveness of Retrieval-Augmented Language Model pre-training (REALM) by fine-tuning on the challenging task of Open-domain Question Answering (Open-QA). We compare against state-of-the-art models for both explicit and implicit knowledge storage on three popular Open-QA benchmarks, and find that we outperform all previous methods by a significant margin (4-16% absolute accuracy), while also providing qualitative benefits such as interpretability and modularity.

Bayesian reward learning from demonstrations enables rigorous safety and uncertainty analysis when performing imitation learning. However, Bayesian reward learning methods are typically computationally intractable for complex control problems. We propose Bayesian Reward Extrapolation (Bayesian REX), a highly efficient Bayesian reward learning algorithm that scales to high-dimensional imitation learning problems by pre-training a low-dimensional feature encoding via self-supervised tasks and then leveraging preferences over demonstrations to perform fast Bayesian inference. Bayesian REX can learn to play Atari games from demonstrations, without access to the game score and can generate 100,000 samples from the posterior over reward functions in only 5 minutes on a personal laptop. Bayesian REX also results in imitation learning performance that is competitive with or better than state-of-the-art methods that only learn point estimates of the reward function. Finally, Bayesian REX enables efficient high-confidence policy evaluation without having access to samples of the reward function. These high-confidence performance bounds can be used to rank the performance and risk of a variety of evaluation policies and provide a way to detect reward hacking behaviors.

Despite substantial progress in signal source separation, results for richly structured data continue to contain perceptible artifacts. In contrast, recent deep generative models can produce authentic samples in a variety of domains that are indistinguishable from samples of the data distribution. This paper introduces a Bayesian approach to source separation that uses deep generative models as priors over the components of a mixture of sources, and noise-annealed Langevin dynamics to sample from the posterior distribution of sources given a mixture. This decouples the source separation problem from generative modeling, enabling us to directly use cutting-edge generative models as priors. The method achieves state-of-the-art performance for MNIST digit separation. We introduce new methodology for evaluating separation quality on richer datasets, providing quantitative evaluation and qualitative discussion of results for CIFAR-10 image separation.

Differentiable architecture search (DARTS) is a prevailing NAS solution to identify architectures. Based on the continuous relaxation of the architecture space, DARTS learns a differentiable architecture weight and largely reduces the search cost. However, its stability has been challenged for yielding deteriorating architectures as the search proceeds. We find that the precipitous validation loss landscape, which leads to a dramatic performance drop when distilling the final architecture, is an essential factor that causes instability. Based on this observation, we propose a perturbation-based regularization - SmoothDARTS (SDARTS), to smooth the loss landscape and improve the generalizability of DARTS-based methods. In particular, our new formulations stabilize DARTS-based methods by either random smoothing or adversarial attack. The search trajectory on NAS-Bench-1Shot1 demonstrates the effectiveness of our approach and due to the improved stability, we achieve performance gain across various search spaces on 4 datasets. Furthermore, we mathematically show that SDARTS implicitly regularizes the Hessian norm of the validation loss, which accounts for a smoother loss landscape and improved performance.

Learning from demonstrations can be challenging when the quality of demonstrations is diverse, and even more so when the quality is unknown and there is no additional information to estimate the quality. We propose a new method for imitation learning in such scenarios. We show that simple quality-estimation approaches might fail due to compounding error, and fix this issue by jointly estimating both the quality and reward using a variational approach. Our method is easy to implement within reinforcement-learning frameworks and also achieves state-of-the-art performance on continuous-control benchmarks.Our work enables scalable and data-efficient imitation learning under more realistic settings than before.

Despite the remarkable performance of deep neural networks on various computer vision tasks, they are known to be susceptible to adversarial perturbations, which makes it challenging to deploy them in real-world safety-critical applications. In this paper, we conjecture that the leading cause of adversarial vulnerability is the distortion in the latent feature space, and provide methods to suppress them effectively. Explicitly, we define \emph{vulnerability} for each latent feature and then propose a new loss for adversarial learning, \emph{Vulnerability Suppression (VS)} loss, that aims to minimize the feature-level vulnerability during training. We further propose a Bayesian framework to prune features with high vulnerability to reduce both vulnerability and loss on adversarial samples. We validate our \emph{Adversarial Neural Pruning with Vulnerability Suppression (ANP-VS)} method on multiple benchmark datasets, on which it not only obtains state-of-the-art adversarial robustness but also improves the performance on clean examples, using only a fraction of the parameters used by the full network. Further qualitative analysis suggests that the improvements come from the suppression of feature-level vulnerability.

Specifying a Reinforcement Learning (RL) task involves choosing a suitable planning horizon, which is typically modeled by a discount factor. It is known that applying RL algorithms with a lower discount factor can act as a regularizer, improving performance in the limited data regime. Yet the exact nature of this regularizer has not been investigated. In this work, we fill in this gap. For several Temporal-Difference (TD) learning methods, we show an explicit equivalence between using a reduced discount factor and adding an explicit regularization term to the algorithm's loss. Motivated by the equivalence, we empirically study this technique compared to standard L2 regularization by extensive experiments in discrete and continuous domains, using tabular and functional representations. Our experiments suggest the regularization effectiveness is strongly related to properties of the available data, such as size, distribution, and mixing rate.

We present GradientDICE for estimating the density ratio between the state distribution of the target policy and the sampling distribution in off-policy reinforcement learning. GradientDICE fixes several problems of GenDICE (Zhang et al., 2020), the current state-of-the-art for estimating such density ratios. Namely, the optimization problem in GenDICE is not a convex-concave saddle-point problem once nonlinearity in optimization variable parameterization is introduced to ensure positivity, so primal-dual algorithms are not guaranteed to find the desired solution. However, such nonlinearity is essential to ensure the consistency of GenDICE even with a tabular representation. This is a fundamental contradiction, resulting from GenDICE's original formulation of the optimization problem. In GradientDICE, we optimize a different objective from GenDICE by using the Perron-Frobenius theorem and eliminating GenDICE's use of divergence, such that nonlinearity in parameterization is not necessary for GradientDICE, which is provably convergent under linear function approximation.

As the operations of autonomous systems generally affect simultaneously several users, it is crucial that their designs account for fairness considerations. In contrast to standard (deep) reinforcement learning (RL), we investigate the problem of learning a policy that treats its users equitably. In this paper, we formulate this novel RL problem, in which an objective function, which encodes a notion of fairness that we formally define, is optimized. For this problem, we provide a theoretical discussion where we examine the case of discounted rewards and that of average rewards. During this analysis, we notably derive a new result in the standard RL setting, which is of independent interest: it states a novel bound on the approximation error with respect to the optimal average reward of that of a policy optimal for the discounted reward. Since learning with discounted rewards is generally easier, this discussion further justifies finding a fair policy for the average reward by learning a fair policy for the discounted reward. Thus, we describe how several classic deep RL algorithms can be adapted to our fair optimization problem, and we validate our approach with extensive experiments in three different domains.

One of the most effective algorithms for differentially private learning and optimization is \emph{objective perturbation}. This technique augments a given optimization problem (e.g. deriving from an ERM problem) with a random linear term, and then exactly solves it. However, to date, analyses of this approach crucially rely on the convexity and smoothness of the objective function. We give two algorithms that extend this approach substantially. The first algorithm requires nothing except boundedness of the loss function, and operates over a discrete domain. Its privacy and accuracy guarantees hold even without assuming convexity. We are able to extend traditional analyses of objective perturbation by introducing a novel normalization step into the algorithm, which provides enough stability to be differentially private even without second-order conditions. The second algorithm operates over a continuous domain and requires only that the loss function be bounded and Lipschitz in its continuous parameter. Its privacy analysis does not even require convexity. Its accuracy analysis does require convexity, but does not require second order conditions like smoothness. We complement our theoretical results with an empirical evaluation of the non-convex case, in which we use an integer program solver as our optimization oracle. We find that for the problem …

Recent work showed that overparameterized autoencoders can be trained to implement associative memory via iterative maps, when the trained input-output Jacobian of the network has all of its eigenvalue norms strictly below one. Here, we theoretically analyze this phenomenon for sigmoid networks by leveraging recent developments in deep learning theory, especially the correspondence between training neural networks in the infinite-width limit and performing kernel regression with the Neural Tangent Kernel (NTK). We find that overparameterized sigmoid autoencoders can have attractors in the NTK limit for both training with a single example and multiple examples under certain conditions. In particular, for multiple training examples, we find that the norm of the largest Jacobian eigenvalue drops below one with increasing input norm, leading to associative memory.

Machine learning research has advanced in multiple aspects, including model structures and learning methods. The effort to automate such research, known as AutoML, has also made significant progress. However, this progress has largely focused on the architecture of neural networks, where it has relied on sophisticated expert-designed layers as building blocks---or similarly restrictive search spaces. Our goal is to show that AutoML can go further: it is possible today to automatically discover complete machine learning algorithms just using basic mathematical operations as building blocks. We demonstrate this by introducing a novel framework that significantly reduces human bias through a generic search space. Despite the vastness of this space, evolutionary search can still discover two-layer neural networks trained by backpropagation. These simple neural networks can then be surpassed by evolving directly on tasks of interest, e.g. CIFAR-10 variants, where modern techniques emerge in the top algorithms, such as bilinear interactions, normalized gradients, and weight averaging. Moreover, evolution adapts algorithms to different task types: e.g., dropout-like techniques appear when little data is available. We believe these preliminary successes in discovering machine learning algorithms from scratch indicate a promising new direction for the field.

Classical approaches for one-class problems such as one-class SVM and isolation forest require careful feature engineering when applied to structured domains like images. State-of-the-art methods aim to leverage deep learning to learn appropriate features via two main approaches. The first approach based on predicting transformations (Golan & El-Yaniv, 2018; Hendrycks et al., 2019a) while successful in some domains, crucially depends on an appropriate domain-specific set of transformations that are hard to obtain in general. The second approach of minimizing a classical one-class loss on the learned final layer representations, e.g., DeepSVDD (Ruff et al., 2018) suffers from the fundamental drawback of representation collapse. In this work, we propose Deep Robust One Class Classification (DROCC) that is both applicable to most standard domains without requiring any side-information and robust to representation collapse. DROCC is based on the assumption that the points from the class of interest lie on a well-sampled, locally linear low dimensional manifold. Empirical evaluation demonstrates that DROCC is highly effective in two different one-class problem settings and on a range of real-world datasets across different domains: tabular data, images (CIFAR and ImageNet), audio, and time-series, offering up to 20% increase in accuracy over the state-of-the-art in anomaly detection.

Estimating the score, i.e., the gradient of log density function, from a set of samples generated by an unknown distribution is a fundamental task in inference and learning of probabilistic models that involve flexible yet intractable densities. Kernel estimators based on Stein's methods or score matching have shown promise, however their theoretical properties and relationships have not been fully-understood. We provide a unifying view of these estimators under the framework of regularized nonparametric regression. It allows us to analyse existing estimators and construct new ones with desirable properties by choosing different hypothesis spaces and regularizers. A unified convergence analysis is provided for such estimators. Finally, we propose score estimators based on iterative regularization that enjoy computational benefits from curl-free kernels and fast convergence.

We develop a novel method, called PoWER-BERT, for improving the inference time of the popular BERT model, while maintaining the accuracy. It works by: a) exploiting redundancy pertaining to word-vectors (intermediate encoder outputs) and eliminating the redundant vectors. b) determining which word-vectors to eliminate by developing a strategy for measuring their significance, based on the self-attention mechanism. c) learning how many word-vectors to eliminate by augmenting the BERT model and the loss function. Experiments on the standard GLUE benchmark shows that PoWER-BERT achieves up to 4.5x reduction in inference time over BERT with < 1% loss in accuracy. We show that PoWER-BERT offers significantly better trade-off between accuracy and inference time compared to prior methods. We demonstrate that our method attains up to 6.8x reduction in inference time with < 1% loss in accuracy when applied over ALBERT, a highly compressed version of BERT. The code for PoWER-BERT is publicly available at https://github.com/IBM/PoWER-BERT.

Fine-tuning the deep convolution neural network (CNN) using a pre-trained model helps transfer knowledge learned from larger datasets to the target task. While the accuracy could be largely improved even when the training dataset is small, the transfer learning outcome is similar with the pre-trained one with closed CNN weights[17], as the backpropagation here brings less updates to deeper CNN layers. In this work, we propose RIFLE - a simple yet effective strategy that deepens backpropagation in transfer learning settings, through periodically ReInitializing the Fully-connected LayEr with random scratch during the fine-tuning procedure. RIFLE brings significant perturbation to the backpropagation process and leads to deep CNN weights update, while the affects of perturbation can be easily converged throughout the overall learning procedure. The experiments show that the use of RIFLE significantly improves deep transfer learning accuracy on a wide range of datasets, outperforming known tricks for the similar purpose, such as dropout, dropconnect, stochastic depth, and cyclic learning rate, under the same settings with 0.5%-2% higher testing accuracy. Empirical cases and ablation studies further indicate RIFLE brings meaningful updates to deep CNN layers with accuracy improved.

System identification is a key step for model-based control, estimator design, and output prediction. This work considers the offline identification of partially observed nonlinear systems. We empirically show that the certainty-equivalent approximation to expectation-maximization can be a reliable and scalable approach for high-dimensional deterministic systems, which are common in robotics. We formulate certainty-equivalent expectation-maximization as block coordinate-ascent, and provide an efficient implementation. The algorithm is tested on a simulated system of coupled Lorenz attractors, demonstrating its ability to identify high-dimensional systems that can be intractable for particle-based approaches. Our approach is also used to identify the dynamics of an aerobatic helicopter. By augmenting the state with unobserved fluid states, a model is learned that predicts the acceleration of the helicopter better than state-of-the-art approaches. The codebase for this work is available at https://github.com/sisl/CEEM.

Transformers have increasingly outperformed gated RNNs in obtaining new state-of-the-art results on supervised tasks involving text sequences. Inspired by this trend, we study the question of how Transformer-based models can improve the performance of sequential decision-making agents. We present the Working Memory Graph (WMG), an agent that employs multi-head self-attention to reason over a dynamic set of vectors representing observed and recurrent state. We evaluate WMG in three environments featuring factored observation spaces: a Pathfinding environment that requires complex reasoning over past observations, BabyAI gridworld levels that involve variable goals, and Sokoban which emphasizes future planning. We find that the combination of WMG's Transformer-based architecture with factored observation spaces leads to significant gains in learning efficiency compared to baseline architectures across all tasks. WMG demonstrates how Transformer-based models can dramatically boost sample efficiency in RL environments for which observations can be factored.

We develop an effective generation of adversarial attacks on neural models that output a sequence of probability distributions rather than a sequence of single values. This setting includes the recently proposed deep probabilistic autoregressive forecasting models that estimate the probability distribution of a time series given its past and achieve state-of-the-art results in a diverse set of application domains. The key technical challenge we address is how to effectively differentiate through the Monte-Carlo estimation of statistics of the output sequence joint distribution. Additionally, we extend prior work on probabilistic forecasting to the Bayesian setting which allows conditioning on future observations, instead of only on past observations. We demonstrate that our approach can successfully generate attacks with small input perturbations in two challenging tasks where robust decision making is crucial -- stock market trading and prediction of electricity consumption.

Recommendation systems often face exploration-exploitation tradeoffs: the system can only learn about the desirability of new options by recommending them to some user. Such systems can thus be modeled as multi-armed bandit settings; however, users are self-interested and cannot be made to follow recommendations. We ask whether exploration can nevertheless be performed in a way that scrupulously respects agents' interests---i.e., by a system that acts as a fiduciary. More formally, we introduce a model in which a recommendation system faces an exploration-exploitation tradeoff under the constraint that it can never recommend any action that it knows yields lower reward in expectation than an agent would achieve if it acted alone. Our main contribution is a positive result: an asymptotically optimal, incentive compatible, and ex-ante individually rational recommendation algorithm.

Individual fairness is an intuitive definition of algorithmic fairness that addresses some of the drawbacks of group fairness. Despite its benefits, it depends on a task specific fair metric that encodes our intuition of what is fair and unfair for the ML task at hand, and the lack of a widely accepted fair metric for many ML tasks is the main barrier to broader adoption of individual fairness. In this paper, we present two simple ways to learn fair metrics from a variety of data types. We show empirically that fair training with the learned metrics leads to improved fairness on three machine learning tasks susceptible to gender and racial biases. We also provide theoretical guarantees on the statistical performance of both approaches.

Deep autoregressive models compute point likelihood estimates of individual data points. However, many applications (i.e., database cardinality estimation), require estimating range densities, a capability that is under-explored by current neural density estimation literature. In these applications, fast and accurate range density estimates over high-dimensional data directly impact user-perceived performance. In this paper, we explore a technique for accelerating range density estimation over deep autoregressive models. This technique, called variable skipping, exploits the sparse structure of range density queries to avoid sampling unnecessary variables during approximate inference. We show that variable skipping provides 10-100x efficiency improvements when targeting challenging high-quantile error metrics, enables complex applications such as text pattern matching, and can be realized via a simple data augmentation procedure without changing the usual maximum likelihood objective.

Sampling is a fundamental technique, and sampling without replacement is often desirable when duplicate samples are not beneficial. Within machine learning, sampling is useful for generating diverse outputs from a trained model. We present an elegant procedure for sampling without replacement from a broad class of randomized programs, including generative neural models that construct outputs sequentially. Our procedure is efficient even for exponentially-large output spaces. Unlike prior work, our approach is incremental, i.e., samples can be drawn one at a time, allowing for increased flexibility. We also present a new estimator for computing expectations from samples drawn without replacement. We show that incremental sampling without replacement is applicable to many domains, e.g., program synthesis and combinatorial optimization.

There is a recent surge of interest in designing deep architectures based on the update steps in traditional algorithms, or learning neural networks to improve and replace traditional algorithms. While traditional algorithms have certain stopping criteria for outputting results at different iterations, many algorithm-inspired deep models are restricted to a fixed-depth'' for all inputs. Similar to algorithms, the optimal depth of a deep architecture may be different for different input instances, either to avoidover-thinking'', or because we want to compute less for operations converged already. In this paper, we tackle this varying depth problem using a steerable architecture, where a feed-forward deep model and a variational stopping policy are learned together to sequentially determine the optimal number of layers for each input instance. Training such architecture is very challenging. We provide a variational Bayes perspective and design a novel and effective training procedure which decomposes the task into an oracle model learning stage and an imitation stage. Experimentally, we show that the learned deep model along with the stopping policy improves the performances on a diverse set of tasks, including learning sparse recovery, few-shot meta learning, and computer vision tasks.

Convolutional neural networks are among the most successful architectures in deep learning with this success at least partially attributable to the efficacy of spatial invariance as an inductive bias. Locally connected layers, which differ from convolutional layers only in their lack of spatial invariance, usually perform poorly in practice. However, these observations still leave open the possibility that some degree of relaxation of spatial invariance may yield a better inductive bias than either convolution or local connectivity. To test this hypothesis, we design a method to relax the spatial invariance of a network layer in a controlled manner; we create a \textit{low-rank} locally connected layer, where the filter bank applied at each position is constructed as a linear combination of basis set of filter banks with spatially varying combining weights. By varying the number of basis filter banks, we can control the degree of relaxation of spatial invariance. In experiments with small convolutional networks, we find that relaxing spatial invariance improves classification accuracy over both convolution and locally connected layers across MNIST, CIFAR-10, and CelebA datasets, thus suggesting that spatial invariance may be an overly restrictive prior.

The translation equivariance of convolutional layers enables CNNs to generalize well on image problems. While translation equivariance provides a powerful inductive bias for images, we often additionally desire equivariance to other transformations, such as rotations, especially for non-image data. We propose a general method to construct a convolutional layer that is equivariant to transformations from any specified Lie group with a surjective exponential map. Incorporating equivariance to a new group requires implementing only the group exponential and logarithm maps, enabling rapid prototyping. Showcasing the simplicity and generality of our method, we apply the same model architecture to images, ball-and-stick molecular data, and Hamiltonian dynamical systems. For Hamiltonian systems, the equivariance of our models is especially impactful, leading to exact conservation of linear and angular momentum.

Inspired by progress in unsupervised representation learning for natural language, we examine whether similar models can learn useful representations for images. We train a sequence Transformer to auto-regressively predict pixels, without incorporating knowledge of the 2D input structure. Despite training on low-resolution ImageNet without labels, we find that a GPT-2 scale model learns strong image representations as measured by linear probing, fine-tuning, and low-data classification. On CIFAR-10, we achieve 96.3% accuracy with a linear probe, outperforming a supervised Wide ResNet, and 99.0% accuracy with full fine-tuning, matching the top supervised pre-trained models. We are also competitive with self-supervised benchmarks on ImageNet when substituting pixels for a VQVAE encoding, achieving 69.0% top-1 accuracy on a linear probe of our features.

This paper investigates the intriguing question of whether we can create learning algorithms that automatically generate training data, learning environments, and curricula in order to help AI agents rapidly learn. We show that such algorithms are possible via Generative Teaching Networks (GTNs), a general approach that is, in theory, applicable to supervised, unsupervised, and reinforcement learning, although our experiments only focus on the supervised case. GTNs are deep neural networks that generate data and/or training environments that a learner (e.g. a freshly initialized neural network) trains on for a few SGD steps before being tested on a target task. We then differentiate \emph{through the entire learning process} via meta-gradients to update the GTN parameters to improve performance on the target task. This paper introduces GTNs, discusses their potential, and showcases that they can substantially accelerate learning. We also demonstrate a practical and exciting application of GTNs: accelerating the evaluation of candidate architectures for neural architecture search (NAS). GTN-NAS improves the NAS state of the art, finding higher performing architectures when controlling for the search proposal mechanism. GTN-NAS also is competitive with the overall state of the art approaches, which achieve top performance while using orders of magnitude less computation than …

Discrete choice models with unobserved heterogeneity are commonly used Econometric models for dynamic Economic behavior which have been adopted in practice to predict behavior of individuals and firms from schooling and job choices to strategic decisions in market competition. These models feature optimizing agents who choose among a finite set of options in a sequence of periods and receive choice-specific payoffs that depend on both variables that are observed by the agent and recorded in the data and variables that are only observed by the agent but not recorded in the data. Existing work in Econometrics assumes that optimizing agents are fully rational and requires finding a functional fixed point to find the optimal policy. We show that in an important class of discrete choice models the value function is globally concave in the policy. That means that simple algorithms that do not require fixed point computation, such as the policy gradient algorithm, globally converge to the optimal policy. This finding can both be used to relax behavioral assumption regarding the optimizing agents and to facilitate Econometric analysis of dynamic behavior. In particular, we demonstrate significant computational advantages in using a simple implementation policy gradient algorithm over existing “nested fixed …

We study the properties of a leave-node-out jackknife procedure for network data. Under the sparse graphon model, we prove an Efron-Stein-type inequality, showing that the network jackknife leads to conservative estimates of the variance (in expectation) for any network functional that is invariant to node permutation. For a general class of count functionals, we also establish consistency of the network jackknife. We complement our theoretical analysis with a range of simulated and real-data examples and show that the network jackknife offers competitive performance in cases where other resampling methods are known to be valid. In fact, for several network statistics, we see that the jackknife provides more accurate inferences compared to related methods such as subsampling.

Many applications, including natural language processing, sensor networks, collaborative filtering, and federated learning, call for estimating discrete distributions from data collected in batches, some of which may be untrustworthy, erroneous, faulty, or even adversarial. Previous estimators for this setting ran in exponential time, and for some regimes required a suboptimal number of batches. We provide the first polynomial-time estimator that is optimal in the number of batches and achieves essentially the best possible estimation accuracy.

Lagrangian methods are widely used algorithms for constrained optimization problems, but their learning dynamics exhibit oscillations and overshoot which, when applied to safe reinforcement learning, leads to constraint-violating behavior during agent training. We address this shortcoming by proposing a novel Lagrange multiplier update method that utilizes derivatives of the constraint function. We take a controls perspective, wherein the traditional Lagrange multiplier update behaves as \emph{integral} control; our terms introduce \emph{proportional} and \emph{derivative} control, achieving favorable learning dynamics through damping and predictive measures. We apply our PID Lagrangian methods in deep RL, setting a new state of the art in Safety Gym, a safe RL benchmark. Lastly, we introduce a new method to ease controller tuning by providing invariance to the relative numerical scales of reward and cost. Our extensive experiments demonstrate improved performance and hyperparameter robustness, while our algorithms remain nearly as simple to derive and implement as the traditional Lagrangian approach.

Federated learning is a key scenario in modern large-scale machine learning where the data remains distributed over a large number of clients and the task is to learn a centralized model without transmitting the client data. The standard optimization algorithm used in this setting is Federated Averaging (FedAvg) due to its low communication cost. We obtain a tight characterization of the convergence of FedAvg and prove that heterogeneity (non-iid-ness) in the client's data results in a `drift' in the local updates resulting in poor performance.

As a solution, we propose a new algorithm (SCAFFOLD) which uses control variates (variance reduction) to correct for the `client drift'. We prove that SCAFFOLD requires significantly fewer communication rounds and is not affected by data heterogeneity or client sampling. Further, we show that (for quadratics) SCAFFOLD can take advantage of similarity in the client's data yielding even faster convergence. The latter is the first result to quantify the usefulness of local-steps in distributed optimization.

Since hardware resources are limited, the objective of training deep learning models is typically to maximize accuracy subject to the time and memory constraints of training and inference. We study the impact of model size in this setting, focusing on Transformer models for NLP tasks that are limited by compute: self-supervised pretraining and high-resource machine translation. We first show that even though smaller Transformer models execute faster per iteration, wider and deeper models converge in significantly fewer steps. Moreover, this acceleration in convergence typically outpaces the additional computational overhead of using larger models. Therefore, the most compute-efficient training strategy is to counterintuitively train extremely large models but stop after a small number of iterations. This leads to an apparent trade-off between the training efficiency of large Transformer models and the inference efficiency of small Transformer models. However, we show that large models are more robust to compression techniques such as quantization and pruning than small models. Consequently, one can get the best of both worlds: heavily compressed, large models achieve higher accuracy than lightly compressed, small models.

Deep energy-based models (EBMs) are very flexible in distribution parametrization but computationally challenging because of the intractable partition function. They are typically trained via maximum likelihood, using contrastive divergence to approximate the gradient of the KL divergence between data and model distribution. While KL divergence has many desirable properties, other f-divergences have shown advantages in training implicit density generative models such as generative adversarial networks. In this paper, we propose a general variational framework termed f-EBM to train EBMs using any desired f-divergence. We introduce a corresponding optimization algorithm and prove its local convergence property with non-linear dynamical systems theory. Experimental results demonstrate the superiority of f-EBM over contrastive divergence, as well as the benefits of training EBMs using f-divergences other than KL.

A growing body of research has shown that many classifiers are susceptible to adversarial examples -- small strategic modifications to test inputs that lead to misclassification. In this work, we study general non-parametric methods, with a view towards understanding when they are robust to these modifications. We establish general conditions under which non-parametric methods are r-consistent -- in the sense that they converge to optimally robust and accurate classifiers in the large sample limit.

Concretely, our results show that when data is well-separated, nearest neighbors and kernel classifiers are r-consistent, while histograms are not. For general data distributions, we prove that preprocessing by Adversarial Pruning (Yang et. al., 2019)-- that makes data well-separated -- followed by nearest neighbors or kernel classifiers also leads to r-consistency.

Much recent progress in applications of machine learning models to NLP has been driven by benchmarks that evaluate models across a wide variety of tasks. However, these broad-coverage benchmarks have been mostly limited to English, and despite an increasing interest in multilingual models, a benchmark that enables the comprehensive evaluation of such methods on a diverse range of languages and tasks is still missing. To this end, we introduce the Cross-lingual TRansfer Evaluation of Multilingual Encoders (XTREME) benchmark, a multi-task benchmark for evaluating the cross-lingual generalization capabilities of multilingual representations across 40 languages and 9 tasks. We demonstrate that while models tested on English reach human performance on many tasks, there is still a sizable gap in the performance of cross-lingually transferred models, particularly on syntactic and sentence retrieval tasks. There is also a wide spread of results across languages. We will release the benchmark to encourage research on cross-lingual learning methods that transfer linguistic knowledge across a diverse and representative set of languages and tasks.

The proliferation of medical monitoring devices makes it possible to track health vitals at high frequency, enabling the development of dynamic health risk scores that change with the underlying readings. Survival analysis, in particular hazard estimation, is well-suited to analyzing this stream of data to predict disease onset as a function of the time-varying vitals. This paper introduces the software package BoXHED (pronounced `box-head') for nonparametrically estimating hazard functions via gradient boosting. BoXHED 1.0 is a novel tree-based implementation of the generic estimator proposed in Lee et al. (2017), which was designed for handling time-dependent covariates in a fully nonparametric manner. BoXHED is also the first publicly available software implementation for Lee et al. (2017). Applying BoXHED to cardiovascular disease onset data from the Framingham Heart Study reveals novel interaction effects among known risk factors, potentially resolving an open question in clinical literature.

The goal of neural-symbolic computation is to integrate the connectionist and symbolist paradigms. Prior methods learn the neural-symbolic models using reinforcement learning (RL) approaches, which ignore the error propagation in the symbolic reasoning module and thus converge slowly with sparse rewards. In this paper, we address these issues and close the loop of neural-symbolic learning by (1) introducing the grammar model as a symbolic prior to bridge neural perception and symbolic reasoning, and (2) proposing a novel back-search algorithm which mimics the top-down human-like learning procedure to propagate the error through the symbolic reasoning module efficiently. We further interpret the proposed learning framework as maximum likelihood estimation using Markov chain Monte Carlo sampling and the back-search algorithm as a Metropolis-Hastings sampler. The experiments are conducted on two weakly-supervised neural-symbolic tasks: (1) handwritten formula recognition on the newly introduced HWF dataset; (2) visual question answering on the CLEVR dataset. The results show that our approach significantly outperforms the RL methods in terms of performance, converging speed, and data efficiency. Our code and data are released at https://liqing-ustc.github.io/NGS.

A longstanding goal in the theory of deep learning is to characterize the conditions under which a given neural network architecture will be trainable, and if so, how well it might generalize to unseen data. In this work, we provide such a characterization in the limit of very wide and very deep networks, for which the analysis simplifies considerably. For wide networks, the trajectory under gradient descent is governed by the Neural Tangent Kernel (NTK), and for deep networks the NTK itself maintains only weak data dependence. By analyzing the spectrum of the NTK, we formulate necessary conditions for trainability and generalization across a range of architectures, including Fully Connected Networks (FCNs) and Convolutional Neural Networks (CNNs). We identify large regions of hyperparameter space for which networks can memorize the training set but completely fail to generalize. We find that CNNs without global average pooling behave almost identically to FCNs, but that CNNs with pooling have markedly different and often better generalization performance. These theoretical results are corroborated experimentally on CIFAR10 for a variety of network architectures.

We include a \href{https://colab.research.google.com/github/google/neural-tangents/blob/master/notebooks/disentanglingtrainabilityand_generalization.ipynb}{colab} notebook that reproduces the essential results of the paper.

Efficient numerical solvers for sparse linear systems are crucial in science and engineering. One of the fastest methods for solving large-scale sparse linear systems is algebraic multigrid (AMG). The main challenge in the construction of AMG algorithms is the selection of the prolongation operator---a problem-dependent sparse matrix which governs the multiscale hierarchy of the solver and is critical to its efficiency. Over many years, numerous methods have been developed for this task, and yet there is no known single right answer except in very special cases. Here we propose a framework for learning AMG prolongation operators for linear systems with sparse symmetric positive (semi-) definite matrices. We train a single graph neural network to learn a mapping from an entire class of such matrices to prolongation operators, using an efficient unsupervised loss function. Experiments on a broad class of problems demonstrate improved convergence rates compared to classical AMG, demonstrating the potential utility of neural networks for developing sparse system solvers.

Recent research shows that sublevel sets of the loss surfaces of overparameterized networks are connected, exactly or approximately. We describe and compare experimentally a panel of methods used to connect two low-loss points by a low-loss curve on this surface. Our methods vary in accuracy and complexity. Most of our methods are based on ''macroscopic'' distributional assumptions and are insensitive to the detailed properties of the points to be connected. Some methods require a prior training of a ''global connection model'' which can then be applied to any pair of points. The accuracy of the method generally correlates with its complexity and sensitivity to the endpoint detail.

Mixture of linear regressions is a popular learning theoretic model that is used widely to represent heterogeneous data. In the simplest form, this model assumes that the labels are generated from either of two different linear models and mixed together. Recent works of Yin et al. and Krishnamurthy et al., 2019, focus on an experimental design setting of model recovery for this problem. It is assumed that the features can be designed and queried with to obtain their label. When queried, an oracle randomly selects one of the two different sparse linear models and generates a label accordingly. How many such oracle queries are needed to recover both of the models simultaneously? This question can also be thought of as a generalization of the well-known compressed sensing problem (Cand`es and Tao, 2005, Donoho, 2006). In this work we address this query complexity problem and provide efficient algorithms that improves on the previously best known results.

The upper confidence reinforcement learning (\UCRL) strategy introduced in \citep{jaksch2010near} is a popular method to perform regret minimization in unknown discrete Markov Decision Processes under the average-reward criterion. Despite its nice and generic theoretical regret guarantees, this strategy and its variants have remained until now mostly theoretical as numerical experiments on simple environments exhibit long burn-in phases before the learning takes place. In pursuit of practical efficiency, we present \UCRLnew, following the lines of \UCRL, but with two key modifications: First, it uses state-of-the-art time-uniform concentration inequalities, to compute confidence sets on the reward and (component-wise) transition distributions for each state-action pair. Further, to tighten exploration, it uses an adaptive computation of the support of each transition distributions, which in turn enables us to revisit the extended value iteration procedure to optimize over distributions with reduced support by disregarding low probability transitions, while still ensuring near-optimism. We demonstrate, through numerical experiments on standard environments, that reducing exploration this way yields a substantial numerical improvement compared to \UCRL\ and its variants. On the theoretical side, these key modifications enable us to derive a regret bound for \UCRLnew\ improving on \UCRL, that for the first time makes appear notions of local diameter …

Neural networks utilize the softmax as a building block in classification tasks, which contains an overconfidence problem and lacks an uncertainty representation ability. As a Bayesian alternative to the softmax, we consider a random variable of a categorical probability over class labels. In this framework, the prior distribution explicitly models the presumed noise inherent in the observed label, which provides consistent gains in generalization performance in multiple challenging tasks. The proposed method inherits advantages of Bayesian approaches that achieve better uncertainty estimation and model calibration. Our method can be implemented as a plug-and-play loss function with negligible computational overhead compared to the softmax with the cross-entropy loss function.

During the past five years the Bayesian deep learning community has developed increasingly accurate and efficient approximate inference procedures that allow for Bayesian inference in deep neural networks. However, despite this algorithmic progress and the promise of improved uncertainty quantification and sample efficiency there are---as of early 2020---no publicized deployments of Bayesian neural networks in industrial practice. In this work we cast doubt on the current understanding of Bayes posteriors in popular deep neural networks: we demonstrate through careful MCMC sampling that the posterior predictive induced by the Bayes posterior yields systematically worse predictions when compared to simpler methods including point estimates obtained from SGD. Furthermore, we demonstrate that predictive performance is improved significantly through the use of a ``cold posterior'' that overcounts evidence. Such cold posteriors sharply deviate from the Bayesian paradigm but are commonly used as heuristic in Bayesian deep learning papers. We put forward several hypotheses that could explain cold posteriors and evaluate the hypotheses through experiments. Our work questions the goal of accurate posterior approximations in Bayesian deep learning: If the true Bayes posterior is poor, what is the use of more accurate approximations? Instead, we argue that it is timely to focus on understanding the …

In this work, we propose ParaNet, a non-autoregressive seq2seq model that converts text to spectrogram. It is fully convolutional and brings 46.7 times speed-up over the lightweight Deep Voice 3 at synthesis, while obtaining reasonably good speech quality. ParaNet also produces stable alignment between text and speech on the challenging test sentences by iteratively improving the attention in a layer-by-layer manner. Furthermore, we build the parallel text-to-speech system by applying various parallel neural vocoders, which can synthesize speech from text through a single feed-forward pass. We also explore a novel VAE-based approach to train the inverse autoregressive flow~(IAF) based parallel vocoder from scratch, which avoids the need for distillation from a separately trained WaveNet as previous work.

The reliability of machine learning systems critically assumes that the associations between features and labels remain similar between training and test distributions. However, unmeasured variables, such as confounders, break this assumption---useful correlations between features and labels at training time can become useless or even harmful at test time. For example, high obesity is generally predictive for heart disease, but this relation may not hold for smokers who generally have lower rates of obesity and higher rates of heart disease. We present a framework for making models robust to spurious correlations by leveraging humans' common sense knowledge of causality. Specifically, we use human annotation to augment each training example with a potential unmeasured variable (i.e. an underweight patient with heart disease may be a smoker), reducing the problem to a covariate shift problem. We then introduce a new distributionally robust optimization objective over unmeasured variables (UV-DRO) to control the worst-case loss over possible test- time shifts. Empirically, we show improvements of 5--10% on a digit recognition task confounded by rotation, and 1.5--5% on the task of analyzing NYPD Police Stops confounded by location.

The Shapley value has become the basis for several methods that attribute the prediction of a machine-learning model on an input to its base features. The use of the Shapley value is justified by citing the uniqueness result from~\cite{Shapley53}, which shows that it is the only method that satisfies certain good properties (\emph{axioms}). There are, however, a multiplicity of ways in which the Shapley value is operationalized for model explanation. These differ in how they reference the model, the training data, and the explanation context. Hence they differ in output, rendering the uniqueness result inapplicable. Furthermore, the techniques that rely on they training data produce non-intuitive attributions, for instance unused features can still receive attribution.

In this paper, we use the axiomatic approach to study the differences between some of the many operationalizations of the Shapley value for attribution. We discuss a technique called Baseline Shapley (BShap), provide a proper uniqueness result for it, and contrast it with two other techniques from prior literature, Integrated Gradients~\cite{STY17} and Conditional Expectation Shapley~\cite{Lundberg2017AUA}.

We propose a novel framework for structured bandits, which we call an influence diagram bandit. Our framework captures complex statistical dependencies between actions, latent variables, and observations; and thus unifies and extends many existing models, such as combinatorial semi-bandits, cascading bandits, and low-rank bandits. We develop novel online learning algorithms that learn to act efficiently in our models. The key idea is to track a structured posterior distribution of model parameters, either exactly or approximately. To act, we sample model parameters from their posterior and then use the structure of the influence diagram to find the most optimistic action under the sampled parameters. We empirically evaluate our algorithms in three structured bandit problems, and show that they perform as well as or better than problem-specific state-of-the-art baselines.

We study a security threat to reinforcement learning where an attacker poisons the learning environment to force the agent into executing a target policy chosen by the attacker. As a victim, we consider RL agents whose objective is to find a policy that maximizes average reward in undiscounted infinite-horizon problem settings. The attacker can manipulate the rewards or the transition dynamics in the learning environment at training-time and is interested in doing so in a stealthy manner. We propose an optimization framework for finding an \emph{optimal stealthy attack} for different measures of attack cost. We provide sufficient technical conditions under which the attack is feasible and provide lower/upper bounds on the attack cost. We instantiate our attacks in two settings: (i) an \emph{offline} setting where the agent is doing planning in the poisoned environment, and (ii) an \emph{online} setting where the agent is learning a policy using a regret-minimization framework with poisoned feedback. Our results show that the attacker can easily succeed in teaching any target policy to the victim under mild conditions and highlight a significant security threat to reinforcement learning agents in practice.

While sorting is an important procedure in computer science, the argsort operator - which takes as input a vector and returns its sorting permutation - has a discrete image and thus zero gradients almost everywhere. This prohibits end-to-end, gradient-based learning of models that rely on the argsort operator. A natural way to overcome this problem is to replace the argsort operator with a continuous relaxation. Recent work has shown a number of ways to do this, but the relaxations proposed so far are computationally complex. In this work we propose a simple continuous relaxation for the argsort operator which has the following qualities: it can be implemented in three lines of code, achieves state-of-the-art performance, is easy to reason about mathematically - substantially simplifying proofs - and is faster than competing approaches. We open source the code to reproduce all of the experiments and results.

We propose a novel approach for preserving topological structures of the input space in latent representations of autoencoders. Using persistent homology, a technique from topological data analysis, we calculate topological signatures of both the input and latent space to derive a topological loss term. Under weak theoretical assumptions, we construct this loss in a differentiable manner, such that the encoding learns to retain multi-scale connectivity information. We show that our approach is theoretically well-founded and that it exhibits favourable latent representations on a synthetic manifold as well as on real-world image data sets, while preserving low reconstruction errors.

Label shift refers to the phenomenon where the prior class probability p(y) changes between the training and test distributions, while the conditional probability p(x|y) stays fixed. Label shift arises in settings like medical diagnosis, where a classifier trained to predict disease given symptoms must be adapted to scenarios where the baseline prevalence of the disease is different. Given estimates of p(y|x) from a predictive model, Saerens et al. proposed an efficient maximum likelihood algorithm to correct for label shift that does not require model retraining, but a limiting assumption of this algorithm is that p(y|x) is calibrated, which is not true of modern neural networks. Recently, Black Box Shift Learning (BBSL) and Regularized Learning under Label Shifts (RLLS) have emerged as state-of-the-art techniques to cope with label shift when a classifier does not output calibrated probabilities, but both methods require model retraining with importance weights and neither has been benchmarked against maximum likelihood. Here we (1) show that combining maximum likelihood with a type of calibration we call bias-corrected calibration outperforms both BBSL and RLLS across diverse datasets and distribution shifts, (2) prove that the maximum likelihood objective is concave, and (3) introduce a principled strategy for estimating source-domain priors …

Modern recommendation and notification systems must be robust to data imbalance, limitations on the number of recommendations/notifications, and heterogeneous engagement profiles across users. The pAp@k metric, which combines the partial-AUC and the precision@k metrics, was recently proposed to evaluate such recommendation systems and has been used in real-world deployments. Conceptually, pAp@k measures the probability of correctly ranking a top-ranked positive instance over top-ranked negative instances. Due to the combinatorial aspect surfaced by top-ranked points, little is known about the characteristics and optimization methods of pAp@k. In this paper, we analyze the learning-theoretic properties of pAp@k, particularly its benefits in evaluating modern recommender systems, and propose novel surrogates that are consistent under certain data regularity conditions. We then provide gradient descent based algorithms to optimize the surrogates directly. Our analysis and experimental evaluation suggest that pAp@k indeed exhibits a certain dual behavior with respect to partial-AUC and precision@k. Moreover, the proposed methods outperform all the baselines in various applications. Taken together, our results motivate the use of pAp@k for large-scale recommender systems with heterogeneous user-engagement.

The classical bias-variance trade-off predicts that bias decreases and variance increase with model complexity, leading to a U-shaped risk curve. Recent work calls this into question for neural networks and other over-parameterized models, for which it is often observed that larger models generalize better. We provide a simple explanation of this by measuring the bias and variance of neural networks: while the bias is {\em monotonically decreasing} as in the classical theory, the variance is {\em unimodal} or bell-shaped: it increases then decreases with the width of the network. We vary the network architecture, loss function, and choice of dataset and confirm that variance unimodality occurs robustly for all models we considered. The risk curve is the sum of the bias and variance curves and displays different qualitative shapes depending on the relative scale of bias and variance, with the double descent in the recent literature as a special case. We corroborate these empirical results with a theoretical analysis of two-layer linear networks with random first layer. Finally, evaluation on out-of-distribution data shows that most of the drop in accuracy comes from increased bias while variance increases by a relatively small amount. Moreover, we find that deeper models decrease bias …

Adversarial training augments the training set with perturbations to improve the robust error (over worst-case perturbations), but it often leads to an increase in the standard error (on unperturbed test inputs). Previous explanations for this tradeoff rely on the assumption that no predictor in the hypothesis class has low standard and robust error. In this work, we precisely characterize the effect of augmentation on the standard error in linear regression when the optimal linear predictor has zero standard and robust error. In particular, we show that the standard error could increase even when the augmented perturbations have noiseless observations from the optimal linear predictor. We then prove that the recently proposed robust self-training (RST) estimator improves robust error without sacrificing standard error for noiseless linear regression. Empirically, for neural networks, we find that RST with different adversarial training methods improves both standard and robust error for random and adversarial rotations and adversarial l_infty perturbations in CIFAR-10.

We study "adversarial scaling", a multi-armed bandit model where rewards have a stochastic and an adversarial component. Our model captures display advertising where the "click-through-rate" can be decomposed to a (fixed across time) arm-quality component and a non-stochastic user-relevance component (fixed across arms). Despite the relative stochasticity of our model, we demonstrate two settings where most bandit algorithms suffer. On the positive side, we show that two algorithms, one from the action elimination and one from the mirror descent family are adaptive enough to be robust to adversarial scaling. Our results shed light on the robustness of adaptive parameter selection in stochastic bandits, which may be of independent interest.

We study the question of how to imitate tasks across domains with discrepancies such as embodiment, viewpoint, and dynamics mismatch. Many prior works require paired, aligned demonstrations and an additional RL step that requires environment interactions. However, paired, aligned demonstrations are seldom obtainable and RL procedures are expensive. In this work, we formalize the Domain Adaptive Imitation Learning (DAIL) problem - a unified framework for imitation learning in the presence of viewpoint, embodiment, and/or dynamics mismatch. Informally, DAIL is the process of learning how to perform a task optimally, given demonstrations of the task in a distinct domain. We propose a two step approach to DAIL: alignment followed by adaptation. In the alignment step we execute a novel unsupervised MDP alignment algorithm, Generative Adversarial MDP Alignment (GAMA), to learn state and action correspondences from \emph{unpaired, unaligned} demonstrations. In the adaptation step we leverage the correspondences to zero-shot imitate tasks across domains. To describe when DAIL is feasible via alignment and adaptation, we introduce a theory of MDP alignability. We experimentally evaluate GAMA against baselines in embodiment, viewpoint, and dynamics mismatch scenarios where aligned demonstrations don't exist and show the effectiveness of our approach

Cooperative multi-agent decision making involves a group of agents cooperatively solving learning problems while communicating over a network with delays. In this paper, we consider the kernelised contextual bandit problem, where the reward obtained by an agent is an arbitrary linear function of the contexts' images in the related reproducing kernel Hilbert space (RKHS), and a group of agents must cooperate to collectively solve their unique decision problems. For this problem, we propose Coop-KernelUCB, an algorithm that provides near-optimal bounds on the per-agent regret, and is both computationally and communicatively efficient. For special cases of the cooperative problem, we also provide variants of Coop-KernelUCB that provides optimal per-agent regret. In addition, our algorithm generalizes several existing results in the multi-agent bandit setting. Finally, on a series of both synthetic and real-world multi-agent network benchmarks, we demonstrate that our algorithm significantly outperforms existing benchmarks.

Learning with noisy labels is a common challenge in supervised learning. Existing approaches often require practitioners to specify noise rates, i.e., a set of parameters controlling the severity of label noises in the problem, and the specifications are either assumed to be given or estimated using additional steps. In this work, we introduce a new family of loss functions that we name as peer loss functions, which enables learning from noisy labels and does not require a priori specification of the noise rates. Peer loss functions work within the standard empirical risk minimization (ERM) framework. We show that, under mild conditions, performing ERM with peer loss functions on the noisy data leads to the optimal or a near-optimal classifier as if performing ERM over the clean training data, which we do not have access to. We pair our results with an extensive set of experiments. Peer loss provides a way to simplify model development when facing potentially noisy training labels, and can be promoted as a robust candidate loss function in such situations.

We define a quantum version of Expectation-Maximization (QEM), a fundamental tool in unsupervised machine learning, often used to solve Maximum Likelihood (ML) and Maximum A Posteriori (MAP) estimation problems. We use QEM to fit a Gaussian Mixture Model, and show how to generalize it to fit mixture models with base distributions in the exponential family. Given quantum access to a dataset, our algorithm has convergence and precision guarantees similar to the classical algorithm, while the runtime is polylogarithmic in the number of elements in the training set and polynomial in other parameters, such as the dimension of the feature space and the number of components in the mixture. We discuss the performance of the algorithm on a dataset that is expected to be classified successfully by classical EM and provide guarantees for its runtime.

We describe a new approach for managing aleatoric uncertainty in the Reinforcement Learning (RL) paradigm. Instead of selecting actions according to a single statistic, we propose a distributional method based on the second-order stochastic dominance (SSD) relation. This compares the inherent dispersion of random returns induced by actions, producing a comprehensive evaluation of the environment’s uncertainty. The necessary conditions for SSD require estimators to predict accurate second moments. To accommodate this, we map the distributional RL problem to a Wasserstein gradient flow, treating the distributional Bellman residual as a potential energy functional. We propose a particle-based algorithm for which we prove optimality and convergence. Our experiments characterize the algorithm’s performance and demonstrate how uncertainty and performance are better balanced using an SSD policy than with other risk measures.

Many computer vision applications require solving multiple tasks in real-time. A neural network can be trained to solve multiple tasks simultaneously using multi-task learning. This can save computation at inference time as only a single network needs to be evaluated. Unfortunately, this often leads to inferior overall performance as task objectives can compete, which consequently poses the question: which tasks should and should not be learned together in one network when employing multi-task learning? We study task cooperation and competition in several different learning settings and propose a framework for assigning tasks to a few neural networks such that cooperating tasks are computed by the same neural network, while competing tasks are computed by different networks. Our framework offers a time-accuracy trade-off and can produce better accuracy using less inference time than not only a single large multi-task neural network but also many single-task networks.

Neural networks have a remarkable capacity for contextual processing—using recent or nearby inputs to modify processing of current input. For example, in natural language, contextual processing is necessary to correctly interpret negation (e.g. phrases such as "not bad"). However, our ability to understand how networks process context is limited. Here, we propose general methods for reverse engineering recurrent neural networks (RNNs) to identify and elucidate contextual processing. We apply these methods to understand RNNs trained on sentiment classification. This analysis reveals inputs that induce contextual effects, quantifies the strength and timescale of these effects, and identifies sets of these inputs with similar properties. Additionally, we analyze contextual effects related to differential processing of the beginning and end of documents. Using the insights learned from the RNNs we improve baseline Bag-of-Words models with simple extensions that incorporate contextual modification, recovering greater than 90% of the RNN's performance increase over the baseline. This work yields a new understanding of how RNNs process contextual information, and provides tools that should provide similar insight more broadly.

Learning from unordered sets is a fundamental learning setup, which is attracting increasing attention. Research in this area has focused on the case where elements of the set are represented by feature vectors, and far less emphasis has been given to the common case where set elements themselves adhere to certain symmetries. That case is relevant to numerous applications, from deblurring image bursts to multi-view 3D shape recognition and reconstruction. In this paper, we present a principled approach to learning sets of general symmetric elements. We first characterize the space of linear layers that are equivariant both to element reordering and to the inherent symmetries of elements, like translation in the case of images. We further show that networks that are composed of these layers, called Deep Sets for Symmetric elements layers (DSS), are universal approximators of both invariant and equivariant functions. DSS layers are also straightforward to implement. Finally, we show that they improve over existing set-learning architectures in a series of experiments with images, graphs, and point-clouds.

Many AI problems, in robotics and other domains, are goal-directed, essentially seeking a trajectory leading to some goal state. Reinforcement learning (RL), building on Bellman's optimality equation, naturally optimizes for a single goal, yet can be made goal-directed by augmenting the state with the goal. Instead, we propose a new RL framework, derived from a dynamic programming equation for the all pairs shortest path (APSP) problem, which naturally solves goal-directed queries. We show that this approach has computational benefits for both standard and approximate dynamic programming. Interestingly, our formulation prescribes a novel protocol for computing a trajectory: instead of predicting the next state given its predecessor, as in standard RL, a goal-conditioned trajectory is constructed by first predicting an intermediate state between start and goal, partitioning the trajectory into two. Then, recursively, predicting intermediate points on each sub-segment, until a complete trajectory is obtained. We call this trajectory structure a sub-goal tree. Building on it, we additionally extend the policy gradient methodology to recursively predict sub-goals, resulting in novel goal-based algorithms. Finally, we apply our method to neural motion planning, where we demonstrate significant improvements compared to standard RL on navigating a 7-DoF robot arm between obstacles.

Recently there have been several attempts to extend Nesterov's accelerated algorithm to smooth stochastic and variance-reduced optimization. In this paper, we show that there is a simpler approach to acceleration: applying optimistic online learning algorithms and querying the gradient oracle at the online average of the intermediate optimization iterates. In particular, we tighten a recent result of Cutkosky (2019) to demonstrate theoretically that online iterate averaging results in a reduced optimization gap, independently of the algorithm involved. We show that carefully combining this technique with existing generic optimistic online learning algorithms yields the optimal accelerated rates for optimizing strongly-convex and non-strongly-convex, possibly composite objectives, with deterministic as well as stochastic first-order oracles. We further extend this idea to variance-reduced optimization. Finally, we also provide ``universal'' algorithms that achieve the optimal rate for smooth and non-smooth composite objectives simultaneously without further tuning, generalizing the results of Kavis et al. (2019) and solving a number of their open problems.

In self-supervised visual representation learning, a feature extractor is trained on a "pretext task" for which labels can be generated cheaply, without human annotation. A central challenge in this approach is that the feature extractor quickly learns to exploit low-level visual features such as color aberrations or watermarks and then fails to learn useful semantic representations. Much work has gone into identifying such "shortcut" features and hand-designing schemes to reduce their effect. Here, we propose a general framework for mitigating the effect shortcut features. Our key assumption is that those features which are the first to be exploited for solving the pretext task may also be the most vulnerable to an adversary trained to make the task harder. We show that this assumption holds across common pretext tasks and datasets by training a "lens" network to make small image changes that maximally reduce performance in the pretext task. Representations learned with the modified images outperform those learned without in all tested cases. Additionally, the modifications made by the lens reveal how the choice of pretext task and dataset affects the features learned by self-supervision.

Learning a good representation is an essential component for deep reinforcement learning (RL). Representation learning is especially important in multitask and partially observable settings where building a representation of the unknown environment is crucial to solve the tasks. Here we introduce Predictions of Bootstrapped Latents (PBL), a simple and flexible self-supervised representation learning algorithm for multitask deep RL. PBL builds on multistep predictive representations of future observations, and focuses on capturing structured information about environment dynamics. Specifically, PBL trains its representation by predicting latent embeddings of future observations. These latent embeddings are themselves trained to be predictive of the aforementioned representations. These predictions form a bootstrapping effect, allowing the agent to learn more about the key aspects of the environment dynamics. In addition, by defining prediction tasks completely in latent space, PBL provides the flexibility of using multimodal observations involving pixel images, language instructions, rewards and more. We show in our experiments that PBL delivers across-the-board improved performance over state of the art deep RL agents in the DMLab-30 multitask setting.

Initialization, normalization, and skip connections are believed to be three indispensable techniques for training very deep convolutional neural networks and obtaining state-of-the-art performance. This paper shows that deep vanilla ConvNets without normalization nor skip connections can also be trained to achieve surprisingly good performance on standard image recognition benchmarks. This is achieved by enforcing the convolution kernels to be near isometric during initialization and training, as well as by using a variant of ReLU that is shifted towards being isometric. Further experiments show that if combined with skip connections, such near isometric networks can achieve performances on par with (for ImageNet) and better than (for COCO) the standard ResNet, even without normalization at all. Our code is available at https://github.com/HaozhiQi/ISONet.

Likelihood-free (a.k.a. simulation-based) inference problems are inverse problems with expensive, or intractable, forward models. ODE inverse problems are commonly treated as likelihood-free, as their forward map has to be numerically approximated by an ODE solver. This, however, is not a fundamental constraint but just a lack of functionality in classic ODE solvers, which do not return a likelihood but a point estimate. To address this shortcoming, we employ Gaussian ODE filtering (a probabilistic numerical method for ODEs) to construct a local Gaussian approximation to the likelihood. This approximation yields tractable estimators for the gradient and Hessian of the (log-)likelihood. Insertion of these estimators into existing gradient-based optimization and sampling methods engenders new solvers for ODE inverse problems. We demonstrate that these methods outperform standard likelihood-free approaches on three benchmark-systems.

In order to compute fast approximations to the singular value decompositions (SVD) of very large matrices, randomized sketching algorithms have become a leading approach. However, a key practical difficulty of sketching an SVD is that the user does not know how far the sketched singular vectors/values are from the exact ones. Indeed, the user may be forced to rely on analytical worst-case error bounds, which may not account for the unique structure of a given problem. As a result, the lack of tools for error estimation often leads to much more computation than is really necessary. To overcome these challenges, this paper develops a fully data-driven bootstrap method that numerically estimates the actual error of sketched singular vectors/values. Furthermore, the method is computationally inexpensive, because it operates only on sketched objects, and hence it requires no extra passes over the full matrix being factored.

Many clustering algorithms lead to cluster assignments that are hard to explain, partially because they depend on all the features of the data in a complicated way. To improve interpretability, we consider using a small decision tree to partition a data set into clusters, so that clusters can be characterized in a straightforward manner. We study this problem from a theoretical viewpoint, measuring cluster quality by the k-means and k-medians objectives. In terms of negative results, we show that popular top-down decision tree algorithms may lead to clusterings with arbitrarily large cost, and any clustering based on a tree with k leaves must incur an Omega(log k) approximation factor compared to the optimal clustering. On the positive side, for two means/medians, we show that a single threshold cut can achieve a constant factor approximation, and we give nearly-matching lower bounds; for general k > 2, we design an efficient algorithm that leads to an O(k) approximation to the optimal k-medians and an O(k^2) approximation to the optimal k-means. Prior to our work, no algorithms were known with provable guarantees independent of dimension and input size.

We consider learning a multi-class classification model in the federated setting, where each user has access to the positive data associated with only a single class. As a result, during each federated learning round, the users need to locally update the classifier without having access to the features and the model parameters for the negative classes. Thus, naively employing conventional decentralized learning such as distributed SGD or Federated Averaging may lead to trivial or extremely poor classifiers. In particular, for embedding based classifiers, all the class embeddings might collapse to a single point. To address this problem, we propose a generic framework for training with only positive labels, namely Federated Averaging with Spreadout (FedAwS), where the server imposes a geometric regularizer after each round to encourage classes to be spreadout in the embedding space. We show, both theoretically and empirically, that FedAwS can almost match the performance of conventional learning where users have access to negative labels. We further extend the proposed method to settings with large output spaces.

Space-filling designs such as Low Discrepancy Sequence (LDS), Latin Hypercube Sampling (LHS) and Jittered Sampling (JS) were proposed for fully parallel hyperparameter search, and were shown to be more effective than random and grid search. We prove that LHS and JS outperform random search only by a constant factor. Consequently, we introduce a new sampling approach based on the reshaping of the search distribution, and we show both theoretically and numerically that it leads to significant gains over random search. Two methods are proposed for the reshaping: Recentering (when the distribution of the optimum is known), and Cauchy transformation (when the distribution of the optimum is unknown). The proposed methods are first validated on artificial experiments and simple real-world tests on clustering and Salmon mappings. Then we demonstrate that they drive performance improvement in a wide range of expensive artificial intelligence tasks, namely attend/infer/repeat, video next frame segmentation forecasting and progressive generative adversarial networks.

We present a description of the function space and the smoothness class associated with a convolutional network using the machinery of reproducing kernel Hilbert spaces. We show that the mapping associated with a convolutional network expands into a sum involving elementary functions akin to spherical harmonics. The functional decomposition can be related to functional ANOVA decompositions in nonparametric statistics. Building off this functional characterization, we obtain statistical bounds which highlight an interesting trade-off between the approximation error and the estimation error.

Optimally solving decentralized partially observable Markov decision processes under either full or no information sharing received significant attention in recent years. However, little is known about how partial information sharing affects existing theory and algorithms. This paper addresses this question for a team of two agents, with one-sided information sharing---\ie both agents have imperfect information about the state of the world, but only one has access to what the other sees and does. From the perspective of a central planner, we show that the original problem can be reformulated into an equivalent information-state Markov decision process and solved as such. Besides, we prove that the optimal value function exhibits a specific form of uniform continuity. We also present a heuristic search algorithm utilizing this property and providing the first results for this family of problems.

In model-based reinforcement learning, planning with an imperfect model of the environment has the potential to harm learning progress. But even when a model is imperfect, it may still contain information that is useful for planning. In this paper, we investigate the idea of using an imperfect model selectively. The agent should plan in parts of the state space where the model would be helpful but refrain from using the model where it would be harmful. An effective selective planning mechanism requires estimating predictive uncertainty, which arises out of aleatoric uncertainty, parameter uncertainty, and model inadequacy, among other sources. Prior work has focused on parameter uncertainty for selective planning. In this work, we emphasize the importance of model inadequacy. We show that heteroscedastic regression can signal predictive uncertainty arising from model inadequacy that is complementary to that which is detected by methods designed for parameter uncertainty, indicating that considering both parameter uncertainty and model inadequacy may be a more promising direction for effective selective planning than either in isolation.

Annotating datasets is one of the main costs in nowadays supervised learning. The goal of weak supervision is to enable models to learn using only forms of labelling which are cheaper to collect, as partial labelling. This is a type of incomplete annotation where, for each datapoint, supervision is cast as a set of labels containing the real one. The problem of supervised learning with partial labelling has been studied for specific instances such as classification, multi-label, ranking or segmentation, but a general framework is still missing. This paper provides a unified framework based on structured prediction and on the concept of {\em infimum loss} to deal with partial labelling over a wide family of learning problems and loss functions. The framework leads naturally to explicit algorithms that can be easily implemented and for which proved statistical consistency and learning rates. Experiments confirm the superiority of the proposed approach over commonly used baselines.

Machine learning and deep learning in particular has been recently used to successfully address many tasks in the domain of code including -- finding and fixing bugs, code completion, decompilation, malware detection, type inference and many others. However, the issue of adversarial robustness of models for code has gone largely unnoticed. In this work, we explore this issue by: (i) instantiating adversarial attacks for code (a domain with discrete and highly structured inputs), (ii) showing that, similar to other domains, neural models for code are vulnerable to adversarial attacks, and (iii) developing a set of novel techniques that enable training robust and accurate models of code.

Attribution methods aim to explain a neural network's prediction by highlighting the most relevant image areas. A popular approach is to backpropagate (BP) a custom relevance score using modified rules, rather than the gradient. We analyze an extensive set of modified BP methods: Deep Taylor Decomposition, Layer-wise Relevance Propagation (LRP), Excitation BP, PatternAttribution, DeepLIFT, Deconv, RectGrad, and Guided BP. We find empirically that the explanations of all mentioned methods, except for DeepLIFT, are independent of the parameters of later layers. We provide theoretical insights for this surprising behavior and also analyze why DeepLIFT does not suffer from this limitation. Empirically, we measure how information of later layers is ignored by using our new metric, cosine similarity convergence (CSC). The paper provides a framework to assess the faithfulness of new and existing modified BP methods theoretically and empirically.

Acquiring abilities in the absence of a task-oriented reward function is at the frontier of reinforcement learning research. This problem has been studied through the lens of empowerment, which draws a connection between option discovery and information theory. Information-theoretic skill discovery methods have garnered much interest from the community, but little research has been conducted in understanding their limitations. Through theoretical analysis and empirical evidence, we show that existing algorithms suffer from a common limitation -- they discover options that provide a poor coverage of the state space. In light of this, we propose Explore, Discover and Learn (EDL), an alternative approach to information-theoretic skill discovery. Crucially, EDL optimizes the same information-theoretic objective derived from the empowerment literature, but addresses the optimization problem using different machinery. We perform an extensive evaluation of skill discovery methods on controlled environments and show that EDL offers significant advantages, such as overcoming the coverage problem, reducing the dependence of learned skills on the initial state, and allowing the user to define a prior over which behaviors should be learned.

We propose a class of kernel-based two-sample tests, which aim to determine whether two sets of samples are drawn from the same distribution. Our tests are constructed from kernels parameterized by deep neural nets, trained to maximize test power. These tests adapt to variations in distribution smoothness and shape over space, and are especially suited to high dimensions and complex data. By contrast, the simpler kernels used in prior kernel testing work are spatially homogeneous, and adaptive only in lengthscale. We explain how this scheme includes popular classifier-based two-sample tests as a special case, but improves on them in general. We provide the first proof of consistency for the proposed adaptation method, which applies both to kernels on deep features and to simpler radial basis kernels or multiple kernel learning. In experiments, we establish the superior performance of our deep kernels in hypothesis testing on benchmark and real-world data. The code of our deep-kernel-based two-sample tests is available at github.com/fengliu90/DK-for-TST.

Machine-learned predictors, although achieving very good results for inputs resembling training data, cannot possibly provide perfect predictions in all situations. Still, decision-making systems that are based on such predictors need not only to benefit from good predictions but also to achieve a decent performance when the predictions are inadequate. In this paper, we propose a prediction setup for arbitrary metrical task systems (MTS) (e.g., caching, k-server and convex body chasing) and online matching on the line. We utilize results from the theory of online algorithms to show how to make the setup robust. Specifically for caching, we present an algorithm whose performance, as a function of the prediction error, is exponentially better than what is achievable for general MTS. Finally, we present an empirical evaluation of our methods on real world datasets, which suggests practicality.

With continual miniaturization ever more applications of deep learning can be found in embedded systems, where it is common to encounter data with natural representation in the complex domain. To this end we extend Sparse Variational Dropout to complex-valued neural networks and verify the proposed Bayesian technique by conducting a large numerical study of the performance-compression trade-off of C-valued networks on two tasks: image recognition on MNIST-like and CIFAR10 datasets and music transcription on MusicNet. We replicate the state-of-the-art result by Trabelsi et al. (2018) on MusicNet with a complex-valued network compressed by 50-100x at a small performance penalty.

Typical architectures of Generative Adversarial Networks make use of a unimodal latent/input distribution transformed by a continuous generator. Consequently, the modeled distribution always has connected support which is cumbersome when learning a disconnected set of manifolds. We formalize this problem by establishing a "no free lunch" theorem for the disconnected manifold learning stating an upper-bound on the precision of the targeted distribution. This is done by building on the necessary existence of a low-quality region where the generator continuously samples data between two disconnected modes. Finally, we derive a rejection sampling method based on the norm of generator’s Jacobian and show its efficiency on several generators including BigGAN.

We present a framework for autonomously learning a portable representation that describes a collection of low-level continuous environments. We show that these abstract representations can be learned in a task-independent egocentric space specific to the agent that, when grounded with problem-specific information, are provably sufficient for planning. We demonstrate transfer in two different domains, where an agent learns a portable, task-independent symbolic vocabulary, as well as operators expressed in that vocabulary, and then learns to instantiate those operators on a per-task basis. This reduces the number of samples required to learn a representation of a new task.

Generating training examples for supervised tasks is a long sought after goal in AI. We study the problem of heart signal electrocardiogram (ECG) synthesis for improved heartbeat classification. ECG synthesis is challenging: the generation of training examples for such biological-physiological systems is not straightforward, due to their dynamic nature in which the various parts of the system interact in complex ways. However, an understanding of these dynamics has been developed for years in the form of mathematical process simulators. We study how to incorporate this knowledge into the generative process by leveraging a biological simulator for the task of ECG classification. Specifically, we use a system of ordinary differential equations representing heart dynamics, and incorporate this ODE system into the optimization process of a generative adversarial network to create biologically plausible ECG training examples. We perform empirical evaluation and show that heart simulation knowledge during the generation process improves ECG classification.

We propose a direct-to-word sequence model which uses a word network to learn word embeddings from letters. The word network can be integrated seamlessly with arbitrary sequence models including Connectionist Temporal Classification and encoder-decoder models with attention. We show our direct-to-word model can achieve word error rate gains over sub-word level models for speech recognition. We also show that our direct-to-word approach retains the ability to predict words not seen at training time without any retraining. Finally, we demonstrate that a word-level model can use a larger stride than a sub-word level model while maintaining accuracy. This makes the model more efficient both for training and inference.

Knowledge graphs are incomplete by nature, with only a limited number of observed facts from world knowledge being represented as structured relations between entities. To partly address this issue, an important task in statistical relational learning is that of link prediction or knowledge graph completion. Both linear and non-linear models have been proposed to solve the problem of knowledge graph completion, with the former being parameter efficient and interpretable. Bilinear models, while expressive, are prone to overfitting and lead to quadratic growth of parameters in number of relations. Simpler models have become more standard, with certain constraints on bilinear maps as relation parameters. In this work, we propose a factorized bilinear pooling model, commonly used in multi-modal learning, for better fusion of entities and relations, leading to an efficient and constraint-free model. We prove that our model is fully expressive, providing bounds on embedding dimensionality and factorization rank. Our model naturally generalizes TuckER (Balazevic et al., 2019), which has been shown to generalize other models, as efficient low-rank approximation without substantially compromising performance. Due to low-rank approximation, the model complexity can be controlled by the factorization rank, avoiding the possible cubic growth of TuckER. Empirically, we evaluate on real-world datasets, …

Gaussian processes (GP) are one of the most successful frameworks to model uncertainty. However, GP optimization (e.g., GP-UCB) suffers from major scalability issues. Experimental time grows linearly with the number of evaluations, unless candidates are selected in batches (e.g., using GP-BUCB) and evaluated in parallel. Furthermore, computational cost is often prohibitive since algorithms such as GP-BUCB require a time at least quadratic in the number of dimensions and iterations to select each batch.

In this paper, we introduce BBKB (Batch Budgeted Kernel Bandits), the first no-regret GP optimization algorithm that provably runs in near-linear time and selects candidates in batches. This is obtained with a new guarantee for the tracking of the posterior variances that allows BBKB to choose increasingly larger batches, improving over GP-BUCB. Moreover, we show that the same bound can be used to adaptively delay costly updates to the sparse GP approximation used by BBKB, achieving a near-constant per-step amortized cost. These findings are then confirmed in several experiments, where BBKB is much faster than state-of-the-art methods.

Regression forests, based on ensemble approaches such as bagging or boosting, have long been recognized as the leading off-the-shelf method for regression. However, forests rely on a greedy top-down procedure such as CART to learn each tree. We extend a recent algorithm for learning classification trees, Tree Alternating Optimization (TAO), to the regression case, and use it with bagging to construct regression forests of oblique trees, having hyperplane splits at the decision nodes. In a wide range of datasets, we show that the resulting forests exceed the accuracy of state-of-the-art algorithms such as random forests, AdaBoost or gradient boosting, often considerably, while yielding forests that have usually fewer and shallower trees and hence fewer parameters and faster inference overall. This result has an immense practical impact and advocates for the power of optimization in ensemble learning.

The Optimal transport (OT) problem and its associated Wasserstein distance have recently become a topic of great interest in the machine learning community. However, the underlying optimization problem is known to have two major restrictions: (i) it largely depends on the choice of the cost function and (ii) its sample complexity scales exponentially with the dimension. In this paper, we propose a general formulation of a minimax OT problem that can tackle these restrictions by jointly optimizing the cost matrix and the transport plan, allowing us to define a robust distance between distributions. We propose to use a cutting-set method to solve this general problem and show its links and advantages compared to other existing minimax OT approaches. Additionally, we use this method to define a notion of stability allowing us to select the most robust cost matrix. Finally, we provide an experimental study highlighting the efficiency of our approach.

Implicit stochastic models, where the data-generation distribution is intractable but sampling is possible, are ubiquitous in the natural sciences. The models typically have free parameters that need to be inferred from data collected in scientific experiments. A fundamental question is how to design the experiments so that the collected data are most useful. The field of Bayesian experimental design advocates that, ideally, we should choose designs that maximise the mutual information (MI) between the data and the parameters. For implicit models, however, this approach is severely hampered by the high computational cost of computing posteriors and maximising MI, in particular when we have more than a handful of design variables to optimise. In this paper, we propose a new approach to Bayesian experimental design for implicit models that leverages recent advances in neural MI estimation to deal with these issues. We show that training a neural network to maximise a lower bound on MI allows us to jointly determine the optimal design and the posterior. Simulation studies illustrate that this gracefully extends Bayesian experimental design for implicit models to higher design dimensions.

We consider distributions arising from a mixture of causal models, where each model is represented by a directed acyclic graph (DAG). We provide a graphical representation of such mixture distributions and prove that this representation encodes the conditional independence relations of the mixture distribution. We then consider the problem of structure learning based on samples from such distributions. Since the mixing variable is latent, we consider causal structure discovery algorithms such as FCI that can deal with latent variables. We show that such algorithms recover a “union” of the component DAGs and can identify variables whose conditional distribution across the component DAGs vary. We demonstrate our results on synthetic and real data showing that the inferred graph identifies nodes that vary between the different mixture components. As an immediate application, we demonstrate how retrieval of this causal information can be used to cluster samples according to each mixture component.

Marrying topic models and language models exposes language understanding to a broader source of document-level context beyond sentences via topics. While introducing topical semantics in language models, existing approaches incorporate latent document topic proportions and ignore topical discourse in sentences of the document. This work extends the line of research by additionally introducing an explainable topic representation in language understanding, obtained from a set of key terms correspondingly for each latent topic of the proportion. Moreover, we retain sentence-topic association along with document-topic association by modeling topical discourse for every sentence in the document. We present a novel neural composite language modeling (NCLM) framework that exploits both the latent and explainable topics along with topical discourse at sentence-level in a joint learning framework of topic and language models. Experiments over a range of tasks such as language modeling, word sense disambiguation, document classification, retrieval and text generation demonstrate ability of the proposed model in improving language understanding.

Recent advances in deep learning theory have evoked the study of generalizability across different local minima of deep neural networks (DNNs). While current work focused on either discovering properties of good local minima or developing regularization techniques to induce good local minima, no approach exists that can tackle both problems. We achieve these two goals successfully in a unified manner. Specifically, based on the observed Fisher information we propose a metric both strongly indicative of generalizability of local minima and effectively applied as a practical regularizer. We provide theoretical analysis including a generalization bound and empirically demonstrate the success of our approach in both capturing and improving the generalizability of DNNs. Experiments are performed on CIFAR-10, CIFAR-100 and ImageNet for various network architectures.

Interest has been rising lately towards methods representing data in non-Euclidean spaces, e.g. hyperbolic or spherical that provide specific inductive biases useful for certain real-world data properties, e.g. scale-free, hierarchical or cyclical. However, the popular graph neural networks are currently limited in modeling data only via Euclidean geometry and associated vector space operations. Here, we bridge this gap by proposing mathematically grounded generalizations of graph convolutional networks (GCN) to (products of) constant curvature spaces. We do this by i) introducing a unified formalism permitting a differentiable interpolation between all geometries of constant curvature irrespective of their sign, ii) leveraging gyro-barycentric coordinates that generalize the classic Euclidean concept of the center of mass. Our class of models smoothly recover their Euclidean counterparts when the curvature goes to zero from either side. Empirically, we outperform Euclidean GCNs in the tasks of node classification and distortion minimization for symbolic data exhibiting non-Euclidean behavior, according to their discrete curvature.

We tackle the problem disentangling the latent space of an autoencoder in order to separate labelled attribute information from other characteristic information. This then allows us to change selected attributes while preserving other information. Our method, matrix subspace projection, is much simpler than previous approaches to latent space factorisation, for example not requiring multiple discriminators or a careful weighting among their loss functions. Furthermore our new model can be applied to autoencoders as a plugin, and works across diverse domains such as images or text. We demonstrate the utility of our method for attribute manipulation in autoencoders trained across varied domains, using both human evaluation and automated methods. The quality of generation of our new model (e.g. reconstruction, conditional generation) is highly competitive to a number of strong baselines.

We investigate meta-learning procedures in the setting of stochastic linear bandits tasks. The goal is to select a learning algorithm which works well on average over a class of bandits tasks, that are sampled from a task-distribution. Inspired by recent work on learning-to-learn linear regression, we consider a class of bandit algorithms that implement a regularized version of the well-known OFUL algorithm, where the regularization is a square euclidean distance to a bias vector. We first study the benefit of the biased OFUL algorithm in terms of regret minimization. We then propose two strategies to estimate the bias within the learning-to-learn setting. We show both theoretically and experimentally, that when the number of tasks grows and the variance of the task-distribution is small, our strategies have a significant advantage over learning the tasks in isolation.

Support Vector Machines (SVMs) are among the most fundamental tools for binary classification.

In its simplest formulation, an SVM produces a hyperplane separating two classes of data using the largest possible margin to the data. The focus on maximizing the margin has been well motivated through numerous generalization bounds.

In this paper, we revisit and improve the classic generalization bounds in terms of margins. Furthermore, we complement our new generalization bound by a nearly matching lower bound, thus almost settling the generalization performance of SVMs in terms of margins.

We provide an exact analysis of a class of randomized algorithms for solving overdetermined least-squares problems. We consider first-order methods, where the gradients are pre-conditioned by an approximation of the Hessian, based on a subspace embedding of the data matrix. This class of algorithms encompasses several randomized methods among the fastest solvers for least-squares problems. We focus on two classical embeddings, namely, Gaussian projections and subsampled randomized Hadamard transforms (SRHT). Our key technical innovation is the derivation of the limiting spectral density of SRHT embeddings. Leveraging this novel result, we derive the family of normalized orthogonal polynomials of the SRHT density and we find the optimal pre-conditioned first-order method along with its rate of convergence. Our analysis of Gaussian embeddings proceeds similarly, and leverages classical random matrix theory results. In particular, we show that for a given sketch size, SRHT embeddings exhibits a faster rate of convergence than Gaussian embeddings. Then, we propose a new algorithm by optimizing the computational complexity over the choice of the sketching dimension. To our knowledge, our resulting algorithm yields the best known complexity for solving least-squares problems with no condition number dependence.

Supervised learning requires the specification of a loss function to minimise. While the theory of admissible losses from both a computational and statistical perspective is well-developed, these offer a panoply of different choices. In practice, this choice is typically made in an \emph{ad hoc} manner. In hopes of making this procedure more principled, the problem of \emph{learning the loss function} for a downstream task (e.g., classification) has garnered recent interest. However, works in this area have been generally empirical in nature. In this paper, we revisit the {\sc SLIsotron} algorithm of Kakade et al. (2011) through a novel lens, derive a generalisation based on Bregman divergences, and show how it provides a principled procedure for learning the loss. In detail, we cast {\sc SLIsotron} as learning a loss from a family of composite square losses. By interpreting this through the lens of \emph{proper losses}, we derive a generalisation of {\sc SLIsotron} based on Bregman divergences. The resulting {\sc BregmanTron} algorithm jointly learns the loss along with the classifier. It comes equipped with a simple guarantee of convergence for the loss it learns, and its set of possible outputs comes with a guarantee of agnostic approximability of Bayes rule. Experiments indicate …

We propose a modeling framework for event data and aim to answer questions such as {\it when} and {\it why} the next event would happen. Our proposed model excels in small data regime with the ability to incorporate domain knowledge in terms of logic rules. We model the dynamics of the event starts and ends via intensity function with the structures informed by a set of first-order temporal logic rules. Using the softened representation of temporal relations, and a weighted combination of logic rules, our probabilistic model can deal with uncertainty in events. Furthermore, many well-known point processes (e.g., Hawkes process, self-correcting point process) can be interpreted as special cases of our model given simple temporal logic rules. Our model, therefore, riches the family of point processes. We derive a maximum likelihood estimation procedure for our model and show that it can lead to accurate predictions when data are sparse and domain knowledge is critical.

The overestimation bias is one of the major impediments to accurate off-policy learning. This paper investigates a novel way to alleviate the overestimation bias in a continuous control setting. Our method---Truncated Quantile Critics, TQC,---blends three ideas: distributional representation of a critic, truncation of critics prediction, and ensembling of multiple critics. Distributional representation and truncation allow for arbitrary granular overestimation control, while ensembling provides additional score improvements. TQC outperforms the current state of the art on all environments from the continuous control benchmark suite, demonstrating 25% improvement on the most challenging Humanoid environment.

There is growing interest in studying the languages that emerge when neural agents are jointly trained to solve tasks requiring communication through a discrete channel. We investigate here the information-theoretic complexity of such languages, focusing on the basic two-agent, one-exchange setup. We find that, under common training procedures, the emergent languages are subject to an entropy minimization pressure that has also been detected in human language, whereby the mutual information between the communicating agent's inputs and the messages is minimized, within the range afforded by the need for successful communication. That is, emergent languages are (nearly) as simple as the task they are developed for allow them to be. This pressure is amplified as we increase communication channel discreteness. Further, we observe that stronger discrete-channel-driven entropy minimization leads to representations with increased robustness to overfitting and adversarial attacks. We conclude by discussing the implications of our findings for the study of natural and artificial communication systems.

We propose a novel amortized variational inference scheme for an empirical Bayes meta-learning model, where model parameters are treated as latent variables. We learn the prior distribution over model parameters conditioned on limited training data using a variational autoencoder approach. Our framework proposes sharing the same amortized inference network between the conditional prior and variational posterior distributions over the model parameters. While the posterior leverages both the labeled support and query data, the conditional prior is based only on the labeled support data. We show that in earlier work, relying on Monte-Carlo approximation, the conditional prior collapses to a Dirac delta function. In contrast, our variational approach prevents this collapse and preserves uncertainty over the model parameters. We evaluate our approach on the miniImageNet and FC100 datasets, and present results demonstrating its advantages over previous work.

Normalizing flows are a powerful tool for building expressive distributions in high dimensions. So far, most of the literature has concentrated on learning flows on Euclidean spaces. Some problems however, such as those involving angles, are defined on spaces with more complex geometries, such as tori or spheres. In this paper, we propose and compare expressive and numerically stable flows on such spaces. Our flows are built recursively on the dimension of the space, starting from flows on circles, closed intervals or spheres.

The trace regression model, a direct extension of the well-studied linear regression model, allows one to map matrices to real-valued outputs. We here introduce an even more general model, namely the partial-trace regression model, a family of linear mappings from matrix-valued inputs to matrix-valued outputs; this model subsumes the trace regression model and thus the linear regression model. Borrowing tools from quantum information theory, where partial trace operators have been extensively studied, we propose a framework for learning partial trace regression models from data by taking advantage of the so-called low-rank Kraus representation of completely positive maps. We show the relevance of our framework with synthetic and real-world experiments conducted for both i) matrix-to-matrix regression and ii) positive semidefinite matrix completion, two tasks which can be formulated as partial trace regression problems.

we consider the problem of sequential change-point detection where 
both the change-points and the distributions before and after the change are assumed to be unknown. For this problem of primary importance in statistical and sequential learning theory,  we derive a variant of the Bayesian Online Change Point Detector proposed by \cite{fearnhead2007line}
which is easier to analyze than the original version while keeping its powerful message-passing algorithm. 
We provide a non-asymptotic analysis of the false-alarm rate and the detection delay that matches the existing lower-bound. We further provide the first explicit high-probability control of the detection delay for such approach. Experiments on synthetic and real-world data show that this proposal outperforms the state-of-art change-point detection strategy, namely the Improved Generalized Likelihood Ratio (Improved GLR) while compares favorably with the original Bayesian Online Change Point Detection strategy.

We propose a novel Stochastic Frank-Wolfe (a. k. a. conditional gradient) algorithm for constrained smooth finite-sum minimization with a generalized linear prediction/structure. This class of problems includes empirical risk minimization with sparse, low-rank, or other structured constraints. The proposed method is simple to implement, does not require step-size tuning, and has a constant per-iteration cost that is independent of the dataset size. Furthermore, as a byproduct of the method we obtain a stochastic estimator of the Frank-Wolfe gap that can be used as a stopping criterion. Depending on the setting, the proposed method matches or improves on the best computational guarantees for Stochastic Frank-Wolfe algorithms. Benchmarks on several datasets highlight different regimes in which the proposed method exhibits a faster empirical convergence than related methods. Finally, we provide an implementation of all considered methods in an open-source package.

Modern meta-learning approaches for image classification rely on increasingly deep networks to achieve state-of-the-art performance, making batch normalization an essential component of meta-learning pipelines. However, the hierarchical nature of the meta-learning setting presents several challenges that can render conventional batch normalization ineffective, giving rise to the need to rethink normalization in this setting. We evaluate a range of approaches to batch normalization for meta-learning scenarios, and develop a novel approach that we call TaskNorm. Experiments on fourteen datasets demonstrate that the choice of batch normalization has a dramatic effect on both classification accuracy and training time for both gradient based- and gradient-free meta-learning approaches. Importantly, TaskNorm is found to consistently improve performance. Finally, we provide a set of best practices for normalization that will allow fair comparison of meta-learning algorithms.

Many real-world problems require trading off multiple competing objectives. However, these objectives are often in different units and/or scales, which can make it challenging for practitioners to express numerical preferences over objectives in their native units. In this paper we propose a novel algorithm for multi-objective reinforcement learning that enables setting desired preferences for objectives in a scale-invariant way. We propose to learn an action distribution for each objective, and we use supervised learning to fit a parametric policy to a combination of these distributions. We demonstrate the effectiveness of our approach on challenging high-dimensional real and simulated robotics tasks, and show that setting different preferences in our framework allows us to trace out the space of nondominated solutions.

Recently non-convex optimization approaches for solving machine learning problems have gained significant attention. In this paper we explore non-convex boosting in classification by means of integer programming and demonstrate real-world practicability of the approach while circumvent- ing shortcomings of convex boosting approaches. We report results that are comparable to or better than the current state-of-the-art.

This work focuses on the estimation of multiple change-points in a time-varying Ising model that evolves piece-wise constantly. The aim is to identify both the moments at which significant changes occur in the Ising model, as well as the underlying graph structures. For this purpose, we propose to estimate the neighborhood of each node by maximizing a penalized version of its conditional log-likelihood. The objective of the penalization is twofold: it imposes sparsity in the learned graphs and, thanks to a fused-type penalty, it also enforces them to evolve piece-wise constantly. Using few assumptions, we provide two change-points consistency theorems. Those are the first in the context of unknown number of change-points detection in time-varying Ising model. Finally, experimental results on several synthetic datasets and a real-world dataset demonstrate the performance of our method.

Here we present a machine learning framework and model implementation that can learn to simulate a wide variety of challenging physical domains, involving fluids, rigid solids, and deformable materials interacting with one another. Our framework---which we term "Graph Network-based Simulators" (GNS)---represents the state of a physical system with particles, expressed as nodes in a graph, and computes dynamics via learned message-passing. Our results show that our model can generalize from single-timestep predictions with thousands of particles during training, to different initial conditions, thousands of timesteps, and at least an order of magnitude more particles at test time. Our model was robust to hyperparameter choices across various evaluation metrics: the main determinants of long-term performance were the number of message-passing steps, and mitigating the accumulation of error by corrupting the training data with noise. Our GNS framework advances the state-of-the-art in learned physical simulation, and holds promise for solving a wide range of complex forward and inverse problems.

Likelihood-free methods perform parameter inference in stochastic simulator models where evaluating the likelihood is intractable but sampling synthetic data is possible. One class of methods for this likelihood-free problem uses a classifier to distinguish between pairs of parameter-observation samples generated using the simulator and pairs sampled from some reference distribution, which implicitly learns a density ratio proportional to the likelihood. Another popular class of methods fits a conditional distribution to the parameter posterior directly, and a particular recent variant allows for the use of flexible neural density estimators for this task. In this work, we show that both of these approaches can be unified under a general contrastive learning scheme, and clarify how they should be run and compared.

Model-Based Reinforcement Learning (MBRL) offers a promising direction for sample efficient learning, often achieving state of the art results for continuous control tasks. However many existing MBRL methods rely on combining greedy policies with exploration heuristics, and even those which utilize principled exploration bonuses construct dual objectives in an ad hoc fashion. In this paper we introduce Ready Policy One (RP1), a framework that views MBRL as an active learning problem, where we aim to improve the world model in the fewest samples possible. RP1 achieves this by utilizing a hybrid objective function, which crucially adapts during optimization, allowing the algorithm to trade off reward v.s. exploration at different stages of learning. In addition, we introduce a principled mechanism to terminate sample collection once we have a rich enough trajectory batch to improve the model. We rigorously evaluate our method on a variety of continuous control tasks, and demonstrate statistically significant gains over existing approaches.

Intelligent agents should be able to learn useful representations by observing changes in their environment. We model such observations as pairs of non-i.i.d. images sharing at least one of the underlying factors of variation. First, we theoretically show that only knowing how many factors have changed, but not which ones, is sufficient to learn disentangled representations. Second, we provide practical algorithms that learn disentangled representations from pairs of images without requiring annotation of groups, individual factors, or the number of factors that have changed. Third, we perform a large-scale empirical study and show that such pairs of observations are sufficient to reliably learn disentangled representations on several benchmark data sets. Finally, we evaluate our learned representations and find that they are simultaneously useful on a diverse suite of tasks, including generalization under covariate shifts, fairness, and abstract reasoning. Overall, our results demonstrate that weak supervision enables learning of useful disentangled representations in realistic scenarios.

Operator-Valued Kernels (OVKs) and associated vector-valued Reproducing Kernel Hilbert Spaces provide an elegant way to extend scalar kernel methods when the output space is a Hilbert space. Although primarily used in finite dimension for problems like multi-task regression, the ability of this framework to deal with infinite dimensional output spaces unlocks many more applications, such as functional regression, structured output prediction, and structured data representation. However, these sophisticated schemes crucially rely on the kernel trick in the output space, so that most of previous works have focused on the square norm loss function, completely neglecting robustness issues that may arise in such surrogate problems. To overcome this limitation, this paper develops a duality approach that allows to solve OVK machines for a wide range of loss functions. The infinite dimensional Lagrange multipliers are handled through a Double Representer Theorem, and algorithms for \epsilon-insensitive losses and the Huber loss are thoroughly detailed. Robustness benefits are emphasized by a theoretical stability analysis, as well as empirical improvements on structured data applications.

A fundamental trait of intelligence is the ability to achieve goals in the face of novel circumstances, such as making decisions from new action choices. However, standard reinforcement learning assumes a fixed set of actions and requires expensive retraining when given a new action set. To make learning agents more adaptable, we introduce the problem of zero-shot generalization to new actions. We propose a two-stage framework where the agent first infers action representations from action information acquired separately from the task. A policy flexible to varying action sets is then trained with generalization objectives. We benchmark generalization on sequential tasks, such as selecting from an unseen tool-set to solve physical reasoning puzzles and stacking towers with novel 3D shapes. Videos and code are available at https://sites.google.com/view/action-generalization.

We propose a method for training a deterministic deep model that can find and reject out of distribution data points at test time with a single forward pass. Our approach, deterministic uncertainty quantification (DUQ), builds upon ideas of RBF networks. We scale training in these with a novel loss function and centroid updating scheme and match the accuracy of softmax models. By enforcing detectability of changes in the input using a gradient penalty, we are able to reliably detect out of distribution data. Our uncertainty quantification scales well to large datasets, and using a single model, we improve upon or match Deep Ensembles in out of distribution detection on notable difficult dataset pairs such as FashionMNIST vs. MNIST, and CIFAR-10 vs. SVHN.

With a view to bridging the gap between deep learning and symbolic AI, we present a novel end-to-end neural network architecture that learns to form propositional representations with an explicitly relational structure from raw pixel data. In order to evaluate and analyse the architecture, we introduce a family of simple visual relational reasoning tasks of varying complexity. We show that the proposed architecture, when pre-trained on a curriculum of such tasks, learns to generate reusable representations that better facilitate subsequent learning on previously unseen tasks when compared to a number of baseline architectures. The workings of a successfully trained model are visualised to shed some light on how the architecture functions.

Traditional differential privacy is independent of the data distribution. However, this is not well-matched with the modern machine learning context, where models are trained on specific data. As a result, achieving meaningful privacy guarantees in ML often excessively reduces accuracy. We propose Bayesian differential privacy (BDP), which takes into account the data distribution to provide more practical privacy guarantees. We also derive a general privacy accounting method under BDP, building upon the well-known moments accountant. Our experiments demonstrate that in-distribution samples in classic machine learning datasets, such as MNIST and CIFAR-10, enjoy significantly stronger privacy guarantees than postulated by DP, while models maintain high classification accuracy.

Normalizing flows are exact-likelihood generative neural networks which approximately transform samples from a simple prior distribution to samples of the probability distribution of interest. Recent work showed that such generative models can be utilized in statistical mechanics to sample equilibrium states of many-body systems in physics and chemistry. To scale and generalize these results, it is essential that the natural symmetries in the probability density -- in physics defined by the invariances of the target potential -- are built into the flow.
We provide a theoretical sufficient criterion showing that the distribution generated by equivariant normalizing flows is invariant with respect to these symmetries by design. Furthermore, we propose building blocks for flows which preserve symmetries which are usually found in physical/chemical many-body particle systems. Using benchmark systems motivated from molecular physics, we demonstrate that those symmetry preserving flows can provide better generalization capabilities and sampling efficiency.

Recurrent neural networks (RNNs) are instrumental in modelling sequential and time-series data. Yet, when using RNNs to inform decision-making, predictions by themselves are not sufficient — we also need estimates of predictive uncertainty. Existing approaches for uncertainty quantification in RNNs are based predominantly on Bayesian methods; these are computationally prohibitive, and require major alterations to the RNN architecture and training. Capitalizing on ideas from classical jackknife resampling, we develop a frequentist alternative that: (a) does not interfere with model training or compromise its accuracy, (b) applies to any RNN architecture, and (c) provides theoretical coverage guarantees on the estimated uncertainty intervals. Our method derives predictive uncertainty from the variability of the (jackknife) sampling distribution of the RNN outputs, which is estimated by repeatedly deleting “blocks” of (temporally-correlated) training data, and collecting the predictions of the RNN re-trained on the remaining data. To avoid exhaustive re-training, we utilize influence functions to estimate the effect of removing training data blocks on the learned RNN parameters. Using data from a critical care setting, we demonstrate the utility of uncertainty quantification in sequential decision-making.

This paper presents a new Graph Neural Network (GNN) type using feature-wise linear modulation (FiLM). Many standard GNN variants propagate information along the edges of a graph by computing messages based only on the representation of the source of each edge. In GNN-FiLM, the representation of the target node of an edge is used to compute a transformation that can be applied to all incoming messages, allowing feature-wise modulation of the passed information.

Different GNN architectures are compared in extensive experiments on three tasks from the literature, using re-implementations of many baseline methods. Hyperparameters for all methods were found using extensive search, yielding somewhat surprising results: differences between state of the art models are much smaller than reported in the literature and well-known simple baselines that are often not compared to perform better than recently proposed GNN variants. Nonetheless, GNN-FiLM outperforms these methods on a regression task on molecular graphs and performs competitively on other tasks.

Setting regularization parameters for Lasso-type estimators is notoriously difficult, though crucial for obtaining the best accuracy. The most popular hyperparameter optimization approach is grid-search on a held-out dataset. However, grid-search requires to choose a predefined grid of parameters and scales exponentially in the number of parameters. Another class of approaches casts hyperparameter optimization as a bi-level optimization problem, typically solved by gradient descent. The key challenge for these approaches is the estimation of the gradient w.r.t. the hyperparameters. Computing that gradient via forward or backward automatic differentiation usually suffers from high memory consumption, while implicit differentiation typically involves solving a linear system which can be prohibitive and numerically unstable. In addition, implicit differentiation usually assumes smooth loss functions, which is not the case of Lasso-type problems. This work introduces an efficient implicit differentiation algorithm, without matrix inversion, tailored for Lasso-type problems. Our proposal scales to high-dimensional data by leveraging the sparsity of the solutions. Empirically, we demonstrate that the proposed method outperforms a large number of standard methods for hyperparameter optimization.

Online recommender systems often face long delays in receiving feedback, especially when optimizing for some long-term metrics. While mitigating the effects of delays in learning is well-understood in stationary environments, the problem becomes much more challenging when the environment changes. In fact, if the timescale of the change is comparable to the delay, it is impossible to learn about the environment, since the available observations are already obsolete. However, the arising issues can be addressed if intermediate signals are available without delay, such that given those signals, the long-term behavior of the system is stationary. To model this situation, we introduce the problem of stochastic, non-stationary, delayed bandits with intermediate observations. We develop a computationally efficient algorithm based on UCRL, and prove sublinear regret guarantees for its performance. Experimental results demonstrate that our method is able to learn in non-stationary delayed environments where existing methods fail.

Autoregressive models (ARMs) currently hold state-of-the-art performance in likelihood-based modeling of image and audio data. Generally, neural network based ARMs are designed to allow fast inference, but sampling from these models is impractically slow. In this paper, we introduce the predictive sampling algorithm: a procedure that exploits the fast inference property of ARMs in order to speed up sampling, while keeping the model intact. We propose two variations of predictive sampling, namely sampling with ARM fixed-point iteration and learned forecasting modules. Their effectiveness is demonstrated in two settings: i) explicit likelihood modeling on binary MNIST, SVHN and CIFAR10, and ii) discrete latent modeling in an autoencoder trained on SVHN, CIFAR10 and Imagenet32. Empirically, we show considerable improvements over baselines in number of ARM inference calls and sampling speed.

Generative models in molecular design tend to be richly parameterized, data-hungry neural models, as they must create complex structured objects as outputs. Estimating such models from data may be challenging due to the lack of sufficient training data. In this paper, we propose a surprisingly effective self-training approach for iteratively creating additional molecular targets. We first pre-train the generative model together with a simple property predictor. The property predictor is then used as a likelihood model for filtering candidate structures from the generative model. Additional targets are iteratively produced and used in the course of stochastic EM iterations to maximize the log-likelihood that the candidate structures are accepted. A simple rejection (re-weighting) sampler suffices to draw posterior samples since the generative model is already reasonable after pre-training. We demonstrate significant gains over strong baselines for both unconditional and conditional molecular design. In particular, our approach outperforms the previous state-of-the-art in conditional molecular design by over 10% in absolute gain. Finally, we show that our approach is useful in other domains as well, such as program synthesis.

We propose a neural network-based approach that computes a stable and generalizing metric (LSiM) to compare data from a variety of numerical simulation sources. We focus on scalar time-dependent 2D data that commonly arises from motion and transport-based partial differential equations (PDEs). Our method employs a Siamese network architecture that is motivated by the mathematical properties of a metric. We leverage a controllable data generation setup with PDE solvers to create increasingly different outputs from a reference simulation in a controlled environment. A central component of our learned metric is a specialized loss function that introduces knowledge about the correlation between single data samples into the training process. To demonstrate that the proposed approach outperforms existing metrics for vector spaces and other learned, image-based metrics, we evaluate the different methods on a large range of test data. Additionally, we analyze generalization benefits of an adjustable training data difficulty and demonstrate the robustness of LSiM via an evaluation on three real-world data sets.

We consider the problem of learning in Linear Quadratic Control systems whose transition parameters are initially unknown. Recent results in this setting have demonstrated efficient learning algorithms with regret growing with the square root of the number of decision steps. We present new efficient algorithms that achieve, perhaps surprisingly,regret that scales only (poly-)logarithmically with the number of steps, in two scenarios: when only the state transition matrix A is unknown, and when only the state-action transition matrix B is unknown and the optimal policy satisfies a certain non-degeneracy condition. On the other hand, we give a lower bound which shows that when the latter condition is violated, square root regret is unavoidable.

Deep neural networks have dramatically transformed machine learning, but their memory and energy demands are substantial. The requirements of real biological neural networks are rather modest in comparison, and one feature that might underlie this austerity is their sparse connectivity. In deep learning, trainable sparse networks that perform well on a specific task are usually constructed using label-dependent pruning criteria. In this article, we introduce Neural Tangent Transfer, a method that instead finds trainable sparse networks in a label-free manner. Specifically, we find sparse networks whose training dynamics, as characterized by the neural tangent kernel, mimic those of dense networks in function space. Finally, we evaluate our label-agnostic approach on several standard classification tasks and show that the resulting sparse networks achieve higher classification performance while converging faster.

There is a growing amount of literature on the relationship between wide neural networks (NNs) and Gaussian processes (GPs), identifying an equivalence between the two for a variety of NN architectures. This equivalence enables, for instance, accurate approximation of the behaviour of wide Bayesian NNs without MCMC or variational approximations, or characterisation of the distribution of randomly initialised wide NNs optimised by gradient descent without ever running an optimiser. We provide a rigorous extension of these results to NNs involving attention layers, showing that unlike single-head attention, which induces non-Gaussian behaviour, multi-head attention architectures behave as GPs as the number of heads tends to infinity. We further discuss the effects of positional encodings and layer normalisation, and propose modifications of the attention mechanism which lead to improved results for both finite and infinitely wide NNs. We evaluate attention kernels empirically, leading to a moderate improvement upon the previous state-of-the-art on CIFAR-10 for GPs without trainable kernels and advanced data preprocessing. Finally, we introduce new features to the Neural Tangents library (Novak et al.,2020) allowing applications of NNGP/NTK models, with and without attention, to variable-length sequences, with an example on the IMDb reviews dataset.

Attempts to render deep learning models interpretable, data-efficient, and robust have seen some success through hybridisation with rule-based systems, for example, in Neural Theorem Provers (NTPs). These neuro-symbolic models can induce interpretable rules and learn representations from data via back-propagation, while providing logical explanations for their predictions. However, they are restricted by their computational complexity, as they need to consider all possible proof paths for explaining a goal, thus rendering them unfit for large-scale applications. We present Conditional Theorem Provers (CTPs), an extension to NTPs that learns an optimal rule selection strategy via gradient-based optimisation. We show that CTPs are scalable and yield state-of-the-art results on the CLUTRR dataset, which tests systematic generalisation of neural models by learning to reason over smaller graphs and evaluating on larger ones. Finally, CTPs show better link prediction results on standard benchmarks in comparison with other neural-symbolic models, while being explainable.

This paper investigates generalisation in multi-agent games, where the generality of the agent can be evaluated by playing against opponents it hasn't seen during training. We propose two new games with concealed information and complex, non-transitive reward structure (think rock-paper-scissors). It turns out that most current deep reinforcement learning methods fail to efficiently explore the strategy space, thus learning policies that generalise poorly to unseen opponents. We then propose a novel hierarchical agent architecture, where the hierarchy is grounded in the game-theoretic structure of the game -- the top level chooses strategic responses to opponents, while the low level implements them into policy over primitive actions. This grounding facilitates credit assignment across the levels of hierarchy. Our experiments show that the proposed hierarchical agent is capable of generalisation to unseen opponents, while conventional baselines fail to generalise whatsoever.

A recent trend in algorithm design consists of augmenting classic data structures with machine learning models, which are better suited to reveal and exploit patterns and trends in the input data so to achieve outstanding practical improvements in space occupancy and time efficiency.
This is especially known in the context of indexing data structures where, despite few attempts in evaluating their asymptotic efficiency, theoretical results are yet missing in showing that learned indexes are provably better than classic indexes, such as B+ trees and their variants. In this paper, we present the first mathematically-grounded answer to this open problem. We obtain this result by discovering and exploiting a link between the original problem and a mean exit time problem over a proper stochastic process which, we show, is related to the space and time occupancy of those learned indexes. Our general result is then specialised to five well-known distributions: Uniform, Lognormal, Pareto, Exponential, and Gamma; and it is corroborated in precision and robustness by a large set of experiments.

Stochastic gradient descent with momentum (SGDm) is one of the most popular optimization algorithms in deep learning. While there is a rich theory of SGDm for convex problems, the theory is considerably less developed in the context of deep learning where the problem is non-convex and the gradient noise might exhibit a heavy-tailed behavior, as empirically observed in recent studies. In this study, we consider a \emph{continuous-time} variant of SGDm, known as the underdamped Langevin dynamics (ULD), and investigate its asymptotic properties under heavy-tailed perturbations. Supported by recent studies from statistical physics, we argue both theoretically and empirically that the heavy-tails of such perturbations can result in a bias even when the step-size is small, in the sense that \emph{the optima of stationary distribution} of the dynamics might not match \emph{the optima of the cost function to be optimized}. As a remedy, we develop a novel framework, which we coin as \emph{fractional} ULD (FULD), and prove that FULD targets the so-called Gibbs distribution, whose optima exactly match the optima of the original cost. We observe that the Euler discretization of FULD has noteworthy algorithmic similarities with \emph{natural gradient} methods and \emph{gradient clipping}, bringing a new perspective on understanding their role …

We propose inertial versions of block coordinate descent methods for solving non-convex non-smooth composite optimization problems. Our methods possess three main advantages compared to current state-of-the-art accelerated first-order methods: (1) they allow using two different extrapolation points to evaluate the gradients and to add the inertial force (we will empirically show that it is more efficient than using a single extrapolation point), (2) they allow to randomly select the block of variables to update, and (3) they do not require a restarting step. We prove the subsequential convergence of the generated sequence under mild assumptions, prove the global convergence under some additional assumptions, and provide convergence rates. We deploy the proposed methods to solve non-negative matrix factorization (NMF) and show that they compete favorably with the state-of-the-art NMF algorithms. Additional experiments on non-negative approximate canonical polyadic decomposition, also known as nonnegative tensor factorization, are also provided.

Causal inference using observational data is challenging, especially in the bivariate case. Through the minimum description length principle, we link the postulate of independence between the generating mechanisms of the cause and of the effect given the cause to quantile regression. Based on this theory, we develop Bivariate Quantile Causal Discovery (bQCD), a new method to distinguish cause from effect assuming no confounding, selection bias or feedback. Because it uses multiple quantile levels instead of the conditional mean only, bQCD is adaptive not only to additive, but also to multiplicative or even location-scale generating mechanisms. To illustrate the effectiveness of our approach, we perform an extensive empirical comparison on both synthetic and real datasets. This study shows that bQCD is robust across different implementations of the method (i.e., the quantile regression), computationally efficient, and compares favorably to state-of-the-art methods.

We present Graph Random Neural Features (GRNF), a novel embedding method from graph-structured data to real vectors based on a family of graph neural networks. The embedding naturally deals with graph isomorphism and preserves the metric structure of the graph domain, in probability. In addition to being an explicit embedding method, it also allows us to efficiently and effectively approximate graph metric distances (as well as complete kernel functions); a criterion to select the embedding dimension trading off the approximation accuracy with the computational cost is also provided. GRNF can be used within traditional processing methods or as a training-free input layer of a graph neural network. The theoretical guarantees that accompany GRNF ensure that the considered graph distance is metric, hence allowing to distinguish any pair of non-isomorphic graphs.

In complex tasks, such as those with large combinatorial action spaces, random exploration may be too inefficient to achieve meaningful learning progress. In this work, we use a curriculum of progressively growing action spaces to accelerate learning. We assume the environment is out of our control, but that the agent may set an internal curriculum by initially restricting its action space. Our approach uses off-policy reinforcement learning to estimate optimal value functions for multiple action spaces simultaneously and efficiently transfers data, value estimates, and state representations from restricted action spaces to the full task. We show the efficacy of our approach in proof-of-concept control tasks and on challenging large-scale StarCraft micromanagement tasks with large, multi-agent action spaces.

The construction in the recent paper by Du et al. [2019] implies that searching for a near-optimal action in a bandit sometimes requires examining essentially all the actions, even if the learner is given linear features in R^d that approximate the rewards with a small uniform error. We use the Kiefer-Wolfowitz theorem to prove a positive result that by checking only a few actions, a learner can always find an action that is suboptimal with an error of at most O(ε√d) where ε is the approximation error of the features. Thus, features are useful when the approximation error is small relative to the dimensionality of the features. The idea is applied to stochastic bandits and reinforcement learning with a generative model where the learner has access to d-dimensional linear features that approximate the action-value functions for all policies to an accuracy of ε. For linear bandits, we prove a bound on the regret of order d√(n log(k)) + εn√d log(n) with k the number of actions and n the horizon. For RL we show that approximate policy iteration can learn a policy that is optimal up to an additive error of order ε√d/(1 − γ)^2 and using about d/(ε^2(1 − …

Posterior inference with an intractable likelihood is becoming an increasingly common task in scientific domains which rely on sophisticated computer simulations. Typically, these forward models do not admit tractable densities forcing practitioners to rely on approximations. This work introduces a novel approach to address the intractability of the likelihood and the marginal model. We achieve this by learning a flexible amortized estimator which approximates the likelihood-to-evidence ratio. We demonstrate that the learned ratio estimator can be embedded in \textsc{mcmc} samplers to approximate likelihood-ratios between consecutive states in the Markov chain, allowing us to draw samples from the intractable posterior. Techniques are presented to improve the numerical stability and to measure the quality of an approximation. The accuracy of our approach is demonstrated on a variety of benchmarks against well-established techniques. Scientific applications in physics show its applicability.

We study whether a neural network optimizes to the same, linearly connected minimum under different samples of SGD noise (e.g., random data order and augmentation). We find that standard vision models become stable to SGD noise in this way early in training. From then on, the outcome of optimization is determined to a linearly connected region. We use this technique to study iterative magnitude pruning (IMP), the procedure used by work on the lottery ticket hypothesis to identify subnetworks that could have trained in isolation to full accuracy. We find that these subnetworks only reach full accuracy when they are stable to SGD noise, which either occurs at initialization for small-scale settings (MNIST) or early in training for large-scale settings (ResNet-50 and Inception-v3 on ImageNet).

We are interested in how to design reinforcement learning agents that provably reduce the sample complexity for learning new tasks by transferring knowledge from previously-solved ones. The availability of solutions to related problems poses a fundamental trade-off: whether to seek policies that are expected to immediately achieve high (yet sub-optimal) performance in the new task or whether to seek information to quickly identify an optimal solution, potentially at the cost of poor initial behaviour. In this work, we focus on the second objective when the agent has access to a generative model of state-action pairs. First, given a set of solved tasks containing an approximation of the target one, we design an algorithm that quickly identifies an accurate solution by seeking the state-action pairs that are most informative for this purpose. We derive PAC bounds on its sample complexity which clearly demonstrate the benefits of using this kind of prior knowledge. Then, we show how to learn these approximate tasks sequentially by reducing our transfer setting to a hidden Markov model and employing spectral methods to recover its parameters. Finally, we empirically verify our theoretical findings in simple simulated domains.

In this paper, we introduce a powerful and efficient framework for direct optimization of ranking metrics. The problem is ill-posed due to the discrete structure of the loss, and to deal with that, we introduce two important techniques: a stochastic smoothing and a novel gradient estimate based on partial integration. We also address the problem of smoothing bias and present a universal solution for a proper debiasing. To guarantee the global convergence of our method, we adopt a recently proposed Stochastic Gradient Langevin Boosting algorithm. Our algorithm is implemented as a part of the CatBoost gradient boosting library and outperforms the existing approaches on several learning-to-rank datasets. In addition to ranking metrics, our framework applies to any scale-free discrete loss function.

Thompson sampling is an efficient algorithm for sequential decision making, which exploits the posterior uncertainty to address the exploration-exploitation dilemma. There has been significant recent interest in integrating Bayesian neural networks into Thompson sampling. Most of these methods rely on global variable uncertainty for exploration. In this paper, we propose a new probabilistic modeling framework for Thompson sampling, where local latent variable uncertainty is used to sample the mean reward. Variational inference is used to approximate the posterior of the local variable, and semi-implicit structure is further introduced to enhance its expressiveness. Our experimental results on eight contextual bandit benchmark datasets show that Thompson sampling guided by local uncertainty achieves state-of-the-art performance while having low computational complexity.

In modern supervised learning, many deep neural networks are able to interpolate the data: the empirical loss can be driven to near zero on all samples simultaneously. In this work, we explicitly exploit this interpolation property for the design of a new optimization algorithm for deep learning, which we term Adaptive Learning-rates for Interpolation with Gradients (ALI-G). ALI-G retains the two main advantages of Stochastic Gradient Descent (SGD), which are (i) a low computational cost per iteration and (ii) good generalization performance in practice. At each iteration, ALI-G exploits the interpolation property to compute an adaptive learning-rate in closed form. In addition, ALI-G clips the learning-rate to a maximal value, which we prove to be helpful for non-convex problems. Crucially, in contrast to the learning-rate of SGD, the maximal learning-rate of ALI-G does not require a decay schedule. This makes ALI-G considerably easier to tune than SGD. We prove the convergence of ALI-G in various stochastic settings. Notably, we tackle the realistic case where the interpolation property is satisfied up to some tolerance. We also provide experiments on a variety of deep learning architectures and tasks: (i) learning a differentiable neural computer; (ii) training a wide residual network on the …

Recent work has argued that neural networks can be understood theoretically by taking the number of channels to infinity, at which point the outputs become Gaussian process (GP) distributed. However, we note that infinite Bayesian neural networks lack a key facet of the behaviour of real neural networks: the fixed kernel, determined only by network hyperparameters, implies that they cannot do any form of representation learning. The lack of representation or equivalently kernel learning leads to less flexibility and hence worse performance, giving a potential explanation for the inferior performance of infinite networks observed in the literature (e.g. Novak et al. 2019). We give analytic results characterising the prior over representations and representation learning in finite deep linear networks. We show empirically that the representations in SOTA architectures such as ResNets trained with SGD are much closer to those suggested by our deep linear results than by the corresponding infinite network. This motivates the introduction of a new class of network: infinite networks with bottlenecks, which inherit the theoretical tractability of infinite networks while at the same time allowing representation learning.

Entropy regularization in optimal transport (OT) has been the driver of many recent interests for Wasserstein metrics and barycenters in machine learning. It allows to keep the appealing geometrical properties of the unregularized Wasserstein distance while having a significantly lower complexity thanks to Sinkhorn's algorithm. However, entropy brings some inherent smoothing bias, resulting for example in blurred barycenters. This side effect has prompted an increasing temptation in the community to settle for a slower algorithm such as log-domain stabilized Sinkhorn which breaks the parallel structure that can be leveraged on GPUs, or even go back to unregularized OT. Here we show how this bias is tightly linked to the reference measure that defines the entropy regularizer and propose debiased Sinkhorn barycenters that preserve the best of worlds: fast Sinkhorn-like iterations without entropy smoothing. Theoretically, we prove that this debiasing is perfect for Gaussian distributions with equal variance. Empirically, we illustrate the reduced blurring and the computational advantage.

In this paper we propose a scalable, unsupervised approach for detecting anomalies in the Internet of Things (IoT). Complex devices are connected daily and eagerly generate vast streams of multidimensional telemetry. These devices often operate in distinct modes based on external conditions (day/night, occupied/vacant, etc.), and to prevent complete or partial system outage, we would like to recognize as early as possible when these devices begin to operate outside the normal modes. We propose an unsupervised anomaly detection method that creates a negative sample from the positive, observed sample, and trains a classifier to distinguish between positive and negative samples. Using the Concentration Phenomenon, we explain why such a classifier ought to establish suitable decision boundaries between normal and anomalous regions, and show how Integrated Gradients can attribute the anomaly to specific dimensions within the anomalous state vector. We have demonstrated that negative sampling with random forest or neural network classifiers yield significantly higher AUC scores compared to state-of-the-art approaches against benchmark anomaly detection datasets, and a multidimensional, multimodal dataset from real climate control devices. Finally, we describe how negative sampling with neural network classifiers have been successfully deployed at large scale to predict failures in real time in over …

Bayesian optimization has demonstrated impressive success in finding the optimum input x∗ and output f∗ = f(x∗) = max f(x) of a black-box function f. In some applications, however, the optimum output is known in advance and the goal is to find the corresponding optimum input. Existing work in Bayesian optimization (BO) has not effectively exploited the knowledge of f∗ for optimization. In this paper, we consider a new setting in BO in which the knowledge of the optimum output is available. Our goal is to exploit the knowledge about f∗ to search for the input x∗ efficiently. To achieve this goal, we first transform the Gaussian process surrogate using the information about the optimum output. Then, we propose two acquisition functions, called confidence bound minimization and expected regret minimization, which exploit the knowledge about the optimum output to identify the optimum input more efficient. We show that our approaches work intuitively and quantitatively better performance against standard BO methods. We demonstrate real applications in tuning a deep reinforcement learning algorithm on the CartPole problem and XGBoost on Skin Segmentation dataset in which the optimum values are publicly available.

We study a general class of bilevel problems, consisting in the minimization of an upper-level objective which depends on the solution to a parametric fixed-point equation. Important instances arising in machine learning include hyperparameter optimization, meta-learning, and certain graph and recurrent neural networks. Typically the gradient of the upper-level objective (hypergradient) is hard or even impossible to compute exactly, which has raised the interest in approximation methods. We investigate some popular approaches to compute the hypergradient, based on reverse mode iterative differentiation and approximate implicit differentiation. Under the hypothesis that the fixed point equation is defined by a contraction mapping, we present a unified analysis which allows for the first time to quantitatively compare these methods, providing explicit bounds for their iteration complexity. This analysis suggests a hierarchy in terms of computational efficiency among the above methods, with approximate implicit differentiation based on conjugate gradient performing best. We present an extensive experimental comparison among the methods which confirm the theoretical findings.

Un-trained convolutional neural networks have emerged as highly successful tools for image recovery and restoration. They are capable of solving standard inverse problems such as denoising and compressive sensing with excellent results by simply fitting a neural network model to measurements from a single image or signal without the need for any additional training data. For some applications, this critically requires additional regularization in the form of early stopping the optimization. For signal recovery from a few measurements, however, un-trained convolutional networks have an intriguing self-regularizing property: Even though the network can perfectly fit any image, the network recovers a natural image from few measurements when trained with gradient descent until convergence. In this paper, we provide numerical evidence for this property and study it theoretically. We show that---without any further regularization---an un-trained convolutional neural network can approximately reconstruct signals and images that are sufficiently structured, from a near minimal number of random measurements.

Existing domain adaptation focuses on transferring knowledge between domains with categorical indices (e.g., between datasets A and B). However, many tasks involve continuously indexed domains. For example, in medical applications, one often needs to transfer disease analysis and prediction across patients of different ages, where age acts as a continuous domain index. Such tasks are challenging for prior domain adaptation methods since they ignore the underlying relation among domains. In this paper, we propose the first method for continuously indexed domain adaptation. Our approach combines traditional adversarial adaptation with a novel discriminator that models the encoding-conditioned domain index distribution. Our theoretical analysis demonstrates the value of leveraging the domain index to generate invariant features across a continuous range of domains. Our empirical results show that our approach outperforms the state-of-the-art domain adaption methods on both synthetic and real-world medical datasets.

We investigate the generalisation performance of Distributed Gradient Descent with implicit regularisation and random features in the homogenous setting where a network of agents are given data sampled independently from the same unknown distribution. Along with reducing the memory footprint, random features are particularly convenient in this setting as they provide a common parameterisation across agents that allows to overcome previous difficulties in implementing decentralised kernel regression. Under standard source and capacity assumptions, we establish high probability bounds on the predictive performance for each agent as a function of the step size, number of iterations, inverse spectral gap of the communication matrix and number of random features. By tuning these parameters, we obtain statistical rates that are minimax optimal with respect to the total number of samples in the network. The algorithm provides a linear improvement over single-machine gradient descent in memory cost and, when agents hold enough data with respect to the network size and inverse spectral gap, a linear speed up in computational run-time for any network topology. We present simulations that show how the number of random features, iterations and samples impact predictive performance.

Extreme multi-label classification (XMC) is the problem of finding the relevant labels for an input, from a very large universe of possible labels. We consider XMC in the setting where labels are available only for groups of samples - but not for individual ones. Current XMC approaches are not built for such multi-instance multi-label (MIML) training data, and MIML approaches do not scale to XMC sizes. We develop a new and scalable algorithm to impute individual-sample labels from the group labels; this can be paired with any existing XMC method to solve the aggregated label problem. We characterize the statistical properties of our algorithm under mild assumptions, and provide a new end-to-end framework for MIML as an extension. Experiments on both aggregated label XMC and MIML tasks show the advantages over existing approaches.

We present a new method for separating a mixed audio sequence, in which multiple voices speak simultaneously. The new method employs gated neural networks that are trained to separate the voices at multiple processing steps, while maintaining the speaker in each output channel fixed. A different model is trained for every number of possible speakers, and the model with the largest number of speakers is employed to select the actual number of speakers in a given sample. Our method greatly outperforms the current state of the art, which, as we show, is not competitive for more than two speakers.

We study the model selection problem in \textit{conditional average treatment effect} (CATE) prediction. Unlike previous works on this topic, we focus on preserving the rank order of the performance of candidate CATE predictors to enable accurate and stable model selection. To this end, we analyze the model performance ranking problem and formulate guidelines to obtain a better evaluation metric. We then propose a novel metric that can identify the ranking of the performance of CATE predictors with high confidence. Empirical evaluations demonstrate that our metric outperforms existing metrics in both model selection and hyperparameter tuning tasks.

Trained generative models have shown remarkable performance as priors for inverse problems in imaging -- for example, Generative Adversarial Network priors permit recovery of test images from 5-10x fewer measurements than sparsity priors. Unfortunately, these models may be unable to represent any particular image because of architectural choices, mode collapse, and bias in the training dataset. In this paper, we demonstrate that invertible neural networks, which have zero representation error by design, can be effective natural signal priors at inverse problems such as denoising, compressive sensing, and inpainting. Given a trained generative model, we study the empirical risk formulation of the desired inverse problem under a regularization that promotes high likelihood images, either directly by penalization or algorithmically by initialization. For compressive sensing, invertible priors can yield higher accuracy than sparsity priors across almost all undersampling ratios, and due to their lack of representation error, invertible priors can yield better reconstructions than GAN priors for images that have rare features of variation within the biased training set, including out-of-distribution natural images. We additionally compare performance for compressive sensing to unlearned methods, such as the deep decoder, and we establish theoretical bounds on expected recovery error in the case of a …

The multi-armed bandit (MAB) problem is a classical learning task that exemplifies the exploration-exploitation tradeoff. However, standard formulations do not take into account risk. In online decision making systems, risk is a primary concern. In this regard, the mean-variance risk measure is one of the most common objective functions. Existing algorithms for mean-variance optimization in the context of MAB problems have unrealistic assumptions on the reward distributions. We develop Thompson Sampling-style algorithms for mean-variance MAB and provide comprehensive regret analyses for Gaussian and Bernoulli bandits with fewer assumptions. Our algorithms achieve the best known regret bounds for mean-variance MABs and also attain the information-theoretic bounds in some parameter regimes. Empirical simulations show that our algorithms significantly outperform existing LCB-based algorithms for all risk tolerances.

When machine learning models are deployed on a test distribution different from the training distribution, they can perform poorly, but overestimate their performance. In this work, we aim to better estimate a model's performance under distribution shift, without supervision. To do so, we use a set of domain-invariant predictors as a proxy for the unknown, true target labels. Since the error of the resulting risk estimate depends on the target risk of the proxy model, we study generalization of domain-invariant representations and show that the complexity of the latent representation has a significant influence on the target risk. Empirically, our approach (1) enables self-tuning of domain adaptation models, and (2) accurately estimates the target error of given models under distribution shift. Other applications include model selection, deciding early stopping and error detection.

We propose the Interferometric Graph Transform (IGT), which is a new class of deep unsupervised graph convolutional neural network for building graph representations. Our first contribution is to propose a generic, complex-valued spectral graph architecture obtained from a generalization of the Euclidean Fourier transform. We show that our learned representation consists of both discriminative and invariant features, thanks to a novel greedy concave objective. From our experiments, we conclude that our learning procedure exploits the topology of the spectral domain, which is normally a flaw of spectral methods, and in particular our method can recover an analytic operator for vision tasks. We test our algorithm on various and challenging tasks such as image classification (MNIST, CIFAR-10), community detection (Authorship, Facebook graph) and action recognition from 3D skeletons videos (SBU, NTU), exhibiting a new state-of-the-art in spectral graph unsupervised settings.

Generalization across environments is critical to the successful application of reinforcement learning (RL) algorithms to real-world challenges. In this work we propose a method for learning state abstractions which generalize to novel observation distributions in the multi-environment RL setting. We prove that for certain classes of environments, this approach outputs, with high probability, a state abstraction corresponding to the causal feature set with respect to the return. We give empirical evidence that analogous methods for the nonlinear setting can also attain improved generalization over single- and multi-task baselines. Lastly, we provide bounds on model generalization error in the multi-environment setting, in the process showing a connection between causal variable identification and the state abstraction framework for MDPs.

Speech information can be roughly decomposed into four components: language content, timbre, pitch, and rhythm. Obtaining disentangled representations of these components is useful in many speech analysis and generation applications. Recently, state-of-the-art voice conversion systems have led to speech representations that can disentangle speaker-dependent and independent information. However, these systems can only disentangle timbre, while information about pitch, rhythm and content is still mixed together. Further disentangling the remaining speech components is an under-determined problem in the absence of explicit annotations for each component, which are difficult and expensive to obtain. In this paper, we propose SpeechSplit, which can blindly decompose speech into its four components by introducing three carefully designed information bottlenecks. SpeechSplit is among the first algorithms that can separately perform style transfer on timbre, pitch and rhythm without text labels. Our code is publicly available at https://github.com/auspicious3000/SpeechSplit.

Recovering a signal from its Fourier intensity underlies many important applications, including lensless imaging and imaging through scattering media. Conventional algorithms for retrieving the phase suffer when noise is present but display global convergence when given clean data. Neural networks have been used to improve algorithm robustness, but efforts to date are sensitive to initial conditions and give inconsistent performance. Here, we combine iterative methods from phase retrieval with image statistics from deep denoisers, via regularization-by-denoising. The resulting methods inherit the advantages of each approach and outperform other noise-robust phase retrieval algorithms. Our work paves the way for hybrid imaging methods that integrate machine-learned constraints in conventional algorithms.

Adversarial training based on the minimax formulation is necessary for obtaining adversarial robustness of trained models. However, it is conservative or even pessimistic so that it sometimes hurts the natural generalization. In this paper, we raise a fundamental question—do we have to trade off natural generalization for adversarial robustness? We argue that adversarial training is to employ confident adversarial data for updating the current model. We propose a novel formulation of friendly adversarial training (FAT): rather than employing most adversarial data maximizing the loss, we search for least adversarial data (i.e., friendly adversarial data) minimizing the loss, among the adversarial data that are confidently misclassified. Our novel formulation is easy to implement by just stopping the most adversarial data searching algorithms such as PGD (projected gradient descent) early, which we call early-stopped PGD. Theoretically, FAT is justified by an upper bound of the adversarial risk. Empirically, early-stopped PGD allows us to answer the earlier question negatively—adversarial robustness can indeed be achieved without compromising the natural generalization.

Deep reinforcement learning (RL) algorithms have recently achieved remarkable successes in various sequential decision making tasks, leveraging advances in methods for training large deep networks. However, these methods usually require large amounts of training data, which is often a big problem for real-world applications. One natural question to ask is whether learning good representations for states and using larger networks helps in learning better policies. In this paper, we try to study if increasing input dimensionality helps improve performance and sample efficiency of model-free deep RL algorithms. To do so, we propose an online feature extractor network (OFENet) that uses neural nets to produce \textit{good} representations to be used as inputs to an off-policy RL algorithm. Even though the high dimensionality of input is usually thought to make learning of RL agents more difficult, we show that the RL agents in fact learn more efficiently with the high-dimensional representation than with the lower-dimensional state observations. We believe that stronger feature propagation together with larger networks allows RL agents to learn more complex functions of states and thus improves the sample efficiency. Through numerical experiments, we show that the proposed method achieves much higher sample efficiency and better performance. Codes for …

We introduce kernels with random Fourier features in the meta-learning framework for few-shot learning. We propose meta variational random features (MetaVRF) to learn adaptive kernels for the base-learner, which is developed in a latent variable model by treating the random feature basis as the latent variable. We formulate the optimization of MetaVRF as a variational inference problem by deriving an evidence lower bound under the meta-learning framework. To incorporate shared knowledge from related tasks, we propose a context inference of the posterior, which is established by an LSTM architecture. The LSTM-based inference network can effectively integrate the context information of previous tasks with task-specific information, generating informative and adaptive features. The learned MetaVRF can produce kernels of high representational power with a relatively low spectral sampling rate and also enables fast adaptation to new tasks. Experimental results on a variety of few-shot regression and classification tasks demonstrate that MetaVRF delivers much better, or at least competitive, performance compared to existing meta-learning alternatives.

We aim to develop off-policy DRL algorithms that not only exceed state-of-the-art performance but are also simple and minimalistic. For standard continuous control benchmarks, Soft Actor-Critic (SAC), which employs entropy maximization, currently provides state-of-the-art performance. We first demonstrate that the entropy term in SAC addresses action saturation due to the bounded nature of the action spaces, with this insight, we propose a streamlined algorithm with a simple normalization scheme or with inverted gradients. We show that both approaches can match SAC's sample efficiency performance without the need of entropy maximization, we then propose a simple non-uniform sampling method for selecting transitions from the replay buffer during training. Extensive experimental results demonstrate that our proposed sampling scheme leads to state of the art sample efficiency on challenging continuous control tasks. We combine all of our findings into one simple algorithm, which we call Streamlined Off Policy with Emphasizing Recent Experience, for which we provide robust public-domain code.

Plug-and-play (PnP) is a non-convex framework that combines ADMM or other proximal algorithms with advanced denoiser priors. Recently, PnP has achieved great empirical success, especially with the integration of deep learning-based denoisers. However, a key problem of PnP based approaches is that they require manual parameter tweaking. It is necessary to obtain high-quality results across the high discrepancy in terms of imaging conditions and varying scene content. In this work, we present a tuning-free PnP proximal algorithm, which can automatically determine the internal parameters including the penalty parameter, the denoising strength and the terminal time. A key part of our approach is to develop a policy network for automatic search of parameters, which can be effectively learned via mixed model-free and model-based deep reinforcement learning. We demonstrate, through numerical and visual experiments, that the learned policy can customize different parameters for different states, and often more efficient and effective than existing handcrafted criteria. Moreover, we discuss the practical considerations of the plugged denoisers, which together with our learned policy yield state-of-the-art results. This is prevalent on both linear and nonlinear exemplary inverse imaging problems, and in particular, we show promising results on Compressed Sensing MRI and phase retrieval.

Posterior distribution approximation is a central task in Bayesian inference. Stochastic gradient Langevin dynamics (SGLD) and its extensions have been practically used and theoretically studied. While SGLD updates a single particle at a time, ensemble methods that update multiple particles simultaneously have been recently gathering attention. Compared with the naive parallel-chain SGLD that updates multiple particles independently, ensemble methods update particles with their interactions. Thus, these methods are expected to be more particle-efficient than the naive parallel-chain SGLD because particles can be aware of other particles' behavior through their interactions. Although ensemble methods numerically demonstrated their superior performance, no theoretical guarantee exists to assure such particle-efficiency and it is unclear whether those ensemble methods are really superior to the naive parallel-chain SGLD in the non-asymptotic settings. To cope with this problem, we propose a novel ensemble method that uses a non-reversible Markov chain for the interaction, and we present a non-asymptotic theoretical analysis for our method. Our analysis shows that, for the first time, the interaction causes a faster convergence rate than the naive parallel-chain SGLD in the non-asymptotic setting if the discretization error is appropriately controlled. Numerical experiments show that we can control the discretization error by tuning the …

Imitation learning in a high-dimensional environment is challenging. Most inverse reinforcement learning (IRL) methods fail to outperform the demonstrator in such a high-dimensional environment, e.g., Atari domain. To address this challenge, we propose a novel reward learning module to generate intrinsic reward signals via a generative model. Our generative method can perform better forward state transition and backward action encoding, which improves the module's dynamics modeling ability in the environment. Thus, our module provides the imitation agent both the intrinsic intention of the demonstrator and a better exploration ability, which is critical for the agent to outperform the demonstrator. Empirical results show that our method outperforms state-of-the-art IRL methods on multiple Atari games, even with one-life demonstration. Remarkably, our method achieves performance that is up to 5 times the performance of the demonstration.

Many machine learning algorithms are trained and evaluated by splitting data from a single source into training and test sets. While such focus on in-distribution learning scenarios has led to interesting advancement, it has not been able to tell if models are relying on dataset biases as shortcuts for successful prediction (e.g., using snow cues for recognising snowmobiles), resulting in biased models that fail to generalise when the bias shifts to a different class. The cross-bias generalisation problem has been addressed by de-biasing training data through augmentation or re-sampling, which are often prohibitive due to the data collection cost (e.g., collecting images of a snowmobile on a desert) and the difficulty of quantifying or expressing biases in the first place. In this work, we propose a novel framework to train a de-biased representation by encouraging it to be different from a set of representations that are biased by design. This tactic is feasible in many scenarios where it is much easier to define a set of biased representations than to define and quantify bias. We demonstrate the efficacy of our method across a variety of synthetic and real-world biases; our experiments show that the method discourages models from taking bias …

In many real-world applications, data are collected in the form of a stream, whose feature space can evolve over time. For instance, in the environmental monitoring task, features can be dynamically vanished or augmented due to the existence of expired old sensors and deployed new sensors. Furthermore, besides the evolvable feature space, the data distribution is usually changing in the streaming scenario. When both feature space and data distribution are evolvable, it is quite challenging to design algorithms with guarantees, particularly theoretical understandings of generalization ability. To address this difficulty, we propose a novel discrepancy measure for data with evolving feature space and data distribution, named the \emph{evolving discrepancy}. Based on that, we present the generalization error analysis, and the theory motivates the design of a learning algorithm which is further implemented by deep neural networks. Empirical studies on synthetic data verify the rationale of our proposed discrepancy measure, and extensive experiments on real-world tasks validate the effectiveness of our algorithm.

This paper studies binary logistic regression for rare events data, or imbalanced data, where the number of events (observations in one class, often called cases) is significantly smaller than the number of nonevents (observations in the other class, often called controls). We first derive the asymptotic distribution of the maximum likelihood estimator (MLE) of the unknown parameter, which shows that the asymptotic variance convergences to zero in a rate of the inverse of the number of the events instead of the inverse of the full data sample size, indicating that the available information in rare events data is at the scale of the number of events instead of the full data sample size. Furthermore, we prove that under-sampling a small proportion of the nonevents, the resulting under-sampled estimator may have identical asymptotic distribution to the full data MLE. This demonstrates the advantage of under-sampling nonevents for rare events data, because this procedure may significantly reduce the computation and/or data collection costs. Another common practice in analyzing rare events data is to over-sample (replicate) the events, which has a higher computational cost. We show that this procedure may even result in efficiency loss in terms of parameter estimation.

In a standard setting of Bayesian optimization (BO), the objective function evaluation is assumed to be highly expensive. Multi-fidelity Bayesian optimization (MFBO) accelerates BO by incorporating lower fidelity observations available with a lower sampling cost. We propose a novel information-theoretic approach to MFBO, called multi-fidelity max-value entropy search (MF-MES), that enables us to obtain a more reliable evaluation of the information gain compared with existing information-based methods for MFBO. Further, we also propose a parallelization of MF-MES mainly for the asynchronous setting because queries typically occur asynchronously in MFBO due to a variety of sampling costs. We show that most of computations in our acquisition functions can be derived analytically, except for at most only two dimensional numerical integration that can be performed efficiently by simple approximations. We demonstrate effectiveness of our approach by using benchmark datasets and a real-world application to materials science data.

The goal of text generation models is to fit the underlying real probability distribution of text. For performance evaluation, quality and diversity metrics are usually applied. However, it is still not clear to what extend can the quality-diversity evaluation reflect the distribution-fitting goal. In this paper, we try to reveal such relation in a theoretical approach. We prove that under certain conditions, a linear combination of quality and diversity constitutes a divergence metric between the generated distribution and the real distribution. We also show that the commonly used BLEU/Self-BLEU metric pair fails to match any divergence metric, thus propose CR/NRR as a substitute for quality/diversity metric pair.

To analyze high-dimensional and complex data in the real world, deep generative models such as variational autoencoder (VAE) embed data in a reduced dimensional latent space and learn the probabilistic model in the latent space. However, they struggle to reproduce the probability distribution function (PDF) in the input space from that of the latent space accurately. If the embedding were isometric, this problem can be solved since PDFs in both spaces become proportional. To achieve isometric property, we propose Rate-Distortion Optimization guided autoencoder inspired by orthonormal transform coding. We show our method has the following properties: (i) the columns of the Jacobian matrix between two spaces is constantly-scaled orthonormal system and enable to embed data in latent space isometrically; (ii) the PDF of the latent space is proportional to that of the data observation space. Furthermore, our method outperforms state-of-the-art methods in unsupervised anomaly detection with four public datasets.

Over-parameterization is ubiquitous nowadays in training neural networks to benefit both optimization in seeking global optima and generalization in reducing prediction error. However, compressive networks are desired in many real world ap- plications and direct training of small networks may be trapped in local optima. In this paper, in- stead of pruning or distilling over-parameterized models to compressive ones, we propose a new approach based on differential inclusions of in- verse scale spaces. Specifically, it generates a family of models from simple to complex ones that couples a pair of parameters to simultaneously train over-parameterized deep models and structural sparsity on weights of fully connected and convolutional layers. Such a differential inclusion scheme has a simple discretization, pro- posed as Deep structurally splitting Linearized Bregman Iteration (DessiLBI), whose global convergence analysis in deep learning is established that from any initializations, algorithmic iterations converge to a critical point of empirical risks. Experimental evidence shows that DessiLBI achieve comparable and even better performance than the competitive optimizers in exploring the structural sparsity of several widely used backbones on the benchmark datasets. Remarkably, with early stopping, DessiLBI unveils “winning tickets” in early epochs: the effective sparse structure with comparable test accuracy to fully …

In weakly supervised learning, unbiased risk estimator(URE) is a powerful tool for training classifiers when training and test data are drawn from different distributions. Nevertheless, UREs lead to overfitting in many problem settings when the models are complex like deep networks. In this paper, we investigate reasons for such overfitting by studying a weakly supervised problem called learning with complementary labels. We argue the quality of gradient estimation matters more in risk minimization. Theoretically, we show that a URE gives an unbiased gradient estimator(UGE). Practically, however, UGEs may suffer from huge variance, which causes empirical gradients to be usually far away from true gradients during minimization. To this end, we propose a novel surrogate complementary loss(SCL) framework that trades zero bias with reduced variance and makes empirical gradients more aligned with true gradients in the direction. Thanks to this characteristic, SCL successfully mitigates the overfitting issue and improves URE-based methods.

A longstanding problem for Deep Neural Networks (DNNs) is understanding their puzzling ability to generalize well. We approach this problem through the unconventional angle of \textit{cognitive abstraction mechanisms}, drawing inspiration from recent neuroscience work, allowing us to define the Cognitive Neural Activation metric (CNA) for DNNs, which is the correlation between information complexity (entropy) of given input and the concentration of higher activation values in deeper layers of the network. The CNA is highly predictive of generalization ability, outperforming norm-and-sharpness-based generalization metrics on an extensive evaluation of close to 200 network instances comprising a breadth of dataset-architecture combinations, especially in cases where additive noise is present and/or training labels are corrupted. These strong empirical results show the usefulness of the CNA as a generalization metric and encourage further research on the connection between information complexity and representations in the deeper layers of networks in order to better understand the generalization capabilities of DNNs.

Quantization based techniques are the current state-of-the-art for scaling maximum inner product search to massive databases. Traditional approaches to quantization aim to minimize the reconstruction error of the database points. Based on the observation that for a given query, the database points that have the largest inner products are more relevant, we develop a family of anisotropic quantization loss functions. Under natural statistical assumptions, we show that quantization with these loss functions leads to a new variant of vector quantization that more greatly penalizes the parallel component of a datapoint's residual relative to its orthogonal component. The proposed approach, whose implementation is open-source, achieves state-of-the-art results on the public benchmarks available at ann-benchmarks.com.

Off-policy reinforcement learning (RL) using a fixed offline dataset of logged interactions is an important consideration in real world applications. This paper studies offline RL using the DQN replay dataset comprising the entire replay experience of a DQN agent on 60 Atari 2600 games. We demonstrate that recent off-policy deep RL algorithms, even when trained solely on this fixed dataset, outperform the fully trained DQN agent. To enhance generalization in the offline setting, we present Random Ensemble Mixture (REM), a robust Q-learning algorithm that enforces optimal Bellman consistency on random convex combinations of multiple Q-value estimates. Offline REM trained on the DQN replay dataset surpasses strong RL baselines. Ablation studies highlight the role of offline dataset size and diversity as well as the algorithm choice in our positive results. Overall, the results here present an optimistic view that robust RL algorithms trained on sufficiently large and diverse offline datasets can lead to high quality policies. The DQN replay dataset can serve as an offline RL benchmark and is open-sourced.

Learning algorithms are often used in conjunction with expert decision makers in practical scenarios, however this fact is largely ignored when designing these algorithms. In this paper we explore how to learn predictors that can either predict or choose to defer the decision to a downstream expert. Given only samples of the expert's decisions, we give a procedure based on learning a classifier and a rejector and analyze it theoretically. Our approach is based on a novel reduction to cost sensitive learning where we give a consistent surrogate loss for cost sensitive learning that generalizes the cross entropy loss. We show the effectiveness of our approach on a variety of experimental tasks.

We introduce a class of auto-encoder neural networks tailored to data from the natural exponential family (e.g., count data). The architectures are inspired by the problem of learning the filters in a convolutional generative model with sparsity constraints, often referred to as convolutional dictionary learning (CDL). Our work is the first to combine ideas from convolutional generative models and deep learning for data that are naturally modeled with a non-Gaussian distribution (e.g., binomial and Poisson). This perspective provides us with a scalable and flexible framework that can be re-purposed for a wide range of tasks and assumptions on the generative model. Specifically, the iterative optimization procedure for solving CDL, an unsupervised task, is mapped to an unfolded and constrained neural network, with iterative adjustments to the inputs to account for the generative distribution. We also show that the framework can easily be extended for discriminative training, appropriate for a supervised task. We demonstrate 1) that fitting the generative model to learn, in an unsupervised fashion, the latent stimulus that underlies neural spiking data leads to better goodness-of-fit compared to other baselines, 2) competitive performance compared to state-of-the-art algorithms for supervised Poisson image denoising, with significantly fewer parameters, and 3) gradient …

This paper proposes a new loss function for linear autoencoders (LAEs) and analytically identifies the structure of the associated loss surface. Optimizing the conventional Mean Square Error (MSE) loss results in a decoder matrix that spans the principal subspace of the sample covariance of the data, but, owing to an invariance that cancels out in the global map, it will fail to identify the exact eigenvectors. We show here that our proposed loss function eliminates this issue, so the decoder converges to the exact ordered unnormalized eigenvectors of the sample covariance matrix. We characterize the full structure of the new loss landscape by establishing an analytical expression for the set of all critical points, showing that it is a subset of critical points of MSE, and that all local minima are still global. Specifically, the invariant global minima under MSE are shown to become saddle points under the new loss. Additionally, the computational complexity of the loss and its gradients are the same as MSE and, thus, the new loss is not only of theoretical importance but is of practical value, e.g., for low-rank approximation.

The field of algorithms has seen a push for fairness, or the removal of inherent bias, in recent history. In data summarization, where a much smaller subset of a data set is chosen to represent the whole of the data, fairness can be introduced by guaranteeing each "demographic group" a specific portion of the representative subset. Specifically, this paper examines this fair variant of the k-centers problem, where a subset of the data with cardinality k is chosen to minimize distance to the rest of the data. Previous papers working on this problem presented both a 3-approximation algorithm with a super-linear runtime and a linear-time algorithm whose approximation factor is exponential in the number of demographic groups. This paper combines the best of each algorithm by presenting a linear-time algorithm with a guaranteed 3-approximation factor and provides empirical evidence of both the algorithm's runtime and effectiveness.

Weak supervision is a popular method for building machine learning models without relying on ground truth annotations. Instead, it generates probabilistic training labels by estimating the accuracies of multiple noisy labeling sources (e.g., heuristics, crowd workers). Existing approaches use latent variable estimation to model the noisy sources, but these methods can be computationally expensive, scaling superlinearly in the data. In this work, we show that, for a class of latent variable models highly applicable to weak supervision, we can find a closed-form solution to model parameters, obviating the need for iterative solutions like stochastic gradient descent (SGD). We use this insight to build FlyingSquid, a weak supervision framework that runs orders of magnitude faster than previous weak supervision approaches and requires fewer assumptions. In particular, we prove bounds on generalization error without assuming that the latent variable model can exactly parameterize the underlying data distribution. Empirically, we validate FlyingSquid on benchmark weak supervision datasets and find that it achieves the same or higher quality compared to previous approaches without the need to tune an SGD procedure, recovers model parameters 170 times faster on average, and enables new video analysis and online learning applications.

Graph generation techniques are increasingly being adopted for drug discovery. Previous graph generation approaches have utilized relatively small molecular building blocks such as atoms or simple cycles, limiting their effectiveness to smaller molecules. Indeed, as we demonstrate, their performance degrades significantly for larger molecules. In this paper, we propose a new hierarchical graph encoder-decoder that employs significantly larger and more flexible graph motifs as basic building blocks. Our encoder produces a multi-resolution representation for each molecule in a fine-to-coarse fashion, from atoms to connected motifs. Each level integrates the encoding of constituents below with the graph at that level. Our autoregressive coarse-to-fine decoder adds one motif at a time, interleaving the decision of selecting a new motif with the process of resolving its attachments to the emerging molecule. We evaluate our model on multiple molecule generation tasks, including polymers, and show that our model significantly outperforms previous state-of-the-art baselines.

We propose a novel approach to filter bank learning for time-series by considering spectral decompositions of signals defined as a Group Transform. This framework allows us to generalize classical time-frequency transformations such as the Wavelet Transform, and to efficiently learn the representation of signals. While the creation of the wavelet transform filter-bank relies on affine transformations of a mother filter, our approach allows for non-linear transformations. The transformations induced by such maps enable us to span a larger class of signal representations, from wavelet to chirplet-like filters. We propose a parameterization of such a non-linear map such that its sampling can be optimized for a specific task and signal. The Learnable Group Transform can be cast into a Deep Neural Network. The experiments on diverse time-series datasets demonstrate the expressivity of this framework, which competes with state-of-the-art performances.

We study the problem of learning opinions in social networks. The learner observes the states of some sample nodes from a social network, and tries to infer the states of other nodes, based on the structure of the network. We show that sample-efficient learning is impossible when the network exhibits strong noise, and give a polynomial-time algorithm for the problem with nearly optimal sample complexity when the network is sufficiently stable.

Bias in machine learning has manifested injustice in several areas, such as medicine, hiring, and criminal justice. In response, computer scientists have developed myriad definitions of fairness to correct this bias in fielded algorithms. While some definitions are based on established legal and ethical norms, others are largely mathematical. It is unclear whether the general public agrees with these fairness definitions, and perhaps more importantly, whether they understand these definitions. We take initial steps toward bridging this gap between ML researchers and the public, by addressing the question: does a lay audience understand a basic definition of ML fairness? We develop a metric to measure comprehension of three such definitions--demographic parity, equal opportunity, and equalized odds. We evaluate this metric using an online survey, and investigate the relationship between comprehension and sentiment, demographics, and the definition itself.

In this paper, we consider matrix completion with absolute deviation loss and obtain an estimator of the median matrix. Despite several appealing properties of median, the non-smooth absolute deviation loss leads to computational challenge for large-scale data sets which are increasingly common among matrix completion problems. A simple solution to large-scale problems is parallel computing. However, embarrassingly parallel fashion often leads to inefficient estimators. Based on the idea of pseudo data, we propose a novel refinement step, which turns such inefficient estimators into a rate (near-)optimal matrix completion procedure. The refined estimator is an approximation of a regularized least median estimator, and therefore not an ordinary regularized empirical risk estimator. This leads to a non-standard analysis of asymptotic behaviors. Empirical results are also provided to confirm the effectiveness of the proposed method.

We propose an efficient algorithm for solving group synchronization under high levels of corruption and noise, while we focus on rotation synchronization. We first describe our recent theoretically guaranteed message passing algorithm that estimates the corruption levels of the measured group ratios. We then propose a novel reweighted least squares method to estimate the group elements, where the weights are initialized and iteratively updated using the estimated corruption levels. We demonstrate the superior performance of our algorithm over state-of-the-art methods for rotation synchronization using both synthetic and real data.

Submodular function minimization is well studied, and existing algorithms solve it exactly or up to arbitrary accuracy. However, in many applications, such as structured sparse learning or batch Bayesian optimization, the objective function is not exactly submodular, but close. In this case, no theoretical guarantees exist. Indeed, submodular minimization algorithms rely on intricate connections between submodularity and convexity. We show how these relations can be extended to obtain approximation guarantees for minimizing non-submodular functions, characterized by how close the function is to submodular. We also extend this result to noisy function evaluations. Our approximation results are the first for minimizing non-submodular functions, and are optimal, as established by our matching lower bound.

The families of f-divergences (e.g. the Kullback-Leibler divergence) and Integral Probability Metrics (e.g. total variation distance or maximum mean discrepancies) are commonly used in optimization and estimation. In this work, we systematically study the relationship between these two families from the perspective of convex duality. Starting from a tight variational representation of the f-divergence, we derive a generalization of the moment generating function, which we show exactly characterizes the best lower bound of the f-divergence as a function of a given IPM. Using this characterization, we obtain new bounds on IPMs defined by classes of unbounded functions, while also recovering in a unified manner well-known results for bounded and subgaussian functions (e.g. Pinsker's inequality and Hoeffding's lemma).

We consider the problem of estimating a ranking on a set of items from noisy pairwise comparisons given item features. We address the fact that pairwise comparison data often reflects irrational choice, e.g. intransitivity. Our key observation is that two items compared in isolation from other items may be compared based on only a salient subset of features. Formalizing this framework, we propose the salient feature preference model and prove a finite sample complexity result for learning the parameters of our model and the underlying ranking with maximum likelihood estimation. We also provide empirical results that support our theoretical bounds and illustrate how our model explains systematic intransitivity. Finally we demonstrate strong performance of maximum likelihood estimation of our model on both synthetic data and two real data sets: the UT Zappos50K data set and comparison data about the compactness of legislative districts in the US.

We consider the problem of learning Markov Random Fields (including the prototypical example, the Ising model) under the constraint of differential privacy. Our learning goals include both \emph{structure learning}, where we try to estimate the underlying graph structure of the model, as well as the harder goal of \emph{parameter learning}, in which we additionally estimate the parameter on each edge. We provide algorithms and lower bounds for both problems under a variety of privacy constraints -- namely pure, concentrated, and approximate differential privacy. While non-privately, both learning goals enjoy roughly the same complexity, we show that this is not the case under differential privacy. In particular, only structure learning under approximate differential privacy maintains the non-private logarithmic dependence on the dimensionality of the data, while a change in either the learning goal or the privacy notion would necessitate a polynomial dependence. As a result, we show that the privacy constraint imposes a strong separation between these two learning problems in the high-dimensional data regime.

As machine learning black boxes are increasingly being deployed in real-world applications, there has been a growing interest in developing post hoc explanations that summarize the behaviors of these black boxes. However, existing algorithms for generating such explanations have been shown to lack stability and robustness to distribution shifts. We propose a novel framework for generating robust and stable explanations of black box models based on adversarial training. Our framework optimizes a minimax objective that aims to construct the highest fidelity explanation with respect to the worst-case over a set of adversarial perturbations. We instantiate this algorithm for explanations in the form of linear models and decision sets by devising the required optimization procedures. To the best of our knowledge, this work makes the first attempt at generating post hoc explanations that are robust to a general class of adversarial perturbations that are of practical interest. Experimental evaluation with real-world and synthetic datasets demonstrates that our approach substantially improves robustness of explanations without sacrificing their fidelity on the original data distribution.

We study the Cross-Entropy Method (CEM) for the non-convex optimization of a continuous and parameterized objective function and introduce a differentiable variant that enables us to differentiate the output of CEM with respect to the objective function's parameters. In the machine learning setting this brings CEM inside of the end-to-end learning pipeline where this has otherwise been impossible. We show applications in a synthetic energy-based structured prediction task and in non-convex continuous control. In the control setting we show how to embed optimal action sequences into a lower-dimensional space. This enables us to use policy optimization to fine-tune modeling components by differentiating through the CEM-based controller.

It is increasingly common to encounter data in the form of cross-sectional population measurements over time, particularly in biomedical settings. Recent attempts to model individual trajectories from this data use optimal transport to create pairwise matchings between time points. However, these methods cannot model non-linear paths common in many underlying dynamic systems. We establish a link between continuous normalizing flows and dynamic optimal transport to model the expected paths of points over time. Continuous normalizing flows are generally under constrained, as they are allowed to take an arbitrary path from the source to the target distribution. We present {\em TrajectoryNet}, which controls the continuous paths taken between distributions. We show how this is particularly applicable for studying cellular dynamics in data from single-cell RNA sequencing (scRNA-seq) technologies, and that TrajectoryNet improves upon recently proposed static optimal transport-based models that can be used for interpolating cellular distributions.

Generative flows are promising tractable models for density modeling that define probabilistic distributions with invertible transformations. However, tractability imposes architectural constraints on generative flows. In this work, we study a previously overlooked constraint that all the intermediate representations must have the same dimensionality with the data due to invertibility, limiting the width of the network. We propose VFlow to tackle this constraint on dimensionality. VFlow augments the data with extra dimensions and defines a maximum evidence lower bound (ELBO) objective for estimating the distribution of augmented data jointly with the variational data augmentation distribution. Under mild assumptions, we show that the maximum ELBO solution of VFlow is always better than the original maximum likelihood solution. For image density modeling on the CIFAR-10 dataset, VFlow achieves a new state-of-the-art 2.98 bits per dimension.

We present and investigate a novel application domain for deep reinforcement learning (RL): droplet routing on digital microfluidic biochips (DMFBs). A DMFB, composed of a two-dimensional electrode array, manipulates discrete fluid droplets to automatically execute biochemical protocols such as high-throughput DNA sequencing and point-of-care clinical diagnosis. However, a major concern associated with the use of DMFBs is that electrodes in a biochip can degrade over time. Droplet-transportation operations associated with the degraded electrodes can fail, thereby compromising the integrity of the bioassay outcome. While it is not feasible to detect the degradation of an electrode by simply examining its appearance, we show that casting droplet transportation as an RL problem enables the training of deep network policies to capture the underlying health conditions of electrodes and to provide reliable fluidic operations. We propose a new RL-based droplet-routing flow that can be used for various sizes of DMFBs, and demonstrate reliable execution of an epigenetic bioassay with the RL droplet router on a fabricated DMFB. To facilitate further research, we also present a simulation environment based on the OpenAI Gym Interface for RL-guided droplet-routing problems on DMFBs.

We develop a generic data-driven method for estimator selection in off-policy policy evaluation settings. We establish a strong performance guarantee for the method, showing that it is competitive with the oracle estimator, up to a constant factor. Via in-depth case studies in contextual bandits and reinforcement learning, we demonstrate the generality and applicability of the method. We also perform comprehensive experiments, demonstrating the empirical efficacy of our approach and comparing with related approaches. In both case studies, our method compares favorably with existing methods.

The accuracy of modern machine learning algorithms deteriorates severely on adversarially manipulated test data. Optimal adversarial risk quantifies the best error rate of any classifier in the presence of adversaries, and optimal adversarial classifiers are sought that minimize adversarial risk. In this paper, we investigate the optimal adversarial risk and optimal adversarial classifiers from an optimal transport perspective. We present a new and simple approach to show that the optimal adversarial risk for binary classification with 0 − 1 loss function is completely characterized by an optimal transport cost between the probability distributions of the two classes, for a suitably defined cost function. We propose a novel coupling strategy that achieves the optimal transport cost for several univariate distributions like Gaussian, uniform and triangular. Using the optimal couplings, we obtain the optimal adversarial classifiers in these settings and show how they differ from optimal classifiers in the absence of adversaries. Based on our analysis, we evaluate algorithm-independent fundamental limits on adversarial risk for CIFAR-10, MNIST, Fashion-MNIST and SVHN datasets, and Gaussian mixtures based on them.

Derivative-free optimization (DFO) has recently gained a lot of momentum in machine learning, spawning interest in the community to design faster methods for problems where gradients are not accessible. While some attention has been given to the concept of acceleration in the DFO literature, existing stochastic algorithms for objective functions with a finite-sum structure have not been shown theoretically to achieve an accelerated rate of convergence. Algorithms that use acceleration in such a setting are prone to instabilities, making it difficult to reach convergence. In this work, we exploit the finite-sum structure of the objective in order to design a variance-reduced DFO algorithm that provably yields acceleration. We prove rates of convergence for both smooth convex and strongly-convex finite-sum objective functions. Finally, we validate our theoretical results empirically on several tasks and datasets.

We design and analyze CascadeBAI, an algorithm for finding the best set of K items, also called an arm, within the framework of cascading bandits. An upper bound on the time complexity of CascadeBAI is derived by overcoming a crucial analytical challenge, namely, that of probabilistically estimating the amount of available feedback at each step. To do so, we define a new class of random variables (r.v.'s) which we term as left-sided sub-Gaussian r.v.'s; these are r.v.'s whose cumulant generating functions (CGFs) can be bounded by a quadratic only for non-positive arguments of the CGFs. This enables the application of a sufficiently tight Bernstein-type concentration inequality. We show, through the derivation of a lower bound on the time complexity, that the performance of CascadeBAI is optimal in some practical regimes. Finally, extensive numerical simulations corroborate the efficacy of CascadeBAI as well as the tightness of our upper bound on its time complexity.

Causal effect identifiability is concerned with establishing the effect of intervening on a set of variables on another set of variables from observational or interventional distributions under causal assumptions that are usually encoded in the form of a causal graph. Most of the results of this literature implicitly assume that every variable modeled in the graph is measured in the available distributions. In practice, however, the data collections of the different studies considered do not measure the same variables, consistently. In this paper, we study the causal effect identifiability problem when the available distributions encompass different sets of variables, which we refer to as identification under partial-observability. We study a number of properties of the factors that comprise a causal effect under various levels of abstraction, and then characterize the relationship between them with respect to their status relative to the identification of a targeted intervention. We establish a sufficient graphical criterion for determining whether the effects are identifiable from partially-observed distributions. Finally, building on these graphical properties, we develop an algorithm that returns a formula for a causal effect in terms of the available distributions.

In many applications areas---lending, education, and online recommenders, for example---fairness and equity concerns emerge when a machine learning system interacts with a dynamically changing environment to produce both immediate and long-term effects for individuals and demographic groups. We discuss causal directed acyclic graphs (DAGs) as a unifying framework for the recent literature on fairness in such dynamical systems. We show that this formulation affords several new directions of inquiry to the modeler, where sound causal assumptions can be expressed and manipulated. We emphasize the importance of computing interventional quantities in the dynamical fairness setting, and show how causal assumptions enable simulation (when environment dynamics are known) and estimation by adjustment (when dynamics are unknown) of intervention on short- and long-term outcomes, at both the group and individual levels.

Convolutional Neural Networks (CNNs) are typically constructed by stacking multiple building blocks, each of which contains a normalization layer such as batch normalization (BN) and a rectified linear function such as ReLU. However, this work shows that the combination of normalization and rectified linear function leads to inhibited channels, which have small magnitude and contribute little to the learned feature representation, impeding the generalization ability of CNNs. Unlike prior arts that simply removed the inhibited channels, we propose to ``wake them up'' during training by designing a novel neural building block, termed Channel Equilibrium (CE) block, which enables channels at the same layer to contribute equally to the learned representation. We show that CE is able to prevent inhibited channels both empirically and theoretically. CE has several appealing benefits. (1) It can be integrated into many advanced CNN architectures such as ResNet and MobileNet, outperforming their original networks. (2) CE has an interesting connection with the Nash Equilibrium, a well-known solution of a non-cooperative game. (3) Extensive experiments show that CE achieves state-of-the-art performance on various challenging benchmarks such as ImageNet and COCO.

Solving large complex partial differential equations (PDEs), such as those that arise in computational fluid dynamics (CFD), is a computationally expensive process. This has motivated the use of deep learning approaches to approximate the PDE solutions, yet the simulation results predicted from these approaches typically do not generalize well to truly novel scenarios. In this work, we develop a hybrid (graph) neural network that combines a traditional graph convolutional network with an embedded differentiable fluid dynamics simulator inside the network itself. By combining an actual CFD simulator (run on a much coarser resolution representation of the problem) with the graph network, we show that we can both generalize well to new situations and benefit from the substantial speedup of neural network CFD predictions, while also substantially outperforming the coarse CFD simulation alone.

We provide the first non-asymptotic analysis for finding stationary points of nonsmooth, nonconvex functions. In particular, we study the class of Hadamard semi-differentiable functions, perhaps the largest class of nonsmooth functions for which the chain rule of calculus holds. This class contains important examples such as ReLU neural networks and others with non-differentiable activation functions. First, we show that finding an epsilon-stationary point with first-order methods is impossible in finite time. Therefore, we introduce the notion of (delta, epsilon)-stationarity, a generalization that allows for a point to be within distance delta of an epsilon-stationary point and reduces to epsilon-stationarity for smooth functions. We propose a series of randomized first-order methods and analyze their complexity of finding a (delta, epsilon)-stationary point. Furthermore, we provide a lower bound and show that our stochastic algorithm has min-max optimal dependence on delta. Empirically, our methods perform well for training ReLU neural networks.

Data containing human or social attributes may over- or under-represent groups with respect to salient social attributes such as gender or race, which can lead to biases in downstream applications. This paper presents an algorithmic framework that can be used as a data preprocessing method towards mitigating such bias. Unlike prior work, it can efficiently learn distributions over large domains, controllably adjust the representation rates of protected groups and achieve target fairness metrics such as statistical parity, yet remains close to the empirical distribution induced by the given dataset. Our approach leverages the principle of maximum entropy – amongst all distributions satisfying a given set of constraints, we should choose the one closest in KL-divergence to a given prior. While maximum entropy distributions can succinctly encode distributions over large domains, they can be difficult to compute. Our main contribution is an instantiation of this framework for our set of constraints and priors, which encode our bias mitigation goals, and that runs in time polynomial in the dimension of the data. Empirically, we observe that samples from the learned distribution have desired representation rates and statistical rates, and when used for training a classifier incurs only a slight loss in accuracy …

Recent years have witnessed intensive research interests on training deep neural networks (DNNs) more efficiently by quantization-based compression methods, which facilitate DNNs training in two ways: (1) activations are quantized to shrink the memory consumption, and (2) gradients are quantized to decrease the communication cost. However, existing methods mostly use a uniform mechanism that quantizes the values evenly. Such a scheme may cause a large quantization variance and slow down the convergence in practice.

In this work, we introduce TinyScript, which applies a non-uniform quantization algorithm to both activations and gradients. TinyScript models the original values by a family of Weibull distributions and searches for ''quantization knobs'' that minimize quantization variance. We also discuss the convergence of the non-uniform quantization algorithm on DNNs with varying depths, shedding light on the number of bits required for convergence. Experiments show that TinyScript always obtains lower quantization variance, and achieves comparable model qualities against full precision training using 1-2 bits less than the uniform-based counterpart.

Gaussian Process Factor Analysis (GPFA) has been broadly applied to the problem of identifying smooth, low-dimensional temporal structure underlying large-scale neural recordings. However, spike trains are non-Gaussian, which motivates combining GPFA with discrete observation models for binned spike count data. The drawback to this approach is that GPFA priors are not conjugate to count model likelihoods, which makes inference challenging. Here we address this obstacle by introducing a fast, approximate inference method for non-conjugate GPFA models. Our approach uses orthogonal second-order polynomials to approximate the nonlinear terms in the non-conjugate log-likelihood, resulting in a method we refer to as polynomial approximate log-likelihood (PAL) estimators. This approximation allows for accurate closed-form evaluation of marginal likelihoods and fast numerical optimization for parameters and hyperparameters. We derive PAL estimators for GPFA models with binomial, Poisson, and negative binomial observations and find the PAL estimation is highly accurate, and achieves faster convergence times compared to existing state-of-the-art inference methods. We also find that PAL hyperparameters can provide sensible initialization for black box variational inference (BBVI), which improves BBVI accuracy. We demonstrate that PAL estimators achieve fast and accurate extraction of latent structure from multi-neuron spike train data.

Dataset replication is a useful tool for assessing whether improvements in test accuracy on a specific benchmark correspond to improvements in models' ability to generalize reliably. In this work, we present unintuitive yet significant ways in which standard approaches to dataset replication introduce statistical bias, skewing the resulting observations. We study ImageNet-v2, a replication of the ImageNet dataset on which models exhibit a significant (11-14%) drop in accuracy, even after controlling for selection frequency, a human-in-the-loop measure of data quality. We show that after remeasuring selection frequencies and correcting for statistical bias, only an estimated 3.6% of the original 11.7% accuracy drop remains unaccounted for. We conclude with concrete recommendations for recognizing and avoiding bias in dataset replication. Code for our study is publicly available: https://git.io/data-rep-analysis.

Efficient exploration remains a challenging problem in reinforcement learning, especially for those tasks where rewards from environments are sparse. In this work, we introduce an exploration approach based on a novel implicit generative modeling algorithm to estimate a Bayesian uncertainty of the agent's belief of the environment dynamics. Each random draw from our generative model is a neural network that instantiates the dynamic function, hence multiple draws would approximate the posterior, and the variance in the predictions based on this posterior is used as an intrinsic reward for exploration. We design a training algorithm for our generative model based on the amortized Stein Variational Gradient Descent. In experiments, we demonstrate the effectiveness of this exploration algorithm in both pure exploration tasks and a downstream task, comparing with state-of-the-art intrinsic reward-based exploration approaches, including two recent approaches based on an ensemble of dynamic models. In challenging exploration tasks, our implicit generative model consistently outperforms competing approaches regarding data efficiency in exploration.

How can multiple distributed entities train a shared deep net on their private data while protecting data privacy? This paper introduces InstaHide, a simple encryption of training images. Encrypted images can be used in standard deep learning pipelines (PyTorch, Federated Learning etc.) with no additional setup or infrastructure. The encryption has a minor effect on test accuracy (unlike differential privacy).

Encryption consists of mixing the image with a set of other images (in the sense of Mixup data augmentation technique (Zhang et al., 2018)) followed by applying a random pixel-wise mask on the mixed image. Other contributions of this paper are: (a) Use of large public dataset of images (e.g. ImageNet) for mixing during encryption; this improves security. (b) Experiments demonstrating effectiveness in protecting privacy against known attacks while preserving model accuracy. (c) Theoretical analysis showing that successfully attacking privacy requires attackers to solve a difficult computational problem. (d) Demonstration that Mixup alone is insecure as (contrary to recent proposals), by showing some efficient attacks. (e) Release of a challenge dataset to allow design of new attacks.

Individuals, or organizations, cooperate with or compete against one another in a wide range of practical situations. Such strategic interactions are often modeled as games played on networks, where an individual's payoff depends not only on her action but also on that of her neighbors. The current literature has largely focused on analyzing the characteristics of network games in the scenario where the structure of the network, which is represented by a graph, is known beforehand. It is often the case, however, that the actions of the players are readily observable while the underlying interaction network remains hidden. In this paper, we propose two novel frameworks for learning, from the observations on individual actions, network games with linear-quadratic payoffs, and in particular, the structure of the interaction network. Our frameworks are based on the Nash equilibrium of such games and involve solving a joint optimization problem for the graph structure and the individual marginal benefits. Both synthetic and real-world experiments demonstrate the effectiveness of the proposed frameworks, which have theoretical as well as practical implications for understanding strategic interactions in a network environment.

Learning controllable and generalizable representation of multivariate data with desired structural properties remains a fundamental problem in machine learning. In this paper, we present a novel framework for learning generative models with various underlying structures in the latent space. We represent the inductive bias in the form of mask variables to model the dependency structure in the graphical model and extend the theory of multivariate information bottleneck~\cite{mib} to enforce it. Our model provides a principled approach to learn a set of semantically meaningful latent factors that reflect various types of desired structures like capturing correlation or encoding invariance, while also offering the flexibility to automatically estimate the dependency structure from data. We show that our framework unifies many existing generative models and can be applied to a variety of tasks, including multi-modal data modeling, algorithmic fairness, and out-of-distribution generalization.

Designing efficient algorithms for combinatorial optimization appears ubiquitously in various scientific fields. Recently, deep reinforcement learning (DRL) frameworks have gained considerable attention as a new approach: they can automate the design of a solver while relying less on sophisticated domain knowledge of the target problem. However, the existing DRL solvers determine the solution using a number of stages proportional to the number of elements in the solution, which severely limits their applicability to large-scale graphs. In this paper, we seek to resolve this issue by proposing a novel DRL scheme, coined learning what to defer (LwD), where the agent adaptively shrinks or stretch the number of stages by learning to distribute the element-wise decisions of the solution at each stage. We apply the proposed framework to the maximum independent set (MIS) problem, and demonstrate its significant improvement over the current state-of-the-art DRL scheme. We also show that LwD can outperform the conventional MIS solvers on large-scale graphs having millions of vertices, under a limited time budget.

This paper searches for the optimal neural architecture by minimizing a proxy of validation loss. Existing neural architecture search (NAS) methods used to discover the optimal neural architecture that best fits the validation examples given the up-to-date network weights. However, back propagation with a number of validation examples could be time consuming, especially when it needs to be repeated many times in NAS. Though these intermediate validation results are invaluable, they would be wasted if we cannot use them to predict the future from the past. In this paper, we propose to approximate the validation loss landscape by learning a mapping from neural architectures to their corresponding validate losses. The optimal neural architecture thus can be easily identified as the minimum of this proxy validation loss landscape. A novel sampling strategy is further developed for an efficient approximation of the loss landscape. Theoretical analysis indicates that our sampling strategy can reach a lower error rate and a lower label complexity compared with a uniform sampling. Experimental results on benchmarks demonstrate that the architecture searched by the proposed algorithm can achieve a satisfactory accuracy with less time cost.

When training an estimator such as a neural network for tasks like image denoising, it is often preferred to train one estimator and apply it to all noise levels. The de facto training protocol to achieve this goal is to train the estimator with noisy samples whose noise levels are uniformly distributed across the range of interest. However, why should we allocate the samples uniformly? Can we have more training samples that are less noisy, and fewer samples that are more noisy? What is the optimal distribution? How do we obtain such a distribution? The goal of this paper is to address this training sample distribution problem from a minimax risk optimization perspective. We derive a dual ascent algorithm to determine the optimal sampling distribution of which the convergence is guaranteed as long as the set of admissible estimators is closed and convex. For estimators with non-convex admissible sets such as deep neural networks, our dual formulation converges to a solution of the convex relaxation. We discuss how the algorithm can be implemented in practice. We evaluate the algorithm on linear estimators and deep networks.

The goal of universal machine translation is to learn to translate between any pair of languages, given pairs of translated documents for \emph{some} of these languages. Despite impressive empirical results and an increasing interest in massively multilingual models, theoretical analysis on translation errors made by such universal machine translation models is only nascent. In this paper, we take one step towards better understanding of universal machine translation by first proving an impossibility theorem in the general case. In particular, we derive a lower bound on the translation error in the many-to-one translation setting, which shows that any algorithm aiming to learn shared sentence representations among multiple language pairs has to make a large translation error on at least one of the translation tasks, if no assumption on the structure of the languages is made. On the positive side, we show that if the documents follow a natural encoder-decoder generative process, then we can expect a natural notion of ``generalization'': a linear number of pairs, rather than quadratic, suffices. Our theory also explains what kinds of connection graphs between pairs of languages are better suited: ones with longer paths result in worse sample complexity in terms of the total number of …

We study Nesterov's accelerated gradient method with constant step-size and momentum parameters in the stochastic approximation setting (unbiased gradients with bounded variance) and the finite-sum setting (where randomness is due to sampling mini-batches). To build better insight into the behavior of Nesterov's method in stochastic settings, we focus throughout on objectives that are smooth, strongly-convex, and twice continuously differentiable. In the stochastic approximation setting, Nesterov's method converges to a neighborhood of the optimal point at the same accelerated rate as in the deterministic setting. Perhaps surprisingly, in the finite-sum setting, we prove that Nesterov's method may diverge with the usual choice of step-size and momentum, unless additional conditions on the problem related to conditioning and data coherence are satisfied. Our results shed light as to why Nesterov's method may fail to converge or achieve acceleration in the finite-sum setting.

In the current era of personalized recommendation, one major interest is to develop an optimal individualized decision rule that assigns individuals with the best treatment option according to their covariates. Estimation of optimal decision rules (ODR) has been extensively investigated recently, however, at present, no testing procedure is proposed to verify whether these ODRs are significantly better than the naive decision rule that always assigning individuals to a fixed treatment option. In this paper, we propose a testing procedure for detecting the existence of an ODR that is better than the naive decision rule under the randomized trials. We construct the proposed test based on the difference of estimated value functions using the augmented inverse probability weighted method. The asymptotic distributions of the proposed test statistic under the null and local alternative hypotheses are established. Based on the established asymptotic distributions, we further develop a sample size calculation formula for testing the existence of an ODR in designing A/B tests. Extensive simulations and a real data application to a schizophrenia clinical trial data are conducted to demonstrate the empirical validity of the proposed methods.

We propose a simple but effective data-driven channel pruning algorithm, which compresses deep neural networks in a differentiable way by exploiting the characteristics of operations. The proposed approach makes a joint consideration of batch normalization (BN) and rectified linear unit (ReLU) for channel pruning; it estimates how likely the two successive operations deactivate each feature map and prunes the channels with high probabilities. To this end, we learn differentiable masks for individual channels and make soft decisions throughout the optimization procedure, which facilitates to explore larger search space and train more stable networks. The proposed framework enables us to identify compressed models via a joint learning of model parameters and channel pruning without an extra procedure of fine-tuning. We perform extensive experiments and achieve outstanding performance in terms of the accuracy of output networks given the same amount of resources when compared with the state-of-the-art methods.

The use of black-box optimization for the design of new biological sequences is an emerging research area with potentially revolutionary impact. The cost and latency of wet-lab experiments requires methods that find good sequences in few experimental rounds of large batches of sequences --- a setting that off-the-shelf black-box optimization methods are ill-equipped to handle. We find that the performance of existing methods varies drastically across optimization tasks, posing a significant obstacle to real-world applications. To improve robustness, we propose Population-Based Black-Box Optimization (P3BO), which generates batches of sequences by sampling from an ensemble of methods. The number of sequences sampled from any method is proportional to the quality of sequences it previously proposed, allowing P3BO to combine the strengths of individual methods while hedging against their innate brittleness. Adapting the hyper-parameters of each of the methods online using evolutionary optimization further improves performance. Through extensive experiments on in-silico optimization tasks, we show that P3BO outperforms any single method in its population, proposing higher quality sequences as well as more diverse batches. As such, P3BO and Adaptive-P3BO are a crucial step towards deploying ML to real-world sequence design.

Many real-world control problems involve conflicting objectives where we desire a dense and high-quality set of control policies that are optimal for different objective preferences (called Pareto-optimal). While extensive research in multi-objective reinforcement learning (MORL) has been conducted to tackle such problems, multi-objective optimization for complex continuous robot control is still under-explored. In this work, we propose an efficient evolutionary learning algorithm to find the Pareto set approximation for continuous robot control problems, by extending a state-of-the-art RL algorithm and presenting a novel prediction model to guide the learning process. In addition to efficiently discovering the individual policies on the Pareto front, we construct a continuous set of Pareto-optimal solutions by Pareto analysis and interpolation. Furthermore, we design seven multi-objective RL environments with continuous action space, which is the first benchmark platform to evaluate MORL algorithms on various robot control problems. We test the previous methods on the proposed benchmark problems, and the experiments show that our approach is able to find a much denser and higher-quality set of Pareto policies than the existing algorithms.

Domain shift is a fundamental problem in visual recognition which typically arises when the source and target data follow different distributions. The existing domain adaptation approaches which tackle this problem work in the "closed-set" setting with the assumption that the source and the target data share exactly the same classes of objects. In this paper, we tackle a more realistic problem of the "open-set" domain shift where the target data contains additional classes that were not present in the source data. More specifically, we introduce an end-to-end Progressive Graph Learning (PGL) framework where a graph neural network with episodic training is integrated to suppress underlying conditional shift and adversarial learning is adopted to close the gap between the source and target distributions. Compared to the existing open-set adaptation approaches, our approach guarantees to achieve a tighter upper bound of the target error. Extensive experiments on three standard open-set benchmarks evidence that our approach significantly outperforms the state-of-the-arts in open-set domain adaptation.

Integer programming is a general optimization framework with a wide variety of applications, e.g., in scheduling, production planning, and graph optimization. As Integer Programs (IPs) model many provably hard to solve problems, modern IP solvers rely on heuristics. These heuristics are often human-designed, and tuned over time using experience and data. The goal of this work is to show that the performance of those solvers can be greatly enhanced using reinforcement learning (RL). In particular, we investigate a specific methodology for solving IPs, known as the Cutting Plane Method. This method is employed as a subroutine by all modern IP solvers. We present a deep RL formulation, network architecture, and algorithms for intelligent adaptive selection of cutting planes (aka cuts). Across a wide range of IP tasks, we show that our trained RL agent significantly outperforms human-designed heuristics, and effectively generalizes to larger instances and across IP problem classes. The trained agent is also demonstrated to benefit the popular downstream application of cutting plane methods in Branch-and-Cut algorithm, which is the backbone of state-of-the-art commercial IP solvers.

We build a Bayesian contextual classification model using an optimistic score ratio for robust binary classification when there is limited information on the class-conditional, or contextual, distribution. The optimistic score searches for the distribution that is most plausible to explain the observed outcomes in the testing sample among all distributions belonging to the contextual ambiguity set which is prescribed using a limited structural constraint on the mean vector and the covariance matrix of the underlying contextual distribution. We show that the Bayesian classifier using the optimistic score ratio is conceptually attractive, delivers solid statistical guarantees and is computationally tractable. We showcase the power of the proposed optimistic score ratio classifier on both synthetic and empirical data.

Spectral functions of large matrices contains important structural information about the underlying data, and is thus becoming increasingly important. Many times, large matrices representing real-world data are sparse or doubly sparse (i.e., sparse in both rows and columns), and are accessed as a stream of updates, typically organized in row-order. In this setting, where space (memory) is the limiting resource, all known algorithms require space that is polynomial in the dimension of the matrix, even for sparse matrices. We address this challenge by providing the first algorithms whose space requirement is independent of the matrix dimension, assuming the matrix is doubly-sparse and presented in row-order. Our algorithms approximate the Schatten p-norms, which we use in turn to approximate other spectral functions, such as logarithm of the determinant, trace of matrix inverse, and Estrada index. We validate these theoretical performance bounds by numerical experiments on real-world matrices representing social networks. We further prove that multiple passes are unavoidable in this setting, and show extensions of our primary technique, including a trade-off between space requirements and number of passes.

Cooperation is often implicitly assumed when learning from other agents. Cooperation implies that the agent selecting the data, and the agent learning from the data, have the same goal, that the learner infer the intended hypothesis. Recent models in human and machine learning have demonstrated the possibility of cooperation. We seek foundational theoretical results for cooperative inference by Bayesian agents through sequential data. We develop novel approaches analyzing consistency, rate of convergence and stability of Sequential Cooperative Bayesian Inference (SCBI). Our analysis of the effectiveness, sample efficiency and robustness show that cooperation is not only possible but theoretically well-founded. We discuss implications for human-human and human-machine cooperation.

Given data with noisy labels, over-parameterized deep networks can gradually memorize the data, and fit everything in the end. Although equipped with corrections for noisy labels, many learning methods in this area still suffer overfitting due to undesired memorization. In this paper, to relieve this issue, we propose stochastic integrated gradient underweighted ascent (SIGUA): in a mini-batch, we adopt gradient descent on good data as usual, and learning-rate-reduced gradient ascent} on bad data; the proposal is a versatile approach where data goodness or badness is w.r.t. desired or undesired memorization given a base learning method. Technically, SIGUA pulls optimization back for generalization when their goals conflict with each other; philosophically, SIGUA shows forgetting undesired memorization can reinforce desired memorization. Experiments demonstrate that SIGUA successfully robustifies two typical base learning methods, so that their performance is often significantly improved.

Owing to their ability to both effectively integrate information over long time horizons and scale to massive amounts of data, self-attention architectures have recently shown breakthrough success in natural language processing (NLP). Harnessing the transformer’s ability to process long time horizons of information could provide a similar performance boost in partially observable reinforcement learning (RL) domains, but the large-scale transformers used in NLP have yet to be successfully applied to the RL setting. In this work we demonstrate that the standard transformer architecture is difficult to optimize, which was previously observed in the supervised learning setting but becomes especially pronounced with RL objectives. We propose architectural modifications that substantially improve the stability and learning speed of the original Transformer and XL variant. The proposed architecture, the Gated Transformer-XL (GTrXL), surpasses LSTMs on challenging memory environments and achieves state-of-the-art results on the multi-task DMLab-30 benchmark suite, exceeding the performance of an external memory architecture. We show that the GTrXL has stability and performance that consistently matches or exceeds a competitive LSTM baseline, including on more reactive tasks where memory is less critical.

Modern deep learning models employ considerably more parameters than required to fit the training data. Whereas conventional statistical wisdom suggests such models should drastically overfit, in practice these models generalize remarkably well. An emerging paradigm for describing this unexpected behavior is in terms of a \emph{double descent} curve, in which increasing a model's capacity causes its test error to first decrease, then increase to a maximum near the interpolation threshold, and then decrease again in the overparameterized regime. Recent efforts to explain this phenomenon theoretically have focused on simple settings, such as linear regression or kernel regression with unstructured random features, which we argue are too coarse to reveal important nuances of actual neural networks. We provide a precise high-dimensional asymptotic analysis of generalization under kernel regression with the Neural Tangent Kernel, which characterizes the behavior of wide neural networks optimized with gradient descent. Our results reveal that the test error has nonmonotonic behavior deep in the overparameterized regime and can even exhibit additional peaks and descents when the number of parameters scales quadratically with the dataset size.

Label distribution covers a certain number of labels, representing the degree to which each label describes the instance. The learning process on the instances labeled by label distributions is called label distribution learning (LDL). Unfortunately, many training sets only contain simple logical labels rather than label distributions due to the difficulty of obtaining the label distributions directly. To solve this problem, we consider the label distributions as the latent vectors and infer the label distributions from the logical labels in the training datasets by using variational inference. After that, we induce a predictive model to train the label distribution data by employing the multi-output regression technique. The recovery experiment on thirteen real-world LDL datasets and the predictive experiment on ten multi-label learning datasets validate the advantage of our approach over the state-of-the-art approaches.