Adversarial or test time robustness measures the susceptibility of a classifier to perturbations to the test input. While there has been a flurry of recent work on designing defenses against such perturbations, the theory of adversarial robustness is not well understood. In order to make progress on this, we focus on the problem of understanding generalization in adversarial settings, via the lens of Rademacher complexity. We give upper and lower bounds for the adversarial empirical Rademacher complexity of linear hypotheses with adversarial perturbations measured in $l_r$-norm for an arbitrary $r \geq 1$. We then extend our analysis to provide Rademacher complexity lower and upper bounds for a single ReLU unit. Finally, we give adversarial Rademacher complexity bounds for feed-forward neural networks with one hidden layer.

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.

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 for identifying the Condorcet winner in CPE-DB.

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 standard Monte Carlo solutions), one can leverage machine learning tools and data simulated in the neighborhood of a parameter to improve estimates of quantities of interest. We demonstrate the efficacy of ACORE with both theoretical and empirical results. Our implementation is available on Github.

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.

The best-known and most commonly used technique for distribution-property estimation uses a plug-in estimator, with empirical frequency replacing the underlying distribution. We present novel linear-time-computable estimators that significantly ``amplify'' the effective amount of data available. For a large variety of distribution properties including four of the most popular ones and for every underlying distribution, they achieve the accuracy that the empirical-frequency plug-in estimators would attain using a logarithmic-factor more samples. Specifically, for Shannon entropy and a broad class of Lipschitz properties including the $L_1$ distance to a fixed distribution, the new estimators use $n$ samples to achieve the accuracy attained by the empirical estimators with $n\log n$ samples. For support-size and coverage, the new estimators use $n$ samples to achieve the performance of empirical frequency with sample size $n$ times the logarithm of the property value. Significantly strengthening the traditional min-max formulation, these results hold not only for the worst distributions, but for each and every underlying distribution. Furthermore, the logarithmic amplification factors are optimal. Experiments on a wide variety of distributions show that the new estimators outperform the previous state-of-the-art estimators designed for each specific property.

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}.

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.

The problem of maximizing nonnegative monotone submodular functions under a certain constraint has been intensively studied in the last decade, and a wide range of efficient approximation algorithms have been developed for this problem. Many machine learning problems, including data summarization and influence maximization, can be naturally modeled as the problem of maximizing monotone submodular functions. However, when such applications involve sensitive data about individuals, their privacy concerns should be addressed. In this paper, we study the problem of maximizing monotone submodular functions subject to matroid constraints in the framework of differential privacy. We provide $(1-\frac{1}{\mathrm{e}})$-approximation algorithm which improves upon the previous results in terms of approximation guarantee. This is done with an almost cubic number of function evaluations in our algorithm. Moreover, we study $k$-submodularity, a natural generalization of submodularity. We give the first $\frac{1}{2}$-approximation algorithm that preserves differential privacy for maximizing monotone $k$-submodular functions subject to matroid constraints. The approximation ratio is asymptotically tight and is obtained with an almost linear number of function evaluations.

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 give a local search based algorithm for $k$-median and $k$-means (and more generally for any $k$-clustering with $\ell_p$ norm cost function) from the perspective of individual fairness. More precisely, for a point $x$ in a point set $P$ of size $n$, let $r(x)$ be the minimum radius such that the ball of radius $r(x)$ centered at $x$ has at least $n/k$ points from $P$. Intuitively, if a set of $k$ random points are chosen from $P$ as centers, every point $x\in P$ expects to have a center within radius $r(x)$. An individually fair clustering provides such a guarantee for every point $x\in P$. This notion of fairness was introduced in [Jung et al., 2019] where they showed how to get an approximately feasible $k$-clustering with respect to this fairness condition. In this work, we show how to get an approximately \emph{optimal} such fair $k$-clustering. The $k$-median ($k$-means) cost of our solution is within a constant factor of the cost of an optimal fair $k$-clustering, and our solution approximately satisfies the fairness condition (also within a constant factor).

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.

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.

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.

Studies of acquiring appropriate continuous representations of a discrete objects such as graph and knowledge based data have been conducted by many researches in the field of machine learning. In this paper, we introduce Nested SubSpace arrangement (NSS arrangement), a comprehensive framework for representation learning. We show that existing embedding techniques can be regarded as a member of NSS arrangement. Based on the concept of the NSS arrangement, we implemented Disk-ANChor ARrangement (DANCAR), a representation learning method specializing to reproduce general graphs. Numerical experiments have shown that DANCAR has successfully embedded WordNet in ${\mathbb R}^{20}$ with the F1 score of 0.993 in the reconstruction task. DANCAR is also suitable for visualization to understand the characteristics of graph.

While the impact of variational inference (VI) on posterior inference in a fixed generative model is well-characterized, its role in regularizing a learned generative model when used in variational autoencoders (VAEs) is poorly understood. We study the regularizing effects of variational distributions on learning in generative models from two perspectives. First, we analyze the role that the choice of variational family plays in imparting uniqueness to the learned model by restricting the set of optimal generative models. Second, we study the regularization effect of the variational family on the local geometry of the decoding model. This analysis uncovers the regularizer implicit in the $\beta$-VAE objective, and leads to an approximation consisting of a deterministic autoencoding objective plus analytic regularizers that depend on the Hessian or Jacobian of the decoding model, unifying VAEs with recent heuristics proposed for training regularized autoencoders. We empirically verify these findings, observing that the proposed deterministic objective exhibits similar behavior to the $\beta$-VAE in terms of objective value and sample quality.

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.

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.

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.

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.

In the paper, we propose a class of accelerated stochastic gradient-free and projection-free (a.k.a., zeroth-order Frank-Wolfe) methods to solve the constrained stochastic and finite-sum nonconvex optimization. Specifically, we propose an accelerated stochastic zeroth-order Frank-Wolfe (Acc-SZOFW) method based on the variance reduced technique of SPIDER/SpiderBoost and a novel momentum accelerated technique. Moreover, under some mild conditions, we prove that the Acc-SZOFW has the function query complexity of $O(d\sqrt{n}\epsilon^{-2})$ for finding an $\epsilon$-stationary point in the finite-sum problem, which improves the exiting best result by a factor of $O(\sqrt{n}\epsilon^{-2})$, and has the function query complexity of $O(d\epsilon^{-3})$ in the stochastic problem, which improves the exiting best result by a factor of $O(\epsilon^{-1})$. To relax the large batches required in the Acc-SZOFW, we further propose a novel accelerated stochastic zeroth-order Frank-Wolfe (Acc-SZOFW*) based on a new variance reduced technique of STORM, which still reaches the function query complexity of $O(d\epsilon^{-3})$ in the stochastic problem without relying on any large batches. In particular, we present an accelerated framework of the Frank-Wolfe methods based on the proposed momentum accelerated technique. The extensive experimental results on black-box adversarial attack and robust black-box classification demonstrate the efficiency of our algorithms.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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 true population-level importance of a variable in a prediction task provides useful knowledge about the underlying data-generating mechanism and can help in deciding which measurements to collect in subsequent experiments. Valid statistical inference on this importance is a key component in understanding the population of interest. We present a computationally efficient procedure for estimating and obtaining valid statistical inference on the \textbf{S}hapley \textbf{P}opulation \textbf{V}ariable \textbf{I}mportance \textbf{M}easure (SPVIM). Although the computational complexity of the true SPVIM scales exponentially with the number of variables, we propose an estimator based on randomly sampling only $\Theta(n)$ feature subsets given $n$ observations. We prove that our estimator converges at an asymptotically optimal rate. Moreover, by deriving the asymptotic distribution of our estimator, we construct valid confidence intervals and hypothesis tests. Our procedure has good finite-sample performance in simulations, and for an in-hospital mortality prediction task produces similar variable importance estimates when different machine learning algorithms are applied.

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.

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.

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.

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.

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.

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.

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 real world, our datasets often contain outliers. Most existing algorithms for handling outliers take high time complexities ({\em e.g.} quadratic or cubic complexity). {\em Coreset} is a popular approach for compressing data so as to speed up the optimization algorithms. However, the current coreset methods cannot be easily extended to handle the case with outliers. In this paper, we propose a new variant of coreset technique, {\em layered sampling}, to deal with two fundamental robust optimization problems: {\em $k$-median/means clustering with outliers} and {\em linear regression with outliers}. This new coreset method is in particular suitable to speed up the iterative algorithms (which often improve the solution within a local range) for those robust optimization problems.

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.

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.

Distribution shift is a major obstacle to the deployment of current deep learning models on real-world problems. Let $Y$ be the class label and $X$ the features. We focus on one type of distribution shift, \textit{ label shift}, where the label marginal distribution $P_Y$ changes but the conditional distribution $P_{X|Y}$ does not. Most existing methods estimate the density ratio between the source- and target-domain label distributions by density matching. However, these methods are either computationally infeasible for large-scale data or restricted to shift correction for discrete labels. In this paper, we propose an end-to-end Label Transformation Framework (LTF) for correcting label shift, which implicitly models the shift of $P_Y$ and the conditional distribution $P_{X|Y}$ using neural networks. Thanks to the flexibility of deep networks, our framework can handle continuous, discrete, and even multi-dimensional labels in a unified way and is scalable to large data. Moreover, for high dimensional $X$, such as images, we find that the redundant information in $X$ severely degrades the estimation accuracy. To remedy this issue, we propose to match the distribution implied by our generative model and the target-domain distribution in a low-dimensional feature space that discards information irrelevant to $Y$. Both theoretical and empirical studies demonstrate the superiority of our method over previous approaches.

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.

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.

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 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.

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.

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.

Existing multi-armed bandit (MAB) models make two implicit assumptions: an arm generates a payoff only when it is played, and the agent observes every payoff that is generated. This paper introduces synchronization bandits, a MAB variant where all arms generate costs at all times, but the agent observes an arm's instantaneous cost only when the arm is played. Synchronization MABs are inspired by online caching scenarios such as Web crawling, where an arm corresponds to a cached item and playing the arm means downloading its fresh copy from a server. We present MirrorSync, an online learning algorithm for synchronization bandits, establish an adversarial regret of $O(T^{2/3})$ for it, and show how to make it practical.

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.

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.

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 fine-grained control over text generation than existing methods.

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.

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.

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.

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.

While policy-based reinforcement learning (RL) achieves tremendous successes in practice, it is significantly less understood in theory, especially compared with value-based RL. In particular, it remains elusive how to design a provably efficient policy optimization algorithm that incorporates exploration. To bridge such a gap, this paper proposes an \underline{O}ptimistic variant of the \underline{P}roximal \underline{P}olicy \underline{O}ptimization algorithm (OPPO), which follows an ``optimistic version'' of the policy gradient direction. This paper proves that, in the problem of episodic Markov decision process with unknown transition and full-information feedback of adversarial reward, OPPO achieves an $\tilde{O}(\sqrt{|\cS|^2|\cA|H^3 T})$ regret. Here $|\cS|$ is the size of the state space, $|\cA|$ is the size of the action space, $H$ is the episode horizon, and $T$ is the total number of steps. To the best of our knowledge, OPPO is the first provably efficient policy optimization algorithm that explores.

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.

Single-objective black box optimization (also known as zeroth-order optimization) is the process of minimizing a scalar objective $f(x)$, given evaluations at adaptively chosen inputs $x$. In this paper, we consider multi-objective optimization, where $f(x)$ outputs a vector of possibly competing objectives and the goal is to converge to the Pareto frontier. Quantitatively, we wish to maximize the standard \emph{hypervolume indicator} metric, which measures the dominated hypervolume of the entire set of chosen inputs. In this paper, we introduce a novel scalarization function, which we term the \emph{hypervolume scalarization}, and show that drawing random scalarizations from an appropriately chosen distribution can be used to efficiently approximate the \emph{hypervolume indicator} metric. We utilize this connection to show that Bayesian optimization with our scalarization via common acquisition functions, such as Thompson Sampling or Upper Confidence Bound, provably converges to the whole Pareto frontier by deriving tight \emph{hypervolume regret} bounds on the order of $\widetilde{O}(\sqrt{T})$. Furthermore, we highlight the general utility of our scalarization framework by showing that any provably convergent single-objective optimization process can be converted to a multi-objective optimization process with provable convergence guarantees.

Randomized smoothing is the current state-of-the-art defense with provable robustness against $\ell_2$ adversarial attacks. Many works have devised new randomized smoothing schemes for other metrics, such as $\ell_1$ or $\ell_\infty$; however, substantial effort was needed to derive such new guarantees. This begs the question: can we find a general theory for randomized smoothing? We propose a novel framework for devising and analyzing randomized smoothing schemes, and validate its effectiveness in practice. Our theoretical contributions are: (1) we show that for an appropriate notion of "optimal", the optimal smoothing distributions for any "nice" norms have level sets given by the norm's *Wulff Crystal*; (2) we propose two novel and complementary methods for deriving provably robust radii for any smoothing distribution; and, (3) we show fundamental limits to current randomized smoothing techniques via the theory of *Banach space cotypes*. By combining (1) and (2), we significantly improve the state-of-the-art certified accuracy in $\ell_1$ on standard datasets. Meanwhile, we show using (3) that with only label statistics under random input perturbations, randomized smoothing cannot achieve nontrivial certified accuracy against perturbations of $\ell_p$-norm $\Omega(\min(1, d^{\frac{1}{p} - \frac{1}{2}}))$, when the input dimension $d$ is large. We provide code in github.com/tonyduan/rs4a.

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.

Deep semi-supervised learning (SSL) has been recently shown very effectively. However, its performance is seriously decreased when the class distribution is mismatched, among which a common situation is that unlabeled data contains some classes not seen in the labeled data. Efforts on this issue remain to be limited. This paper proposes a simple and effective safe deep SSL method to alleviate the harm caused by it. In theory, the result learned from the new method is never worse than learning from merely labeled data, and it is theoretically guaranteed that its generalization approaches the optimal in the order $O(\sqrt{d\ln(n)/n})$, even faster than the convergence rate in supervised learning associated with massive parameters. In the experiment of benchmark data, unlike the existing deep SSL methods which are no longer as good as supervised learning in 40\% of unseen-class unlabeled data, the new method can still achieve performance gain in more than 60\% of unseen-class unlabeled data. Moreover, the proposal is suitable for many deep SSL algorithms and can be easily extended to handle other cases of class distribution mismatch.

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.

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 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 within the exponential family, which is validated in extensive experiments.

Structured sparsity-inducing $\ell_{1, \infty}$-norm, as a generalization of the classical $\ell_1$-norm, plays an important role in jointly sparse models which select or remove simultaneously all the variables forming a group. However, its resulting problem is more difficult to solve than the conventional $\ell_1$-norm constrained problem. In this paper, we propose an efficient algorithm for Euclidean projection onto $\ell_{1, \infty}$-norm ball. We tackle the projection problem via semismooth Newton algorithm to solve the system of semismooth equations. Meanwhile, exploiting the structure of Jacobian matrix via LU decomposition yields an equivalent algorithm which is proved to terminate after a finite number of iterations. Empirical studies demonstrate that our proposed algorithm outperforms the existing state-of-the-art solver and is promising for the optimization of learning problems with $\ell_{1, \infty}$-norm ball constraint.

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.

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 paper, we propose a novel framework that converts streaming algorithms for monotone submodular maximization into streaming algorithms for non-monotone submodular maximization. This reduction readily leads to the currently tightest deterministic approximation ratio for submodular maximization subject to a $k$-matchoid constraint. Moreover, we propose the first streaming algorithm for monotone submodular maximization subject to $k$-extendible and $k$-set system constraints. Together with our proposed reduction, we obtain $O(k\log k)$ and $O(k^2\log k)$ approximation ratio for submodular maximization subject to the above constraints, respectively. We extensively evaluate the empirical performance of our algorithm against the existing work in a series of experiments including finding the maximum independent set in randomly generated graphs, maximizing linear functions over social networks, movie recommendation, Yelp location summarization, and Twitter data summarization.

We consider a deep ReLU / Leaky ReLU student network trained from the output of a fixed teacher network of the same depth, with Stochastic Gradient Descent (SGD). The student network is \emph{over-realized}: at each layer $l$, the number $n_l$ of student nodes is more than that ($m_l$) of teacher. Under mild conditions on dataset and teacher network, we prove that when the gradient is small at every data sample, each teacher node is \emph{specialized} by at least one student node \emph{at the lowest layer}. For two-layer network, such specialization can be achieved by training on any dataset of \emph{polynomial} size $\mathcal{O}( K^{5/2} d^3 \epsilon^{-1})$. until the gradient magnitude drops to $\mathcal{O}(\epsilon/K^{3/2}\sqrt{d})$. Here $d$ is the input dimension, $K = m_1 + n_1$ is the total number of neurons in the lowest layer of teacher and student. Note that we require a specific form of data augmentation and the sample complexity includes the additional data generated from augmentation. To our best knowledge, we are the first to give polynomial sample complexity for student specialization of training two-layer (Leaky) ReLU networks with finite depth and width in teacher-student setting, and finite complexity for the lowest layer specialization in multi-layer case, without parametric assumption of the input (like Gaussian). Our theory suggests that teacher nodes with large fan-out weights get specialized first when the gradient is still large, while others are specialized with small gradient, which suggests inductive bias in training. This shapes the stage of training as empirically observed in multiple previous works. Experiments on synthetic and CIFAR10 verify our findings. The code is released in \url{https://github.com/facebookresearch/luckmatters}.

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.

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 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.

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 without weight symmetry: further improvement of local rules so that they perform consistently across architectures and the identification of biological implementations for non-local learning mechanisms.

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.

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.