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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

A robustness certificate against adversarial examples is the minimum distance of a given input to the decision boundary of the classifier (or its lower bound). For {\it any} perturbation of the input with a magnitude smaller than the certificate value, the classification output will provably remain unchanged. Computing exact robustness certificates for neural networks is difficult in general since it requires solving a non-convex optimization. In this paper, we provide computationally-efficient robustness certificates for neural networks with differentiable activation functions in two steps. First, we show that if the eigenvalues of the Hessian of the network (curvatures of the network) are bounded (globally or locally), we can compute a robustness certificate in the $l_2$ norm efficiently using convex optimization. Second, we derive a computationally-efficient differentiable upper bound on the curvature of a deep network. We also use the curvature bound as a regularization term during the training of the network to boost its certified robustness. Putting these results together leads to our proposed {\bf C}urvature-based {\bf R}obustness {\bf C}ertificate (CRC) and {\bf C}urvature-based {\bf R}obust {\bf T}raining (CRT). Our numerical results show that CRT leads to significantly higher certified robust accuracy compared to interval-bound propagation based training.

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

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

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

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

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

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

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

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

Frank-Wolfe algorithm is an efficient method for optimizing non-convex constrained problems. However, most of existing methods focus on the first-order case. In real-world applications, the gradient is not always available. To address the problem of lacking gradient in many applications, we propose two new stochastic zeroth-order Frank-Wolfe algorithms and theoretically proved that they have a faster convergence rate than existing methods for non-convex problems. Specifically, the function queries oracle of the proposed faster zeroth-order Frank-Wolfe (FZFW) method is $O(\frac{n^{1/2}d}{\epsilon^2})$ which can match the iteration complexity of the first-order counterpart approximately. As for the proposed faster zeroth-order conditional gradient sliding (FZCGS) method, its function queries oracle is improved to $O(\frac{n^{1/2}d}{\epsilon})$, indicating that its iteration complexity is even better than that of its first-order counterpart NCGS-VR. In other words, the iteration complelxity of the accelerated first-order Frank-Wolfe method NCGS-VR is suboptimal. Then, we proposed a new algorithm to improve its IFO (incremental first-order oracle) to $O(\frac{n^{1/2}}{\epsilon})$. At last, the empirical studies on benchmark datasets validate our theoretical results.

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

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

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

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

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

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

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

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

The evolution of a deep neural network trained by the gradient descent in the overparametrization regime can be described by its neural tangent kernel (NTK) \cite{jacot2018neural, du2018gradient1,du2018gradient2,arora2019fine}. It was observed \cite{arora2019exact} that there is a performance gap between the kernel regression using the limiting NTK and the deep neural networks. We study the dynamic of neural networks of finite width and derive an infinite hierarchy of differential equations, the neural tangent hierarchy (NTH). We prove that the NTH hierarchy truncated at the level $p\geq 2$ approximates the dynamic of the NTK up to arbitrary precision under certain conditions on the neural network width and the data set dimension. The assumptions needed for these approximations become weaker as $p$ increases. Finally, NTH can be viewed as higher order extensions of NTK. In particular, the NTH truncated at $p=2$ recovers the NTK dynamics.

We consider recovering a causal graph in presence of latent variables, where we seek to minimize the cost of interventions used in the recovery process. We consider two intervention cost models: (1) a linear cost model where the cost of an intervention on a subset of variables has a linear form, and (2) an identity cost model where the cost of an intervention is the same, regardless of what variables it is on, i.e., the goal is just to minimize the number of interventions. Under the linear cost model, we give an algorithm to identify the ancestral relations of the underlying causal graph, achieving within a $2$-factor of the optimal intervention cost. This approximation factor can be improved to $1+\eps$ for any $\eps > 0$ under some mild restrictions. Under the identity cost model, we bound the number of interventions needed to recover the entire causal graph, including the latent variables, using a parameterization of the causal graph through a special type of colliders. In particular, we introduce the notion of $p$-colliders, that are colliders between pair of nodes arising from a specific type of conditioning in the causal graph, and provide an upper bound on the number of interventions as a function of the maximum number of $p$-colliders between any two nodes in the causal graph.

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

In this paper, we consider multi-agent learning via online gradient descent in a class of games called $\lambda$-cocoercive games, a fairly broad class of games that admits many Nash equilibria and that properly includes unconstrained strongly monotone games. We characterize the finite-time last-iterate convergence rate for joint OGD learning on $\lambda$-cocoercive games; further, building on this result, we develop a fully adaptive OGD learning algorithm that does not require any knowledge of problem parameter (e.g. cocoercive constant $\lambda$) and show, via a novel double-stopping time technique, that this adaptive algorithm achieves same finite-time last-iterate convergence rate as non-adaptive counterpart. Subsequently, we extend OGD learning to the noisy gradient feedback case and establish last-iterate convergence results--first qualitative almost sure convergence, then quantitative finite-time convergence rates-- all under non-decreasing step-sizes. To our knowledge, we provide the first set of results that fill in several gaps of the existing multi-agent online learning literature, where three aspects--finite-time convergence rates, non-decreasing step-sizes, and fully adaptive algorithms have been unexplored before.

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

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

PageRank is a widely used approach for measuring the importance of a node in a graph. Due to the rapid growth of the graph size in the real world, the importance of computing PageRanks in a distributed environment has been increasingly recognized. However, only a few previous works can provide a provable complexity and accuracy for distributed PageRank computation. Given a constant $d\ge 1$ and a graph of $n$ nodes, the state-of-the-art approach, Radar-Push, uses $O(\log\log{n}+\log{d})$ communication rounds to approximate the PageRanks within a relative error $O(\frac{1}{\log^d{n}})$ under a generalized congested clique distributed model. However, Radar-Push entails as large as $O(\log^{2d+3}{n})$ bits of bandwidth (e.g., the communication cost between a pair of nodes per round) in the worst case. In this paper, we provide a new algorithm that uses asymptotically the same communication round complexity while using only $O(d\log^3{n})$ bits of bandwidth.

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

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

Domain adaptation aims to correct the classifiers when faced with distribution shift between source (training) and target (test) domains. State-of-the-art domain adaptation methods make use of deep networks to extract domain-invariant representations. However, existing methods assume that all the instances in the source domain are correctly labeled; while in reality, it is unsurprising that we may obtain a source domain with noisy labels. In this paper, we are the first to comprehensively investigate how label noise could adversely affect existing domain adaptation methods in various scenarios. Further, we theoretically prove that there exists a method that can essentially reduce the side-effect of noisy source labels in domain adaptation. Specifically, focusing on the generalized target shift scenario, where both label distribution $P_Y$ and the class-conditional distribution $P_{X|Y}$ can change, we discover that the denoising Conditional Invariant Component (DCIC) framework can provably ensures (1) extracting invariant representations given examples with noisy labels in the source domain and unlabeled examples in the target domain and (2) estimating the label distribution in the target domain with no bias. Experimental results on both synthetic and real-world data verify the effectiveness of the proposed method.

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

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

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

Running Stochastic Gradient Descent (SGD) in a decentralized fashion has shown promising results. In this paper we propose Moniqua, a technique that allows decentralized SGD to use quantized communication. We prove in theory that Moniqua communicates a provably bounded number of bits per iteration, while converging at the same asymptotic rate as the original algorithm does with full-precision communication. Moniqua improves upon prior works in that it (1) requires zero additional memory, (2) works with 1-bit quantization, and (3) is applicable to a variety of decentralized algorithms. We demonstrate empirically that Moniqua converges faster with respect to wall clock time than other quantized decentralized algorithms. We also show that Moniqua is robust to very low bit-budgets, allowing $1$-bit-per-parameter communication without compromising validation accuracy when training ResNet20 and ResNet110 on CIFAR10.

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

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

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

In this paper, we present a Bayesian Moment Matching (BMM) based method aimed at solving the initialization problem in Boolean SAT solvers. The initialization problem can be stated as follows: given a SAT formula $\phi$, compute an initial order over the variables of $\phi$ and values/polarity for these variables such that the runtime of SAT solvers on input $\phi$ is minimized. At the start of a solver run, our BMM-based methods compute a posterior probability distribution for an assignment to the variables of the input formula after analyzing its clauses, which will then be used by the solver to initialize its search. We perform extensive experiments to evaluate the efficacy of our BMM-based heuristic against 4 other initialization methods (random, survey propagation, Jeroslow-Wang, and default) in state-of-the-art solvers, MapleCOMSPS and MapleLCMDistChronotBT over the SAT competition 2018 application benchmark, as well as the best-known solvers in the cryptographic category, namely, CryptoMiniSAT, Glucose, and MapleSAT. On the cryptographic benchmark, BMM-based solvers out-perform all other initialization methods. Further, the BMM-based MapleCOMSPS significantly out-perform the same solver using all other initialization methods by 12 additional instances solved and better average runtime, over the SAT 2018 competition benchmark.

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

We provide a computational complexity analysis for the Sinkhorn algorithm that solves the entropic regularized Unbalanced Optimal Transport (UOT) problem between two measures of possibly different masses with at most $n$ components. We show that the complexity of the Sinkhorn algorithm for finding an $\varepsilon$-approximate solution to the UOT problem is of order $\widetilde{\mathcal{O}}(n^2/ \varepsilon)$. To the best of our knowledge, this complexity is better than the best known complexity upper bound of the Sinkhorn algorithm for solving the Optimal Transport (OT) problem, which is of order $\widetilde{\mathcal{O}}(n^2/\varepsilon^2)$. Our proof technique is based on the geometric convergence rate of the Sinkhorn updates to the optimal dual solution of the entropic regularized UOT problem and scaling properties of the primal solution. It is also different from the proof technique used to establish the complexity of the Sinkhorn algorithm for approximating the OT problem since the UOT solution does not need to meet the marginal constraints of the measures.

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

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

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

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

We study the problem of differentially private query release assisted by access to public data. In this problem, the goal is to answer a large class $\mathcal{H}$ of statistical queries with error no more than $\alpha$ using a combination of public and private samples. The algorithm is required to satisfy differential privacy only with respect to the private samples. We study the limits of this task in terms of the private and public sample complexities. Our upper and lower bounds on the private sample complexity have matching dependence on the dual VC-dimension of $\mathcal{H}$. For a large category of query classes, our bounds on the public sample complexity have matching dependence on $\alpha$.

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

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

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

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

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

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

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

We present the first sublinear memory sketch that can be queried to find the nearest neighbors in a dataset. Our online sketching algorithm compresses an N element dataset to a sketch of size $O(N^b \log^3 N)$ in $O(N^{(b+1)} \log^3 N)$ time, where $b < 1$. This sketch can correctly report the nearest neighbors of any query that satisfies a stability condition parameterized by $b$. We achieve sublinear memory performance on stable queries by combining recent advances in locality sensitive hash (LSH)-based estimators, online kernel density estimation, and compressed sensing. Our theoretical results shed new light on the memory-accuracy tradeoff for nearest neighbor search, and our sketch, which consists entirely of short integer arrays, has a variety of attractive features in practice. We evaluate the memory-recall tradeoff of our method on a friend recommendation task in the Google plus social media network. We obtain orders of magnitude better compression than the random projection based alternative while retaining the ability to report the nearest neighbors of practical queries.

We consider the problem of selecting the best estimator among a family of Tikhonov regularized estimators, or, alternatively, to select a linear combination of these regularizers that is as good as the best regularizer in the family. Our theory reveals that if the Tikhonov regularizers share the same penalty matrix with different tuning parameters, a convex procedure based on $Q$-aggregation achieves the mean square error of the best estimator, up to a small error term no larger than $C\sigma^2$, where $\sigma^2$ is the noise level and $C>0$ is an absolute constant. Remarkably, the error term does not depend on the penalty matrix or the number of estimators as long as they share the same penalty matrix, i.e., it applies to any grid of tuning parameters, no matter how large the cardinality of the grid is. This reveals the surprising "cost-free" nature of optimally tuning Tikhonov regularizers, in striking contrast with the existing literature on aggregation of estimators where one typically has to pay a cost of $\sigma^2\log(M)$ where $M$ is the number of estimators in the family. The result holds, more generally, for any family of ordered linear smoothers; this encompasses Ridge regression as well as Principal Component Regression. The result is extended to the problem of tuning Tikhonov regularizers with different penalty matrices.

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

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

Reinforcement learning algorithms usually assume that all actions are always available to an agent. However, both people and animals understand the general link between the features of their environment and the actions that are feasible. Gibson (1977) coined the term "affordances" to describe the fact that certain states enable an agent to do certain actions, in the context of embodied agents. In this paper, we develop a theory of affordances for agents who learn and plan in Markov Decision Processes. Affordances play a dual role in this case. On one hand, they allow faster planning, by reducing the number of actions available in any given situation. On the other hand, they facilitate more efficient and precise learning of transition models from data, especially when such models require function approximation. We establish these properties through theoretical results as well as illustrative examples. We also propose an approach to learn affordances and use it to estimate transition models that are simpler and generalize better.