Minimizing cross-entropy over the softmax scores of a linear map composed with a high-capacity encoder is arguably the most popular choice for training neural networks on supervised learning tasks. However, recent works show that one can directly optimize the encoder instead, to obtain equally (or even more) discriminative representations via a supervised variant of a contrastive objective. In this work, we address the question whether there are fundamental differences in the sought-for representation geometry in the output space of the encoder at minimal loss. Specifically, we prove, under mild assumptions, that both losses attain their minimum once the representations of each class collapse to the vertices of a regular simplex, inscribed in a hypersphere. We provide empirical evidence that this configuration is attained in practice and that reaching a close-to-optimal state typically indicates good generalization performance. Yet, the two losses show remarkably different optimization behavior. The number of iterations required to perfectly fit to data scales superlinearly with the amount of randomly flipped labels for the supervised contrastive loss. This is in contrast to the approximately linear scaling previously reported for networks trained with cross-entropy.

In the vanishing learning rate regime, stochastic gradient descent (SGD) is now relatively well understood. In this work, we propose to study the basic properties of SGD and its variants in the non-vanishing learning rate regime. The focus is on deriving exactly solvable results and discussing their implications. The main contributions of this work are to derive the stationary distribution for discrete-time SGD in a quadratic loss function with and without momentum; in particular, one implication of our result is that the fluctuation caused by discrete-time dynamics takes a distorted shape and is dramatically larger than a continuous-time theory could predict. Examples of applications of the proposed theory considered in this work include the approximation error of variants of SGD, the effect of minibatch noise, the optimal Bayesian inference, the escape rate from a sharp minimum, and the stationary covariance of a few second-order methods including damped Newton's method, natural gradient descent, and Adam.

As its width tends to infinity, a deep neural network's behavior under gradient descent can become simplified and predictable (e.g. given by the Neural Tangent Kernel (NTK)), if it is parametrized appropriately (e.g. the NTK parametrization). However, we show that the standard and NTK parametrizations of a neural network do not admit infinite-width limits that can learn features, which is crucial for pretraining and transfer learning such as with BERT. We propose simple modifications to the standard parametrization to allow for feature learning in the limit. Using the Tensor Programs technique, we derive explicit formulas for such limits. On Word2Vec and few-shot learning on Omniglot via MAML, two canonical tasks that rely crucially on feature learning, we compute these limits exactly. We find that they outperform both NTK baselines and finite-width networks, with the latter approaching the infinite-width feature learning performance as width increases.

Residual networks (ResNets) have displayed impressive results in pattern recognition and, recently, have garnered considerable theoretical interest due to a perceived link with neural ordinary differential equations (neural ODEs). This link relies on the convergence of network weights to a smooth function as the number of layers increases. We investigate the properties of weights trained by stochastic gradient descent and their scaling with network depth through detailed numerical experiments. We observe the existence of scaling regimes markedly different from those assumed in neural ODE literature. Depending on certain features of the network architecture, such as the smoothness of the activation function, one may obtain an alternative ODE limit, a stochastic differential equation or neither of these. These findings cast doubts on the validity of the neural ODE model as an adequate asymptotic description of deep ResNets and point to an alternative class of differential equations as a better description of the deep network limit.

Contrastive learning has recently seen tremendous success in self-supervised learning. So far, however, it is largely unclear why the learned representations generalize so effectively to a large variety of downstream tasks. We here prove that feedforward models trained with objectives belonging to the commonly used InfoNCE family learn to implicitly invert the underlying generative model of the observed data. While the proofs make certain statistical assumptions about the generative model, we observe empirically that our findings hold even if these assumptions are severely violated. Our theory highlights a fundamental connection between contrastive learning, generative modeling, and nonlinear independent component analysis, thereby furthering our understanding of the learned representations as well as providing a theoretical foundation to derive more effective contrastive losses.

Yang (2020) recently showed that the Neural Tangent Kernel (NTK) at initialization has an infinite-width limit for a large class of architectures including modern staples such as ResNet and Transformers. However, their analysis does not apply to training. Here, we show the same neural networks (in the so-called NTK parametrization) during training follow a kernel gradient descent dynamics in function space, where the kernel is the infinite-width NTK. This completes the proof of the architectural universality of NTK behavior. To achieve this result, we apply the Tensor Programs technique: Write the entire SGD dynamics inside a Tensor Program and analyze it via the Master Theorem. To facilitate this proof, we develop a graphical notation for Tensor Programs, which we believe is also an important contribution toward the pedagogy and exposition of the Tensor Programs technique.

In this paper, we introduce a new perspective on training deep neural networks capable of state-of-the-art performance without the need for the expensive over-parameterization by proposing the concept of In-Time Over-Parameterization (ITOP) in sparse training. By starting from a random sparse network and continuously exploring sparse connectivities during training, we can perform an Over-Parameterization over the course of training, closing the gap in the expressibility between sparse training and dense training. We further use ITOP to understand the underlying mechanism of Dynamic Sparse Training (DST) and discover that the benefits of DST come from its ability to consider across time all possible parameters when searching for the optimal sparse connectivity. As long as sufficient parameters have been reliably explored, DST can outperform the dense neural network by a large margin. We present a series of experiments to support our conjecture and achieve the state-of-the-art sparse training performance with ResNet-50 on ImageNet. More impressively, ITOP achieves dominant performance over the overparameterization-based sparse methods at extreme sparsities. When trained with ResNet-34 on CIFAR-100, ITOP can match the performance of the dense model at an extreme sparsity 98%.

We study multi-objective reinforcement learning (RL) where an agent's reward is represented as a vector. In settings where an agent competes against opponents, its performance is measured by the distance of its average return vector to a target set. We develop statistically and computationally efficient algorithms to approach the associated target set. Our results extend Blackwell's approachability theorem~\citep{blackwell1956analog} to tabular RL, where strategic exploration becomes essential. The algorithms presented are adaptive; their guarantees hold even without Blackwell's approachability condition. If the opponents use fixed policies, we give an improved rate of approaching the target set while also tackling the more ambitious goal of simultaneously minimizing a scalar cost function. We discuss our analysis for this special case by relating our results to previous works on constrained RL. To our knowledge, this work provides the first provably efficient algorithms for vector-valued Markov games and our theoretical guarantees are near-optimal.

Exploration in unknown environments is a fundamental problem in reinforcement learning and control. In this work, we study task-guided exploration and determine what precisely an agent must learn about their environment in order to complete a particular task. Formally, we study a broad class of decision-making problems in the setting of linear dynamical systems, a class that includes the linear quadratic regulator problem. We provide instance- and task-dependent lower bounds which explicitly quantify the difficulty of completing a task of interest. Motivated by our lower bound, we propose a computationally efficient experiment-design based exploration algorithm. We show that it optimally explores the environment, collecting precisely the information needed to complete the task, and provide finite-time bounds guaranteeing that it achieves the instance- and task-optimal sample complexity, up to constant factors. Through several examples of the linear quadratic regulator problem, we show that performing task-guided exploration provably improves on exploration schemes which do not take into account the task of interest. Along the way, we establish that certainty equivalence decision making is instance- and task-optimal, and obtain the first algorithm for the linear quadratic regulator problem which is instance-optimal. We conclude with several experiments illustrating the effectiveness of our approach in …

The safe operation of physical systems typically relies on high-quality models. Since a continuous stream of data is generated during run-time, such models are often obtained through the application of Gaussian process regression because it provides guarantees on the prediction error. Due to its high computational complexity, Gaussian process regression must be used offline on batches of data, which prevents applications, where a fast adaptation through online learning is necessary to ensure safety. In order to overcome this issue, we propose the LoG-GP. It achieves a logarithmic update and prediction complexity in the number of training points through the aggregation of locally active Gaussian process models. Under weak assumptions on the aggregation scheme, it inherits safety guarantees from exact Gaussian process regression. These theoretical advantages are exemplarily exploited in the design of a safe and data-efficient, online-learning control policy. The efficiency and performance of the proposed real-time learning approach is demonstrated in a comparison to state-of-the-art methods.

In policy search methods for reinforcement learning (RL), exploration is often performed by injecting noise either in action space at each step independently or in parameter space over each full trajectory. In prior work, it has been shown that with linear policies, a more balanced trade-off between these two exploration strategies is beneficial. However, that method did not scale to policies using deep neural networks. In this paper, we introduce deep coherent exploration, a general and scalable exploration framework for deep RL algorithms for continuous control, that generalizes step-based and trajectory-based exploration. This framework models the last layer parameters of the policy network as latent variables and uses a recursive inference step within the policy update to handle these latent variables in a scalable manner. We find that deep coherent exploration improves the speed and stability of learning of A2C, PPO, and SAC on several continuous control tasks.

In active visual tracking, it is notoriously difficult when distracting objects appear, as distractors often mislead the tracker by occluding the target or bringing a confusing appearance. To address this issue, we propose a mixed cooperative-competitive multi-agent game, where a target and multiple distractors form a collaborative team to play against a tracker and make it fail to follow. Through learning in our game, diverse distracting behaviors of the distractors naturally emerge, thereby exposing the tracker's weakness, which helps enhance the distraction-robustness of the tracker. For effective learning, we then present a bunch of practical methods, including a reward function for distractors, a cross-modal teacher-student learning strategy, and a recurrent attention mechanism for the tracker. The experimental results show that our tracker performs desired distraction-robust active visual tracking and can be well generalized to unseen environments. We also show that the multi-agent game can be used to adversarially test the robustness of trackers.

Many machine learning problems can be formulated as minimax problems such as Generative Adversarial Networks (GANs), AUC maximization and robust estimation, to mention but a few. A substantial amount of studies are devoted to studying the convergence behavior of their stochastic gradient-type algorithms. In contrast, there is relatively little work on understanding their generalization, i.e., how the learning models built from training examples would behave on test examples. In this paper, we provide a comprehensive generalization analysis of stochastic gradient methods for minimax problems under both convex-concave and nonconvex-nonconcave cases through the lens of algorithmic stability. We establish a quantitative connection between stability and several generalization measures both in expectation and with high probability. For the convex-concave setting, our stability analysis shows that stochastic gradient descent ascent attains optimal generalization bounds for both smooth and nonsmooth minimax problems. We also establish generalization bounds for both weakly-convex-weakly-concave and gradient-dominated problems. We report preliminary experimental results to verify our theory.

In performative prediction, predictions guide decision-making and hence can influence the distribution of future data. To date, work on performative prediction has focused on finding performatively stable models, which are the fixed points of repeated retraining. However, stable solutions can be far from optimal when evaluated in terms of the performative risk, the loss experienced by the decision maker when deploying a model. In this paper, we shift attention beyond performative stability and focus on optimizing the performative risk directly. We identify a natural set of properties of the loss function and model-induced distribution shift under which the performative risk is convex, a property which does not follow from convexity of the loss alone. Furthermore, we develop algorithms that leverage our structural assumptions to optimize the performative risk with better sample efficiency than generic methods for derivative-free convex optimization.

This paper quantifies the uncertainty of prediction risk for the min-norm least squares estimator in high-dimensional linear regression models. We establish the asymptotic normality of prediction risk when both the sample size and the number of features tend to infinity. Based on the newly established central limit theorems(CLTs), we derive the confidence intervals of the prediction risk under various scenarios. Our results demonstrate the sample-wise non-monotonicity of the prediction risk and confirm ``more data hurt" phenomenon. Furthermore, the width of confidence intervals indicates that over-parameterization would enlarge the randomness of prediction performance.

Meta-learning, or learning-to-learn, seeks to design algorithms that can utilize previous experience to rapidly learn new skills or adapt to new environments. Representation learning---a key tool for performing meta-learning---learns a data representation that can transfer knowledge across multiple tasks, which is essential in regimes where data is scarce. Despite a recent surge of interest in the practice of meta-learning, the theoretical underpinnings of meta-learning algorithms are lacking, especially in the context of learning transferable representations. In this paper, we focus on the problem of multi-task linear regression---in which multiple linear regression models share a common, low-dimensional linear representation. Here, we provide provably fast, sample-efficient algorithms to address the dual challenges of (1) learning a common set of features from multiple, related tasks, and (2) transferring this knowledge to new, unseen tasks. Both are central to the general problem of meta-learning. Finally, we complement these results by providing information-theoretic lower bounds on the sample complexity of learning these linear features.

There has been recently a significant boost to machine learning with distributed data, in particular with the success of federated learning. A common and very challenging setting is that of vertical or feature partitioned data, when multiple data providers hold different features about common entities. In general, training needs to be preceded by record linkage (RL), a step that finds the correspondence between the observations of the datasets. RL is prone to mistakes in the real world. Despite the importance of the problem, there has been so far no formal assessment of the way in which RL errors impact learning models. Work in the area either use heuristics or assume that the optimal RL is known in advance. In this paper, we provide the first assessment of the problem for supervised learning. For wide sets of losses, we provide technical conditions under which the classifier learned after noisy RL converges (with the data size) to the best classifier that would be learned from mistake-free RL. This yields new insights on the way the pipeline RL + ML operates, from the role of large margin classification on dampening the impact of RL mistakes to clues on how to further optimize RL …

The success of minimax learning problems of generative adversarial networks (GANs) has been observed to depend on the minimax optimization algorithm used for their training. This dependence is commonly attributed to the convergence speed and robustness properties of the underlying optimization algorithm. In this paper, we show that the optimization algorithm also plays a key role in the generalization performance of the trained minimax model. To this end, we analyze the generalization properties of standard gradient descent ascent (GDA) and proximal point method (PPM) algorithms through the lens of algorithmic stability as defined by Bousquet & Elisseeff, 2002 under both convex-concave and nonconvex-nonconcave minimax settings. While the GDA algorithm is not guaranteed to have a vanishing excess risk in convex-concave problems, we show the PPM algorithm enjoys a bounded excess risk in the same setup. For nonconvex-nonconcave problems, we compare the generalization performance of stochastic GDA and GDmax algorithms where the latter fully solves the maximization subproblem at every iteration. Our generalization analysis suggests the superiority of GDA provided that the minimization and maximization subproblems are solved simultaneously with similar learning rates. We discuss several numerical results indicating the role of optimization algorithms in the generalization of learned minimax models.

Many sequential decision problems involve finding a policy that maximizes total reward while obeying safety constraints. Although much recent research has focused on the development of safe reinforcement learning (RL) algorithms that produce a safe policy after training, ensuring safety during training as well remains an open problem. A fundamental challenge is performing exploration while still satisfying constraints in an unknown Markov decision process (MDP). In this work, we address this problem for the chance-constrained setting.We propose a new algorithm, SAILR, that uses an intervention mechanism based on advantage functions to keep the agent safe throughout training and optimizes the agent's policy using off-the-shelf RL algorithms designed for unconstrained MDPs. Our method comes with strong guarantees on safety during "both" training and deployment (i.e., after training and without the intervention mechanism) and policy performance compared to the optimal safety-constrained policy. In our experiments, we show that SAILR violates constraints far less during training than standard safe RL and constrained MDP approaches and converges to a well-performing policy that can be deployed safely without intervention. Our code is available at https://github.com/nolanwagener/safe_rl.

We consider the pure exploration problem in the fixed-budget linear bandit setting. We provide a new algorithm that identifies the best arm with high probability while being robust to unknown levels of observation noise as well as to moderate levels of misspecification in the linear model. Our technique combines prior approaches to pure exploration in the multi-armed bandit problem with optimal experimental design algorithms to obtain both problem dependent and problem independent bounds. Our success probability is never worse than that of an algorithm that ignores the linear structure, but seamlessly takes advantage of such structure when possible. Furthermore, we only need the number of samples to scale with the dimension of the problem rather than the number of arms. We complement our theoretical results with empirical validation.

We provide a unifying view of a large family of previous imitation learning algorithms through the lens of moment matching. At its core, our classification scheme is based on whether the learner attempts to match (1) reward or (2) action-value moments of the expert's behavior, with each option leading to differing algorithmic approaches. By considering adversarially chosen divergences between learner and expert behavior, we are able to derive bounds on policy performance that apply for all algorithms in each of these classes, the first to our knowledge. We also introduce the notion of moment recoverability, implicit in many previous analyses of imitation learning, which allows us to cleanly delineate how well each algorithmic family is able to mitigate compounding errors. We derive three novel algorithm templates (AdVIL, AdRIL, and DAeQuIL) with strong guarantees, simple implementation, and competitive empirical performance.

Deep learning for graph matching (GM) has emerged as an important research topic due to its superior performance over traditional methods and insights it provides for solving other combinatorial problems on graph. While recent deep methods for GM extensively investigated effective node/edge feature learning or downstream GM solvers given such learned features, there is little existing work questioning if the fixed connectivity/topology typically constructed using heuristics (e.g., Delaunay or k-nearest) is indeed suitable for GM. From a learning perspective, we argue that the fixed topology may restrict the model capacity and thus potentially hinder the performance. To address this, we propose to learn the (distribution of) latent topology, which can better support the downstream GM task. We devise two latent graph generation procedures, one deterministic and one generative. Particularly, the generative procedure emphasizes the across-graph consistency and thus can be viewed as a matching-guided co-generative model. Our methods deliver superior performance over previous state-of-the-arts on public benchmarks, hence supporting our hypothesis.

Robust loss functions are essential for training deep neural networks with better generalization power in the presence of noisy labels. Symmetric loss functions are confirmed to be robust to label noise. However, the symmetric condition is overly restrictive. In this work, we propose a new class of loss functions, namely asymmetric loss functions, which are robust to learning from noisy labels for arbitrary noise type. Subsequently, we investigate general theoretical properties of asymmetric loss functions, including classification-calibration, excess risk bound, and noise-tolerance. Meanwhile, we introduce the asymmetry ratio to measure the asymmetry of a loss function, and the empirical results show that a higher ratio will provide better robustness. Moreover, we modify several common loss functions, and establish the necessary and sufficient conditions for them to be asymmetric. Experiments on benchmark datasets demonstrate that asymmetric loss functions can outperform state-of-the-art methods.

The label noise transition matrix, characterizing the probabilities of a training instance being wrongly annotated, is crucial to designing popular solutions to learning with noisy labels. Existing works heavily rely on finding ``anchor points'' or their approximates, defined as instances belonging to a particular class almost surely. Nonetheless, finding anchor points remains a non-trivial task, and the estimation accuracy is also often throttled by the number of available anchor points. In this paper, we propose an alternative option to the above task. Our main contribution is the discovery of an efficient estimation procedure based on a clusterability condition. We prove that with clusterable representations of features, using up to third-order consensuses of noisy labels among neighbor representations is sufficient to estimate a unique transition matrix. Compared with methods using anchor points, our approach uses substantially more instances and benefits from a much better sample complexity. We demonstrate the estimation accuracy and advantages of our estimates using both synthetic noisy labels (on CIFAR-10/100) and real human-level noisy labels (on Clothing1M and our self-collected human-annotated CIFAR-10). Our code and human-level noisy CIFAR-10 labels are available at https://github.com/UCSC-REAL/HOC.

Conditional selective inference (SI) has been actively studied as a new statistical inference framework for data-driven hypotheses. The basic idea of conditional SI is to make inferences conditional on the selection event characterized by a set of linear and/or quadratic inequalities. Conditional SI has been mainly studied in the context of feature selection such as stepwise feature selection (SFS). The main limitation of the existing conditional SI methods is the loss of power due to over-conditioning, which is required for computational tractability. In this study, we develop a more powerful and general conditional SI method for SFS using the homotopy method which enables us to overcome this limitation. The homotopy-based SI is especially effective for more complicated feature selection algorithms. As an example, we develop a conditional SI method for forward-backward SFS with AIC-based stopping criteria and show that it is not adversely affected by the increased complexity of the algorithm. We conduct several experiments to demonstrate the effectiveness and efficiency of the proposed method.

Despite their widespread success, the application of deep neural networks to functional data remains scarce today. The infinite dimensionality of functional data means standard learning algorithms can be applied only after appropriate dimension reduction, typically achieved via basis expansions. Currently, these bases are chosen a priori without the information for the task at hand and thus may not be effective for the designated task. We instead propose to adaptively learn these bases in an end-to-end fashion. We introduce neural networks that employ a new Basis Layer whose hidden units are each basis functions themselves implemented as a micro neural network. Our architecture learns to apply parsimonious dimension reduction to functional inputs that focuses only on information relevant to the target rather than irrelevant variation in the input function. Across numerous classification/regression tasks with functional data, our method empirically outperforms other types of neural networks, and we prove that our approach is statistically consistent with low generalization error.

Structured output prediction problems (e.g., sequential tagging, hierarchical multi-class classification) often involve constraints over the output space. These constraints interact with the learned models to filter infeasible solutions and facilitate in building an accountable system. However, despite constraints are useful, they are often based on hand-crafted rules. This raises a question -- can we mine constraints and rules from data based on a learning algorithm?

In this paper, we present a general framework for mining constraints from data. In particular, we consider the inference in structured output prediction as an integer linear programming (ILP) problem. Then, given the coefficients of the objective function and the corresponding solution, we mine the underlying constraints by estimating the outer and inner polytopes of the feasible set. We verify the proposed constraint mining algorithm in various synthetic and real-world applications and demonstrate that the proposed approach successfully identifies the feasible set at scale. 
In particular, we show that our approach can learn to solve 9x9 Sudoku puzzles and minimal spanning tree problems from examples without providing the underlying rules. Our algorithm can also integrate with a neural network model to learn the hierarchical label structure of a multi-label classification task. Besides, we provide theoretical …

The goal of classification with rejection is to avoid risky misclassification in error-critical applications such as medical diagnosis and product inspection. In this paper, based on the relationship between classification with rejection and cost-sensitive classification, we propose a novel method of classification with rejection by learning an ensemble of cost-sensitive classifiers, which satisfies all the following properties: (i) it can avoid estimating class-posterior probabilities, resulting in improved classification accuracy. (ii) it allows a flexible choice of losses including non-convex ones, (iii) it does not require complicated modifications when using different losses, (iv) it is applicable to both binary and multiclass cases, and (v) it is theoretically justifiable for any classification-calibrated loss. Experimental results demonstrate the usefulness of our proposed approach in clean-labeled, noisy-labeled, and positive-unlabeled classification.

Machine learned models often must abide by certain requirements (e.g., fairness or legal). This has spurred interested in developing approaches that can provably verify whether a model satisfies certain properties. This paper introduces a generic algorithm called Veritas that enables tackling multiple different verification tasks for tree ensemble models like random forests (RFs) and gradient boosted decision trees (GBDTs). This generality contrasts with previous work, which has focused exclusively on either adversarial example generation or robustness checking. Veritas formulates the verification task as a generic optimization problem and introduces a novel search space representation. Veritas offers two key advantages. First, it provides anytime lower and upper bounds when the optimization problem cannot be solved exactly. In contrast, many existing methods have focused on exact solutions and are thus limited by the verification problem being NP-complete. Second, Veritas produces full (bounded suboptimal) solutions that can be used to generate concrete examples. We experimentally show that our method produces state-of-the-art robustness estimates, especially when executed with strict time constraints. This is exceedingly important when checking the robustness of large datasets. Additionally, we show that Veritas enables tackling more real-world verification scenarios.

We study the problem of robust mean estimation and introduce a novel Hamming distance-based measure of distribution shift for coordinate-level corruptions. We show that this measure yields adversary models that capture more realistic corruptions than those used in prior works, and present an information-theoretic analysis of robust mean estimation in these settings. We show that for structured distributions, methods that leverage the structure yield information theoretically more accurate mean estimation. We also focus on practical algorithms for robust mean estimation and study when data cleaning-inspired approaches that first fix corruptions in the input data and then perform robust mean estimation can match the information theoretic bounds of our analysis. We finally demonstrate experimentally that this two-step approach outperforms structure-agnostic robust estimation and provides accurate mean estimation even for high-magnitude corruption.

Metric Multidimensional scaling (MDS) is a classical method for generating meaningful (non-linear) low-dimensional embeddings of high-dimensional data. MDS has a long history in the statistics, machine learning, and graph drawing communities. In particular, the Kamada-Kawai force-directed graph drawing method is equivalent to MDS and is one of the most popular ways in practice to embed graphs into low dimensions. Despite its ubiquity, our theoretical understanding of MDS remains limited as its objective function is highly non-convex. In this paper, we prove that minimizing the Kamada-Kawai objective is NP-hard and give a provable approximation algorithm for optimizing it, which in particular is a PTAS on low-diameter graphs. We supplement this result with experiments suggesting possible connections between our greedy approximation algorithm and gradient-based methods.

Algorithmic stability is a key characteristic to ensure the generalization ability of a learning algorithm. Among different notions of stability, \emph{uniform stability} is arguably the most popular one, which yields exponential generalization bounds. However, uniform stability only considers the worst-case loss change (or so-called sensitivity) by removing a single data point, which is distribution-independent and therefore undesirable. There are many cases that the worst-case sensitivity of the loss is much larger than the average sensitivity taken over the single data point that is removed, especially in some advanced models such as random feature models or neural networks. Many previous works try to mitigate the distribution independent issue by proposing weaker notions of stability, however, they either only yield polynomial bounds or the bounds derived do not vanish as sample size goes to infinity. Given that, we propose \emph{locally elastic stability} as a weaker and distribution-dependent stability notion, which still yields exponential generalization bounds. We further demonstrate that locally elastic stability implies tighter generalization bounds than those derived based on uniform stability in many situations by revisiting the examples of bounded support vector machines, regularized least square regressions, and stochastic gradient descent.

We propose a randomized algorithm with quadratic convergence rate for convex optimization problems with a self-concordant, composite, strongly convex objective function. Our method is based on performing an approximate Newton step using a random projection of the Hessian. Our first contribution is to show that, at each iteration, the embedding dimension (or sketch size) can be as small as the effective dimension of the Hessian matrix. Leveraging this novel fundamental result, we design an algorithm with a sketch size proportional to the effective dimension and which exhibits a quadratic rate of convergence. This result dramatically improves on the classical linear-quadratic convergence rates of state-of-the-art sub-sampled Newton methods. However, in most practical cases, the effective dimension is not known beforehand, and this raises the question of how to pick a sketch size as small as the effective dimension while preserving a quadratic convergence rate. Our second and main contribution is thus to propose an adaptive sketch size algorithm with quadratic convergence rate and which does not require prior knowledge or estimation of the effective dimension: at each iteration, it starts with a small sketch size, and increases it until quadratic progress is achieved. Importantly, we show that the embedding dimension remains …

This paper aims to define, visualize, and analyze the feature complexity that is learned by a DNN. We propose a generic definition for the feature complexity. Given the feature of a certain layer in the DNN, our method decomposes and visualizes feature components of different complexity orders from the feature. The feature decomposition enables us to evaluate the reliability, the effectiveness, and the significance of over-fitting of these feature components. Furthermore, such analysis helps to improve the performance of DNNs. As a generic method, the feature complexity also provides new insights into existing deep-learning techniques, such as network compression and knowledge distillation.

This paper discusses the problem of weakly supervised classification, in which instances are given weak labels that are produced by some label-corruption process. The goal is to derive conditions under which loss functions for weak-label learning are proper and lower-bounded---two essential requirements for the losses used in class-probability estimation. To this end, we derive a representation theorem for proper losses in supervised learning, which dualizes the Savage representation. We use this theorem to characterize proper weak-label losses and find a condition for them to be lower-bounded. From these theoretical findings, we derive a novel regularization scheme called generalized logit squeezing, which makes any proper weak-label loss bounded from below, without losing properness. Furthermore, we experimentally demonstrate the effectiveness of our proposed approach, as compared to improper or unbounded losses. The results highlight the importance of properness and lower-boundedness.

Biclustering structures exist ubiquitously in data matrices and the biclustering problem was first formalized by John Hartigan (1972) to cluster rows and columns simultaneously. In this paper, we develop a theory for the estimation of general biclustering models, where the data is assumed to follow certain statistical distribution with underlying biclustering structure. Due to the existence of latent variables, directly computing the maximal likelihood estimator is prohibitively difficult in practice and we instead consider the variational inference (VI) approach to solve the parameter estimation problem. Although variational inference method generally has good empirical performance, there are very few theoretical results around VI. In this paper, we obtain the precise estimation bound of variational estimator and show that it matches the minimax rate in terms of estimation error under mild assumptions in biclustering setting. Furthermore, we study the convergence property of the coordinate ascent variational inference algorithm, where both local and global convergence results have been provided. Numerical results validate our new theories.

Game optimization has been extensively studied when decision variables lie in a finite-dimensional space, of which solutions correspond to pure strategies at the Nash equilibrium (NE), and the gradient descent-ascent (GDA) method works widely in practice. In this paper, we consider infinite-dimensional zero-sum games by a min-max distributional optimization problem over a space of probability measures defined on a continuous variable set, which is inspired by finding a mixed NE for finite-dimensional zero-sum games. We then aim to answer the following question: \textit{Will GDA-type algorithms still be provably efficient when extended to infinite-dimensional zero-sum games?} To answer this question, we propose a particle-based variational transport algorithm based on GDA in the functional spaces. Specifically, the algorithm performs multi-step functional gradient descent-ascent in the Wasserstein space via pushing two sets of particles in the variable space. By characterizing the gradient estimation error from variational form maximization and the convergence behavior of each player with different objective landscapes, we prove rigorously that the generalized GDA algorithm converges to the NE or the value of the game efficiently for a class of games under the Polyak-\L ojasiewicz (PL) condition. To conclude, we provide complete statistical and convergence guarantees for solving an infinite-dimensional zero-sum …

We investigate the capacity control provided by dropout in various machine learning problems. First, we study dropout for matrix completion, where it induces a distribution-dependent regularizer that equals the weighted trace-norm of the product of the factors. In deep learning, we show that the distribution-dependent regularizer due to dropout directly controls the Rademacher complexity of the underlying class of deep neural networks. These developments enable us to give concrete generalization error bounds for the dropout algorithm in both matrix completion as well as training deep neural networks.

A fundamental obstacle in learning information from data is the presence of nonlinear redundancies and dependencies in it. To address this, we propose a Fourier-based approach to extract relevant information in the supervised setting. We first develop a novel Fourier expansion for functions of correlated binary random variables. This expansion is a generalization of the standard Fourier analysis on the Boolean cube beyond product probability spaces. We further extend our Fourier analysis to stochastic mappings. As an important application of this analysis, we investigate learning with feature subset selection. We reformulate this problem in the Fourier domain and introduce a computationally efficient measure for selecting features. Bridging the Bayesian error rate with the Fourier coefficients, we demonstrate that the Fourier expansion provides a powerful tool to characterize nonlinear dependencies in the features-label relation. Via theoretical analysis, we show that our proposed measure finds provably asymptotically optimal feature subsets. Lastly, we present an algorithm based on our measure and verify our findings via numerical experiments on various datasets.

Randomly perturbing networks during the training process is a commonly used approach to improving generalization performance. In this paper, we present a theoretical study of one particular way of random perturbation, which corresponds to injecting artificial noise to the training data. We provide a precise asymptotic characterization of the training and generalization errors of such randomly perturbed learning problems on a random feature model. Our analysis shows that Gaussian noise injection in the training process is equivalent to introducing a weighted ridge regularization, when the number of noise injections tends to infinity. The explicit form of the regularization is also given. Numerical results corroborate our asymptotic predictions, showing that they are accurate even in moderate problem dimensions. Our theoretical predictions are based on a new correlated Gaussian equivalence conjecture that generalizes recent results in the study of random feature models.

In multi-dimensional classification (MDC), there are multiple class variables in the output space with each of them corresponding to one heterogeneous class space. Due to the heterogeneity of class spaces, it is quite challenging to consider the dependencies among class variables when learning from MDC examples. In this paper, we propose a novel MDC approach named SLEM which learns the predictive model in an encoded label space instead of the original heterogeneous one. Specifically, SLEM works in an encoding-training-decoding framework. In the encoding phase, each class vector is mapped into a real-valued one via three cascaded operations including pairwise grouping, one-hot conversion and sparse linear encoding. In the training phase, a multi-output regression model is learned within the encoded label space. In the decoding phase, the predicted class vector is obtained by adapting orthogonal matching pursuit over outputs of the learned multi-output regression model. Experimental results clearly validate the superiority of SLEM against state-of-the-art MDC approaches.

A key problem in program synthesis is searching over the large space of possible programs. Human programmers might decide the high-level structure of the desired program before thinking about the details; motivated by this intuition, we consider two-level search for program synthesis, in which the synthesizer first generates a plan, a sequence of symbols that describes the desired program at a high level, before generating the program. We propose to learn representations of programs that can act as plans to organize such a two-level search. Discrete latent codes are appealing for this purpose, and can be learned by applying recent work on discrete autoencoders. Based on these insights, we introduce the Latent Programmer (LP), a program synthesis method that first predicts a discrete latent code from input/output examples, and then generates the program in the target language. We evaluate the LP on two domains, demonstrating that it yields an improvement in accuracy, especially on longer programs for which search is most difficult.

Answering complex natural language questions on knowledge graphs (KGQA) is a challenging task. It requires reasoning with the input natural language questions as well as a massive, incomplete heterogeneous KG. Prior methods obtain an abstract structured query graph/tree from the input question and traverse the KG for answers following the query tree. However, they inherently cannot deal with missing links in the KG. Here we present LEGO, a Latent Execution-Guided reasOning framework to handle this challenge in KGQA. LEGO works in an iterative way, which alternates between (1) a Query Synthesizer, which synthesizes a reasoning action and grows the query tree step-by-step, and (2) a Latent Space Executor that executes the reasoning action in the latent embedding space to combat against the missing information in KG. To learn the synthesizer without step-wise supervision, we design a generic latent execution guided bottom-up search procedure to find good execution traces efficiently in the vast query space. Experimental results on several KGQA benchmarks demonstrate the effectiveness of our framework compared with previous state of the art.

Spreadsheet formula prediction has been an important program synthesis problem with many real-world applications. Previous works typically utilize input-output examples as the specification for spreadsheet formula synthesis, where each input-output pair simulates a separate row in the spreadsheet. However, this formulation does not fully capture the rich context in real-world spreadsheets. First, spreadsheet data entries are organized as tables, thus rows and columns are not necessarily independent from each other. In addition, many spreadsheet tables include headers, which provide high-level descriptions of the cell data. However, previous synthesis approaches do not consider headers as part of the specification. In this work, we present the first approach for synthesizing spreadsheet formulas from tabular context, which includes both headers and semi-structured tabular data. In particular, we propose SpreadsheetCoder, a BERT-based model architecture to represent the tabular context in both row-based and column-based formats. We train our model on a large dataset of spreadsheets, and demonstrate that SpreadsheetCoder achieves top-1 prediction accuracy of 42.51%, which is a considerable improvement over baselines that do not employ rich tabular context. Compared to the rule-based system, SpreadsheetCoder assists 82% more users in composing formulas on Google Sheets.

Spatio-temporal forecasting has numerous applications in analyzing wireless, traffic, and financial networks. Many classical statistical models often fall short in handling the complexity and high non-linearity present in time-series data. Recent advances in deep learning allow for better modelling of spatial and temporal dependencies. While most of these models focus on obtaining accurate point forecasts, they do not characterize the prediction uncertainty. In this work, we consider the time-series data as a random realization from a nonlinear state-space model and target Bayesian inference of the hidden states for probabilistic forecasting. We use particle flow as the tool for approximating the posterior distribution of the states, as it is shown to be highly effective in complex, high-dimensional settings. Thorough experimentation on several real world time-series datasets demonstrates that our approach provides better characterization of uncertainty while maintaining comparable accuracy to the state-of-the-art point forecasting methods.

This paper is concerned about a learning algorithm for a probabilistic model of spiking neural networks (SNNs). Jimenez Rezende & Gerstner (2014) proposed a stochastic variational inference algorithm to train SNNs with hidden neurons. The algorithm updates the variational distribution using the score function gradient estimator, whose high variance often impedes the whole learning algorithm. This paper presents an alternative gradient estimator for SNNs based on the path-wise gradient estimator. The main technical difficulty is a lack of a general method to differentiate a realization of an arbitrary point process, which is necessary to derive the path-wise gradient estimator. We develop a differentiable point process, which is the technical highlight of this paper, and apply it to derive the path-wise gradient estimator for SNNs. We investigate the effectiveness of our gradient estimator through numerical simulation.

Diffusion source identification on networks is a problem of fundamental importance in a broad class of applications, including controlling the spreading of rumors on social media, identifying a computer virus over cyber networks, or identifying the disease center during epidemiology. Though this problem has received significant recent attention, most known approaches are well-studied in only very restrictive settings and lack theoretical guarantees for more realistic networks. We introduce a statistical framework for the study of this problem and develop a confidence set inference approach inspired by hypothesis testing. Our method efficiently produces a small subset of nodes, which provably covers the source node with any pre-specified confidence level without restrictive assumptions on network structures. To our knowledge, this is the first diffusion source identification method with a practically useful theoretical guarantee on general networks. We demonstrate our approach via extensive synthetic experiments on well-known random network models, a large data set of real-world networks as well as a mobility network between cities concerning the COVID-19 spreading in January 2020.

We study the problem of learning conditional average treatment effects (CATE) from high-dimensional, observational data with unobserved confounders. Unobserved confounders introduce ignorance---a level of unidentifiability---about an individual's response to treatment by inducing bias in CATE estimates. We present a new parametric interval estimator suited for high-dimensional data, that estimates a range of possible CATE values when given a predefined bound on the level of hidden confounding. Further, previous interval estimators do not account for ignorance about the CATE associated with samples that may be underrepresented in the original study, or samples that violate the overlap assumption. Our interval estimator also incorporates model uncertainty so that practitioners can be made aware of such out-of-distribution data. We prove that our estimator converges to tight bounds on CATE when there may be unobserved confounding and assess it using semi-synthetic, high-dimensional datasets.

Most computer science conferences rely on paper bidding to assign reviewers to papers. Although paper bidding enables high-quality assignments in days of unprecedented submission numbers, it also opens the door for dishonest reviewers to adversarially influence paper reviewing assignments. Anecdotal evidence suggests that some reviewers bid on papers by "friends" or colluding authors, even though these papers are outside their area of expertise, and recommend them for acceptance without considering the merit of the work. In this paper, we study the efficacy of such bid manipulation attacks and find that, indeed, they can jeopardize the integrity of the review process. We develop a novel approach for paper bidding and assignment that is much more robust against such attacks. We show empirically that our approach provides robustness even when dishonest reviewers collude, have full knowledge of the assignment system's internal workings, and have access to the system's inputs. In addition to being more robust, the quality of our paper review assignments is comparable to that of current, non-robust assignment approaches.

Data-driven pricing strategies are becoming increasingly common, where customers are offered a personalized price based on features that are predictive of their valuation of a product. It is desirable for this pricing policy to be simple and interpretable, so it can be verified, checked for fairness, and easily implemented. However, efforts to incorporate machine learning into a pricing framework often lead to complex pricing policies that are not interpretable, resulting in slow adoption in practice. We present a novel, customized, prescriptive tree-based algorithm that distills knowledge from a complex black-box machine learning algorithm, segments customers with similar valuations and prescribes prices in such a way that maximizes revenue while maintaining interpretability. We quantify the regret of a resulting policy and demonstrate its efficacy in applications with both synthetic and real-world datasets.

Intersection over union (IoU) score, also named Jaccard Index, is one of the most fundamental evaluation methods in machine learning. The original IoU computation cannot provide non-zero gradients and thus cannot be directly optimized by nowadays deep learning methods. Several recent works generalized IoU for bounding box regression, but they are not straightforward to adapt for pixelwise prediction. In particular, the original IoU fails to provide effective gradients for the non-overlapping and location-deviation cases, which results in performance plateau. In this paper, we propose PixIoU, a generalized IoU for pixelwise prediction that is sensitive to the distance for non-overlapping cases and the locations in prediction. We provide proofs that PixIoU holds many nice properties as the original IoU. To optimize the PixIoU, we also propose a loss function that is proved to be submodular, hence we can apply the Lov\'asz functions, the efficient surrogates for submodular functions for learning this loss. Experimental results show consistent performance improvements by learning PixIoU over the original IoU for several different pixelwise prediction tasks on Pascal VOC, VOT-2020 and Cityscapes.

We study a fundamental problem in computational chemistry known as molecular conformation generation, trying to predict stable 3D structures from 2D molecular graphs. Existing machine learning approaches usually first predict distances between atoms and then generate a 3D structure satisfying the distances, where noise in predicted distances may induce extra errors during 3D coordinate generation. Inspired by the traditional force field methods for molecular dynamics simulation, in this paper, we propose a novel approach called ConfGF by directly estimating the gradient fields of the log density of atomic coordinates. The estimated gradient fields allow directly generating stable conformations via Langevin dynamics. However, the problem is very challenging as the gradient fields are roto-translation equivariant. We notice that estimating the gradient fields of atomic coordinates can be translated to estimating the gradient fields of interatomic distances, and hence develop a novel algorithm based on recent score-based generative models to effectively estimate these gradients. Experimental results across multiple tasks show that ConfGF outperforms previous state-of-the-art baselines by a significant margin.

Predicting molecular conformations (or 3D structures) from molecular graphs is a fundamental problem in many applications. Most existing approaches are usually divided into two steps by first predicting the distances between atoms and then generating a 3D structure through optimizing a distance geometry problem. However, the distances predicted with such two-stage approaches may not be able to consistently preserve the geometry of local atomic neighborhoods, making the generated structures unsatisfying. In this paper, we propose an end-to-end solution for molecular conformation prediction called ConfVAE based on the conditional variational autoencoder framework. Specifically, the molecular graph is first encoded in a latent space, and then the 3D structures are generated by solving a principled bilevel optimization program. Extensive experiments on several benchmark data sets prove the effectiveness of our proposed approach over existing state-of-the-art approaches. Code is available at \url{https://github.com/MinkaiXu/ConfVAE-ICML21}.

The scarcity of available samples and the high annotation cost of medical data cause a bottleneck in many digital diagnosis tasks based on deep learning. This problem is especially severe in pediatric tumor tasks, due to the small population base of children and high sample diversity caused by the high metastasis rate of related tumors. Targeted research on pediatric tumors is urgently needed but lacks sufficient attention. In this work, we propose a novel model to solve the diagnosis task of small round blue cell tumors (SRBCTs). To solve the problem of high noise and high diversity in the small sample scenario, the model is constrained to pay attention to the valid areas in the pathological image with a masking mechanism, and a length-aware loss is proposed to improve the tolerance to feature diversity. We evaluate this framework on a challenging small sample SRBCTs dataset, whose classification is difficult even for professional pathologists. The proposed model shows the best performance compared with state-of-the-art deep models and generalization on another pathological dataset, which illustrates the potentiality of deep learning applications in difficult small sample medical tasks.

A common workflow in single-cell RNA-seq analysis is to project the data to a latent space, cluster the cells in that space, and identify sets of marker genes that explain the differences among the discovered clusters. A primary drawback to this three-step procedure is that each step is carried out independently, thereby neglecting the effects of the nonlinear embedding and inter-gene dependencies on the selection of marker genes. Here we propose an integrated deep learning framework, Adversarial Clustering Explanation (ACE), that bundles all three steps into a single workflow. The method thus moves away from the notion of "marker genes" to instead identify a panel of explanatory genes. This panel may include genes that are not only enriched but also depleted relative to other cell types, as well as genes that exhibit differences between closely related cell types. Empirically, we demonstrate that ACE is able to identify gene panels that are both highly discriminative and nonredundant, and we demonstrate the applicability of ACE to an image recognition task.

Designing novel protein sequences for a desired 3D topological fold is a fundamental yet non-trivial task in protein engineering. Challenges exist due to the complex sequence--fold relationship, as well as the difficulties to capture the diversity of the sequences (therefore structures and functions) within a fold. To overcome these challenges, we propose Fold2Seq, a novel transformer-based generative framework for designing protein sequences conditioned on a specific target fold. To model the complex sequence--structure relationship, Fold2Seq jointly learns a sequence embedding using a transformer and a fold embedding from the density of secondary structural elements in 3D voxels. On test sets with single, high-resolution and complete structure inputs for individual folds, our experiments demonstrate improved or comparable performance of Fold2Seq in terms of speed, coverage, and reliability for sequence design, when compared to existing state-of-the-art methods that include data-driven deep generative models and physics-based RosettaDesign. The unique advantages of fold-based Fold2Seq, in comparison to a structure-based deep model and RosettaDesign, become more evident on three additional real-world challenges originating from low-quality, incomplete, or ambiguous input structures. Source code and data are available at https://github.com/IBM/fold2seq.

Feedforward computation, such as evaluating a neural network or sampling from an autoregressive model, is ubiquitous in machine learning. The sequential nature of feedforward computation, however, requires a strict order of execution and cannot be easily accelerated with parallel computing. To enable parallelization, we frame the task of feedforward computation as solving a system of nonlinear equations. We then propose to find the solution using a Jacobi or Gauss-Seidel fixed-point iteration method, as well as hybrid methods of both. Crucially, Jacobi updates operate independently on each equation and can be executed in parallel. Our method is guaranteed to give exactly the same values as the original feedforward computation with a reduced (or equal) number of parallelizable iterations, and hence reduced time given sufficient parallel computing power. Experimentally, we demonstrate the effectiveness of our approach in accelerating (i) backpropagation of RNNs, (ii) evaluation of DenseNets, and (iii) autoregressive sampling of MADE and PixelCNN++, with speedup factors between 2.1 and 26 under various settings.

Reliably predicting the products of chemical reactions presents a fundamental challenge in synthetic chemistry. Existing machine learning approaches typically produce a reaction product by sequentially forming its subparts or intermediate molecules. Such autoregressive methods, however, not only require a pre-defined order for the incremental construction but preclude the use of parallel decoding for efficient computation. To address these issues, we devise a non-autoregressive learning paradigm that predicts reaction in one shot. Leveraging the fact that chemical reactions can be described as a redistribution of electrons in molecules, we formulate a reaction as an arbitrary electron flow and predict it with a novel multi-pointer decoding network. Experiments on the USPTO-MIT dataset show that our approach has established a new state-of-the-art top-1 accuracy and achieves at least 27 times inference speedup over the state-of-the-art methods. Also, our predictions are easier for chemists to interpret owing to predicting the electron flows.

Recent work has considered natural variations of the {\em multi-armed bandit} problem, where the reward distribution of each arm is a special function of the time passed since its last pulling. In this direction, a simple (yet widely applicable) model is that of {\em blocking bandits}, where an arm becomes unavailable for a deterministic number of rounds after each play. In this work, we extend the above model in two directions: (i) We consider the general combinatorial setting where more than one arms can be played at each round, subject to feasibility constraints. (ii) We allow the blocking time of each arm to be stochastic. We first study the computational/unconditional hardness of the above setting and identify the necessary conditions for the problem to become tractable (even in an approximate sense). Based on these conditions, we provide a tight analysis of the approximation guarantee of a natural greedy heuristic that always plays the maximum expected reward feasible subset among the available (non-blocked) arms. When the arms' expected rewards are unknown, we adapt the above heuristic into a bandit algorithm, based on UCB, for which we provide sublinear (approximate) regret guarantees, matching the theoretical lower bounds in the limiting case of …

Using logical clauses to represent patterns, Tsetlin Machine (TM) have recently obtained competitive performance in terms of accuracy, memory footprint, energy, and learning speed on several benchmarks. Each TM clause votes for or against a particular class, with classification resolved using a majority vote. While the evaluation of clauses is fast, being based on binary operators, the voting makes it necessary to synchronize the clause evaluation, impeding parallelization. In this paper, we propose a novel scheme for desynchronizing the evaluation of clauses, eliminating the voting bottleneck. In brief, every clause runs in its own thread for massive native parallelism. For each training example, we keep track of the class votes obtained from the clauses in local voting tallies. The local voting tallies allow us to detach the processing of each clause from the rest of the clauses, supporting decentralized learning. This means that the TM most of the time will operate on outdated voting tallies. We evaluated the proposed parallelization across diverse learning tasks and it turns out that our decentralized TM learning algorithm copes well with working on outdated data, resulting in no significant loss in learning accuracy. Furthermore, we show that the approach provides up to 50 times …

Computationally efficient contextual bandits are often based on estimating a predictive model of rewards given contexts and arms using past data. However, when the reward model is not well-specified, the bandit algorithm may incur unexpected regret, so recent work has focused on algorithms that are robust to misspecification. We propose a simple family of contextual bandit algorithms that adapt to misspecification error by reverting to a good safe policy when there is evidence that misspecification is causing a regret increase. Our algorithm requires only an offline regression oracle to ensure regret guarantees that gracefully degrade in terms of a measure of the average misspecification level. Compared to prior work, we attain similar regret guarantees, but we do no rely on a master algorithm, and do not require more robust oracles like online or constrained regression oracles (e.g., Foster et al. (2020), Krishnamurthy et al. (2020)). This allows us to design algorithms for more general function approximation classes.

We consider repair tasks: given a critic (e.g., compiler) that assesses the quality of an input, the goal is to train a fixer that converts a bad example (e.g., code with syntax errors) into a good one (e.g., code with no errors). Existing works create training data consisting of (bad, good) pairs by corrupting good examples using heuristics (e.g., dropping tokens). However, fixers trained on this synthetically-generated data do not extrapolate well to the real distribution of bad inputs. To bridge this gap, we propose a new training approach, Break-It-Fix-It (BIFI), which has two key ideas: (i) we use the critic to check a fixer's output on real bad inputs and add good (fixed) outputs to the training data, and (ii) we train a breaker to generate realistic bad code from good code. Based on these ideas, we iteratively update the breaker and the fixer while using them in conjunction to generate more paired data. We evaluate BIFI on two code repair datasets: GitHub-Python, a new dataset we introduce where the goal is to repair Python code with AST parse errors; and DeepFix, where the goal is to repair C code with compiler errors. BIFI outperforms existing methods, obtaining 90.5% …

Counterfactual estimation using synthetic controls is one of the most successful recent methodological developments in causal inference. Despite its popularity, the current description only considers time series aligned across units and synthetic controls expressed as linear combinations of observed control units. We propose a continuous-time alternative that models the latent counterfactual path explicitly using the formalism of controlled differential equations. This model is directly applicable to the general setting of irregularly-aligned multivariate time series and may be optimized in rich function spaces -- thereby improving on some limitations of existing approaches.

The success of Convolutional Neural Networks (CNNs) in computer vision is mainly driven by their strong inductive bias, which is strong enough to allow CNNs to solve vision-related tasks with random weights, meaning without learning. Similarly, Long Short-Term Memory (LSTM) has a strong inductive bias towards storing information over time. However, many real-world systems are governed by conservation laws, which lead to the redistribution of particular quantities — e.g.in physical and economical systems. Our novel Mass-Conserving LSTM (MC-LSTM) adheres to these conservation laws by extending the inductive bias of LSTM to model the redistribution of those stored quantities. MC-LSTMs set a new state-of-the-art for neural arithmetic units at learning arithmetic operations, such as addition tasks,which have a strong conservation law, as the sum is constant over time. Further, MC-LSTM is applied to traffic forecasting, modeling a pendulum, and a large benchmark dataset in hydrology, where it sets a new state-of-the-art for predicting peak flows. In the hydrology example, we show that MC-LSTM states correlate with real world processes and are therefore interpretable.

We present deep learning methods for the design of arrays and single instances of small antennas. Each design instance is conditioned on a target radiation pattern and is required to conform to specific spatial dimensions and to include, as part of its metallic structure, a set of predetermined locations. The solution, in the case of a single antenna, is based on a composite neural network that combines a simulation network, a hypernetwork, and a refinement network. In the design of the antenna array, we add an additional design level and employ a hypernetwork within a hypernetwork. The learning objective is based on measuring the similarity of the obtained radiation pattern to the desired one. Our experiments demonstrate that our approach is able to design novel antennas and antenna arrays that are compliant with the design requirements, considerably better than the baseline methods. We compare the solutions obtained by our method to existing designs and demonstrate a high level of overlap. When designing the antenna array of a cellular phone, the obtained solution displays improved properties over the existing one.

We present a novel adaptive cruise control (ACC) system namely SAINT-ACC: {S}afety-{A}ware {Int}elligent {ACC} system (SAINT-ACC) that is designed to achieve simultaneous optimization of traffic efficiency, driving safety, and driving comfort through dynamic adaptation of the inter-vehicle gap based on deep reinforcement learning (RL). A novel dual RL agent-based approach is developed to seek and adapt the optimal balance between traffic efficiency and driving safety/comfort by effectively controlling the driving safety model parameters and inter-vehicle gap based on macroscopic and microscopic traffic information collected from dynamically changing and complex traffic environments. Results obtained through over 12,000 simulation runs with varying traffic scenarios and penetration rates demonstrate that SAINT-ACC significantly enhances traffic flow, driving safety and comfort compared with a state-of-the-art approach.

32% of all global deaths in the world are caused by cardiovascular diseases. Early detection, especially for patients with ischemia or cardiac arrhythmia, is crucial. To reduce the time between symptoms onset and treatment, wearable ECG sensors were developed to allow for the recording of the full 12-lead ECG signal at home. However, if even a single lead is not correctly positioned on the body that lead becomes corrupted, making automatic diagnosis on the basis of the full signal impossible. In this work, we present a methodology to reconstruct missing or noisy leads using the theory of Koopman Operators. Given a dataset consisting of full 12-lead ECGs, we learn a dynamical system describing the evolution of the 12 individual signals together in time. The Koopman theory indicates that there exists a high-dimensional embedding space in which the operator which propagates from one time instant to the next is linear. We therefore learn both the mapping to this embedding space, as well as the corresponding linear operator. Armed with this representation, we are able to impute missing leads by solving a least squares system in the embedding space, which can be achieved efficiently due to the sparse structure of the system. …

A landmark challenge for AI is to learn flexible, powerful representations from small numbers of examples. On an important class of tasks, hypotheses in the form of programs provide extreme generalization capabilities from surprisingly few examples. However, whereas large natural few-shot learning image benchmarks have spurred progress in meta-learning for deep networks, there is no comparably big, natural program-synthesis dataset that can play a similar role. This is because, whereas images are relatively easy to label from internet meta-data or annotated by non-experts, generating meaningful input-output examples for program induction has proven hard to scale. In this work, we propose a new way of leveraging unit tests and natural inputs for small programs as meaningful input-output examples for each sub-program of the overall program. This allows us to create a large-scale naturalistic few-shot program-induction benchmark and propose new challenges in this domain. The evaluation of multiple program induction and synthesis algorithms points to shortcomings of current methods and suggests multiple avenues for future work.

Can models with particular structure avoid being biased towards spurious correlation in out-of-distribution (OOD) generalization? Peters et al. (2016) provides a positive answer for linear cases. In this paper, we use a functional modular probing method to analyze deep model structures under OOD setting. We demonstrate that even in biased models (which focus on spurious correlation) there still exist unbiased functional subnetworks. Furthermore, we articulate and confirm the functional lottery ticket hypothesis: the full network contains a subnetwork with proper structure that can achieve better OOD performance. We then propose Modular Risk Minimization to solve the subnetwork selection problem. Our algorithm learns the functional structure from a given dataset, and can be combined with any other OOD regularization methods. Experiments on various OOD generalization tasks corroborate the effectiveness of our method.

In real-world applications, data often come in a growing manner, where the data volume and the number of classes may increase dynamically. This will bring a critical challenge for learning: given the increasing data volume or the number of classes, one has to instantaneously adjust the neural model capacity to obtain promising performance. Existing methods either ignore the growing nature of data or seek to independently search an optimal architecture for a given dataset, and thus are incapable of promptly adjusting the architectures for the changed data. To address this, we present a neural architecture adaptation method, namely Adaptation eXpert (AdaXpert), to efficiently adjust previous architectures on the growing data. Specifically, we introduce an architecture adjuster to generate a suitable architecture for each data snapshot, based on the previous architecture and the different extent between current and previous data distributions. Furthermore, we propose an adaptation condition to determine the necessity of adjustment, thereby avoiding unnecessary and time-consuming adjustments. Extensive experiments on two growth scenarios (increasing data volume and number of classes) demonstrate the effectiveness of the proposed method.

Stochastic differential equations (SDEs) are a staple of mathematical modelling of temporal dynamics. However, a fundamental limitation has been that such models have typically been relatively inflexible, which recent work introducing Neural SDEs has sought to solve. Here, we show that the current classical approach to fitting SDEs may be approached as a special case of (Wasserstein) GANs, and in doing so the neural and classical regimes may be brought together. The input noise is Brownian motion, the output samples are time-evolving paths produced by a numerical solver, and by parameterising a discriminator as a Neural Controlled Differential Equation (CDE), we obtain Neural SDEs as (in modern machine learning parlance) continuous-time generative time series models. Unlike previous work on this problem, this is a direct extension of the classical approach without reference to either prespecified statistics or density functions. Arbitrary drift and diffusions are admissible, so as the Wasserstein loss has a unique global minima, in the infinite data limit \textit{any} SDE may be learnt.

Conformal Predictors (CP) are wrappers around ML models, providing error guarantees under weak assumptions on the data distribution. They are suitable for a wide range of problems, from classification and regression to anomaly detection. Unfortunately, their very high computational complexity limits their applicability to large datasets. In this work, we show that it is possible to speed up a CP classifier considerably, by studying it in conjunction with the underlying ML method, and by exploiting incremental\&decremental learning. For methods such as k-NN, KDE, and kernel LS-SVM, our approach reduces the running time by one order of magnitude, whilst producing exact solutions. With similar ideas, we also achieve a linear speed up for the harder case of bootstrapping. Finally, we extend these techniques to improve upon an optimization of k-NN CP for regression. We evaluate our findings empirically, and discuss when methods are suitable for CP optimization.

Machine learning models are often deployed in different settings than they were trained and validated on, posing a challenge to practitioners who wish to predict how well the deployed model will perform on a target distribution. If an unlabeled sample from the target distribution is available, along with a labeled sample from a possibly different source distribution, standard approaches such as importance weighting can be applied to estimate performance on the target. However, importance weighting struggles when the source and target distributions have non-overlapping support or are high-dimensional. Taking inspiration from fields such as epidemiology and polling, we develop Mandoline, a new evaluation framework that mitigates these issues. Our key insight is that practitioners may have prior knowledge about the ways in which the distribution shifts, which we can use to better guide the importance weighting procedure. Specifically, users write simple "slicing functions" – noisy, potentially correlated binary functions intended to capture possible axes of distribution shift – to compute reweighted performance estimates. We further describe a density ratio estimation framework for the slices and show how its estimation error scales with slice quality and dataset size. Empirical validation on NLP and vision tasks shows that Mandoline can estimate performance …

Methods that infer causal dependence from observational data are central to many areas of science, including medicine, economics, and the social sciences. A variety of theoretical properties of these methods have been proven, but empirical evaluation remains a challenge, largely due to the lack of observational data sets for which treatment effect is known. We describe and analyze observational sampling from randomized controlled trials (OSRCT), a method for evaluating causal inference methods using data from randomized controlled trials (RCTs). This method can be used to create constructed observational data sets with corresponding unbiased estimates of treatment effect, substantially increasing the number of data sets available for evaluating causal inference methods. We show that, in expectation, OSRCT creates data sets that are equivalent to those produced by randomly sampling from empirical data sets in which all potential outcomes are available. We then perform a large-scale evaluation of seven causal inference methods over 37 data sets, drawn from RCTs, as well as simulators, real-world computational systems, and observational data sets augmented with a synthetic response variable. We find notable performance differences when comparing across data from different sources, demonstrating the importance of using data from a variety of sources when evaluating any …

We propose a randomized algorithm with quadratic convergence rate for convex optimization problems with a self-concordant, composite, strongly convex objective function. Our method is based on performing an approximate Newton step using a random projection of the Hessian. Our first contribution is to show that, at each iteration, the embedding dimension (or sketch size) can be as small as the effective dimension of the Hessian matrix. Leveraging this novel fundamental result, we design an algorithm with a sketch size proportional to the effective dimension and which exhibits a quadratic rate of convergence. This result dramatically improves on the classical linear-quadratic convergence rates of state-of-the-art sub-sampled Newton methods. However, in most practical cases, the effective dimension is not known beforehand, and this raises the question of how to pick a sketch size as small as the effective dimension while preserving a quadratic convergence rate. Our second and main contribution is thus to propose an adaptive sketch size algorithm with quadratic convergence rate and which does not require prior knowledge or estimation of the effective dimension: at each iteration, it starts with a small sketch size, and increases it until quadratic progress is achieved. Importantly, we show that the embedding dimension remains …

This paper is concerned about a learning algorithm for a probabilistic model of spiking neural networks (SNNs). Jimenez Rezende & Gerstner (2014) proposed a stochastic variational inference algorithm to train SNNs with hidden neurons. The algorithm updates the variational distribution using the score function gradient estimator, whose high variance often impedes the whole learning algorithm. This paper presents an alternative gradient estimator for SNNs based on the path-wise gradient estimator. The main technical difficulty is a lack of a general method to differentiate a realization of an arbitrary point process, which is necessary to derive the path-wise gradient estimator. We develop a differentiable point process, which is the technical highlight of this paper, and apply it to derive the path-wise gradient estimator for SNNs. We investigate the effectiveness of our gradient estimator through numerical simulation.

A key problem in the theory of meta-learning is to understand how the task distributions influence transfer risk, the expected error of a meta-learner on a new task drawn from the unknown task distribution. In this paper, focusing on fixed design linear regression with Gaussian noise and a Gaussian task (or parameter) distribution, we give distribution-dependent lower bounds on the transfer risk of any algorithm, while we also show that a novel, weighted version of the so-called biased regularized regression method is able to match these lower bounds up to a fixed constant factor. Notably, the weighting is derived from the covariance of the Gaussian task distribution. Altogether, our results provide a precise characterization of the difficulty of meta-learning in this Gaussian setting. While this problem setting may appear simple, we show that it is rich enough to unify the “parameter sharing” and “representation learning” streams of meta-learning; in particular, representation learning is obtained as the special case when the covariance matrix of the task distribution is unknown. For this case we propose to adopt the EM method, which is shown to enjoy efficient updates in our case. The paper is completed by an empirical study of EM. In particular, …

Predicting molecular conformations (or 3D structures) from molecular graphs is a fundamental problem in many applications. Most existing approaches are usually divided into two steps by first predicting the distances between atoms and then generating a 3D structure through optimizing a distance geometry problem. However, the distances predicted with such two-stage approaches may not be able to consistently preserve the geometry of local atomic neighborhoods, making the generated structures unsatisfying. In this paper, we propose an end-to-end solution for molecular conformation prediction called ConfVAE based on the conditional variational autoencoder framework. Specifically, the molecular graph is first encoded in a latent space, and then the 3D structures are generated by solving a principled bilevel optimization program. Extensive experiments on several benchmark data sets prove the effectiveness of our proposed approach over existing state-of-the-art approaches. Code is available at \url{https://github.com/MinkaiXu/ConfVAE-ICML21}.

This paper prescribes a distance between learning tasks modeled as joint distributions on data and labels. Using tools in information geometry, the distance is defined to be the length of the shortest weight trajectory on a Riemannian manifold as a classifier is fitted on an interpolated task. The interpolated task evolves from the source to the target task using an optimal transport formulation. This distance, which we call the "coupled transfer distance" can be compared across different classifier architectures. We develop an algorithm to compute the distance which iteratively transports the marginal on the data of the source task to that of the target task while updating the weights of the classifier to track this evolving data distribution. We develop theory to show that our distance captures the intuitive idea that a good transfer trajectory is the one that keeps the generalization gap small during transfer, in particular at the end on the target task. We perform thorough empirical validation and analysis across diverse image classification datasets to show that the coupled transfer distance correlates strongly with the difficulty of fine-tuning.

The RKHS bandit problem (also called kernelized multi-armed bandit problem) is an online optimization problem of non-linear functions with noisy feedback. Although the problem has been extensively studied, there are unsatisfactory results for some problems compared to the well-studied linear bandit case. Specifically, there is no general algorithm for the adversarial RKHS bandit problem. In addition, high computational complexity of existing algorithms hinders practical application. We address these issues by considering a novel amalgamation of approximation theory and the misspecified linear bandit problem. Using an approximation method, we propose efficient algorithms for the stochastic RKHS bandit problem and the first general algorithm for the adversarial RKHS bandit problem. Furthermore, we empirically show that one of our proposed methods has comparable cumulative regret to IGP-UCB and its running time is much shorter.

Robust loss functions are essential for training deep neural networks with better generalization power in the presence of noisy labels. Symmetric loss functions are confirmed to be robust to label noise. However, the symmetric condition is overly restrictive. In this work, we propose a new class of loss functions, namely asymmetric loss functions, which are robust to learning from noisy labels for arbitrary noise type. Subsequently, we investigate general theoretical properties of asymmetric loss functions, including classification-calibration, excess risk bound, and noise-tolerance. Meanwhile, we introduce the asymmetry ratio to measure the asymmetry of a loss function, and the empirical results show that a higher ratio will provide better robustness. Moreover, we modify several common loss functions, and establish the necessary and sufficient conditions for them to be asymmetric. Experiments on benchmark datasets demonstrate that asymmetric loss functions can outperform state-of-the-art methods.

One of the central problems in machine learning is domain adaptation. Different from past theoretical works, we consider a new model of subpopulation shift in the input or representation space. In this work, we propose a provably effective framework based on label propagation by using an input consistency loss. In our analysis we used a simple but realistic “expansion” assumption, which has been proposed in \citet{wei2021theoretical}. It turns out that based on a teacher classifier on the source domain, the learned classifier can not only propagate to the target domain but also improve upon the teacher. By leveraging existing generalization bounds, we also obtain end-to-end finite-sample guarantees on deep neural networks. In addition, we extend our theoretical framework to a more general setting of source-to-target transfer based on an additional unlabeled dataset, which can be easily applied to various learning scenarios. Inspired by our theory, we adapt consistency-based semi-supervised learning methods to domain adaptation settings and gain significant improvements.

In this work, we propose TimeGrad, an autoregressive model for multivariate probabilistic time series forecasting which samples from the data distribution at each time step by estimating its gradient. To this end, we use diffusion probabilistic models, a class of latent variable models closely connected to score matching and energy-based methods. Our model learns gradients by optimizing a variational bound on the data likelihood and at inference time converts white noise into a sample of the distribution of interest through a Markov chain using Langevin sampling. We demonstrate experimentally that the proposed autoregressive denoising diffusion model is the new state-of-the-art multivariate probabilistic forecasting method on real-world data sets with thousands of correlated dimensions. We hope that this method is a useful tool for practitioners and lays the foundation for future research in this area.

The goal of classification with rejection is to avoid risky misclassification in error-critical applications such as medical diagnosis and product inspection. In this paper, based on the relationship between classification with rejection and cost-sensitive classification, we propose a novel method of classification with rejection by learning an ensemble of cost-sensitive classifiers, which satisfies all the following properties: (i) it can avoid estimating class-posterior probabilities, resulting in improved classification accuracy. (ii) it allows a flexible choice of losses including non-convex ones, (iii) it does not require complicated modifications when using different losses, (iv) it is applicable to both binary and multiclass cases, and (v) it is theoretically justifiable for any classification-calibrated loss. Experimental results demonstrate the usefulness of our proposed approach in clean-labeled, noisy-labeled, and positive-unlabeled classification.

The label noise transition matrix, characterizing the probabilities of a training instance being wrongly annotated, is crucial to designing popular solutions to learning with noisy labels. Existing works heavily rely on finding ``anchor points'' or their approximates, defined as instances belonging to a particular class almost surely. Nonetheless, finding anchor points remains a non-trivial task, and the estimation accuracy is also often throttled by the number of available anchor points. In this paper, we propose an alternative option to the above task. Our main contribution is the discovery of an efficient estimation procedure based on a clusterability condition. We prove that with clusterable representations of features, using up to third-order consensuses of noisy labels among neighbor representations is sufficient to estimate a unique transition matrix. Compared with methods using anchor points, our approach uses substantially more instances and benefits from a much better sample complexity. We demonstrate the estimation accuracy and advantages of our estimates using both synthetic noisy labels (on CIFAR-10/100) and real human-level noisy labels (on Clothing1M and our self-collected human-annotated CIFAR-10). Our code and human-level noisy CIFAR-10 labels are available at https://github.com/UCSC-REAL/HOC.

Contrastive learning has recently seen tremendous success in self-supervised learning. So far, however, it is largely unclear why the learned representations generalize so effectively to a large variety of downstream tasks. We here prove that feedforward models trained with objectives belonging to the commonly used InfoNCE family learn to implicitly invert the underlying generative model of the observed data. While the proofs make certain statistical assumptions about the generative model, we observe empirically that our findings hold even if these assumptions are severely violated. Our theory highlights a fundamental connection between contrastive learning, generative modeling, and nonlinear independent component analysis, thereby furthering our understanding of the learned representations as well as providing a theoretical foundation to derive more effective contrastive losses.

In policy search methods for reinforcement learning (RL), exploration is often performed by injecting noise either in action space at each step independently or in parameter space over each full trajectory. In prior work, it has been shown that with linear policies, a more balanced trade-off between these two exploration strategies is beneficial. However, that method did not scale to policies using deep neural networks. In this paper, we introduce deep coherent exploration, a general and scalable exploration framework for deep RL algorithms for continuous control, that generalizes step-based and trajectory-based exploration. This framework models the last layer parameters of the policy network as latent variables and uses a recursive inference step within the policy update to handle these latent variables in a scalable manner. We find that deep coherent exploration improves the speed and stability of learning of A2C, PPO, and SAC on several continuous control tasks.

Despite their widespread success, the application of deep neural networks to functional data remains scarce today. The infinite dimensionality of functional data means standard learning algorithms can be applied only after appropriate dimension reduction, typically achieved via basis expansions. Currently, these bases are chosen a priori without the information for the task at hand and thus may not be effective for the designated task. We instead propose to adaptively learn these bases in an end-to-end fashion. We introduce neural networks that employ a new Basis Layer whose hidden units are each basis functions themselves implemented as a micro neural network. Our architecture learns to apply parsimonious dimension reduction to functional inputs that focuses only on information relevant to the target rather than irrelevant variation in the input function. Across numerous classification/regression tasks with functional data, our method empirically outperforms other types of neural networks, and we prove that our approach is statistically consistent with low generalization error.

We consider the problem of detecting signals in the rank-one signal-plus-noise data matrix models that generalize the spiked Wishart matrices. We show that the principal component analysis can be improved by pre-transforming the matrix entries if the noise is non-Gaussian. As an intermediate step, we prove a sharp phase transition of the largest eigenvalues of spiked rectangular matrices, which extends the Baik--Ben Arous--P\'ech\'e (BBP) transition. We also propose a hypothesis test to detect the presence of signal with low computational complexity, based on the linear spectral statistics, which minimizes the sum of the Type-I and Type-II errors when the noise is Gaussian.

Minimizing cross-entropy over the softmax scores of a linear map composed with a high-capacity encoder is arguably the most popular choice for training neural networks on supervised learning tasks. However, recent works show that one can directly optimize the encoder instead, to obtain equally (or even more) discriminative representations via a supervised variant of a contrastive objective. In this work, we address the question whether there are fundamental differences in the sought-for representation geometry in the output space of the encoder at minimal loss. Specifically, we prove, under mild assumptions, that both losses attain their minimum once the representations of each class collapse to the vertices of a regular simplex, inscribed in a hypersphere. We provide empirical evidence that this configuration is attained in practice and that reaching a close-to-optimal state typically indicates good generalization performance. Yet, the two losses show remarkably different optimization behavior. The number of iterations required to perfectly fit to data scales superlinearly with the amount of randomly flipped labels for the supervised contrastive loss. This is in contrast to the approximately linear scaling previously reported for networks trained with cross-entropy.

When learning from streaming data, a change in the data distribution, also known as concept drift, can render a previously-learned model inaccurate and require training a new model. We present an adaptive learning algorithm that extends previous drift-detection-based methods by incorporating drift detection into a broader stable-state/reactive-state process. The advantage of our approach is that we can use aggressive drift detection in the stable state to achieve a high detection rate, but mitigate the false positive rate of standalone drift detection via a reactive state that reacts quickly to true drifts while eliminating most false positives. The algorithm is generic in its base learner and can be applied across a variety of supervised learning problems. Our theoretical analysis shows that the risk of the algorithm is (i) statistically better than standalone drift detection and (ii) competitive to an algorithm with oracle knowledge of when (abrupt) drifts occur. Experiments on synthetic and real datasets with concept drifts confirm our theoretical analysis.

We investigate the capacity control provided by dropout in various machine learning problems. First, we study dropout for matrix completion, where it induces a distribution-dependent regularizer that equals the weighted trace-norm of the product of the factors. In deep learning, we show that the distribution-dependent regularizer due to dropout directly controls the Rademacher complexity of the underlying class of deep neural networks. These developments enable us to give concrete generalization error bounds for the dropout algorithm in both matrix completion as well as training deep neural networks.

Continuous-time event sequences represent discrete events occurring in continuous time. Such sequences arise frequently in real-life. Usually we expect the sequences to follow some regular pattern over time. However, sometimes these patterns may be interrupted by unexpected absence or occurrences of events. Identification of these unexpected cases can be very important as they may point to abnormal situations that need human attention. In this work, we study and develop methods for detecting outliers in continuous-time event sequences, including unexpected absence and unexpected occurrences of events. Since the patterns that event sequences tend to follow may change in different contexts, we develop outlier detection methods based on point processes that can take context information into account. Our methods are based on Bayesian decision theory and hypothesis testing with theoretical guarantees. To test the performance of the methods, we conduct experiments on both synthetic data and real-world clinical data and show the effectiveness of the proposed methods.

We present an optimization framework for learning a fair classifier in the presence of noisy perturbations in the protected attributes. Compared to prior work, our framework can be employed with a very general class of linear and linear-fractional fairness constraints, can handle multiple, non-binary protected attributes, and outputs a classifier that comes with provable guarantees on both accuracy and fairness. Empirically, we show that our framework can be used to attain either statistical rate or false positive rate fairness guarantees with a minimal loss in accuracy, even when the noise is large, in two real-world datasets.

A fundamental obstacle in learning information from data is the presence of nonlinear redundancies and dependencies in it. To address this, we propose a Fourier-based approach to extract relevant information in the supervised setting. We first develop a novel Fourier expansion for functions of correlated binary random variables. This expansion is a generalization of the standard Fourier analysis on the Boolean cube beyond product probability spaces. We further extend our Fourier analysis to stochastic mappings. As an important application of this analysis, we investigate learning with feature subset selection. We reformulate this problem in the Fourier domain and introduce a computationally efficient measure for selecting features. Bridging the Bayesian error rate with the Fourier coefficients, we demonstrate that the Fourier expansion provides a powerful tool to characterize nonlinear dependencies in the features-label relation. Via theoretical analysis, we show that our proposed measure finds provably asymptotically optimal feature subsets. Lastly, we present an algorithm based on our measure and verify our findings via numerical experiments on various datasets.

The great success of modern machine learning models on large datasets is contingent on extensive computational resources with high financial and environmental costs. One way to address this is by extracting subsets that generalize on par with the full data. In this work, we propose a general framework, GRAD-MATCH, which finds subsets that closely match the gradient of the \emph{training or validation} set. We find such subsets effectively using an orthogonal matching pursuit algorithm. We show rigorous theoretical and convergence guarantees of the proposed algorithm and, through our extensive experiments on real-world datasets, show the effectiveness of our proposed framework. We show that GRAD-MATCH significantly and consistently outperforms several recent data-selection algorithms and achieves the best accuracy-efficiency trade-off. GRAD-MATCH is available as a part of the CORDS toolkit: \url{https://github.com/decile-team/cords}.

Machine learning algorithms with empirical risk minimization usually suffer from poor generalization performance due to the greedy exploitation of correlations among the training data, which are not stable under distributional shifts. Recently, some invariant learning methods for out-of-distribution (OOD) generalization have been proposed by leveraging multiple training environments to find invariant relationships. However, modern datasets are frequently assembled by merging data from multiple sources without explicit source labels. The resultant unobserved heterogeneity renders many invariant learning methods inapplicable. In this paper, we propose Heterogeneous Risk Minimization (HRM) framework to achieve joint learning of latent heterogeneity among the data and invariant relationship, which leads to stable prediction despite distributional shifts. We theoretically characterize the roles of the environment labels in invariant learning and justify our newly proposed HRM framework. Extensive experimental results validate the effectiveness of our HRM framework.

Methods that infer causal dependence from observational data are central to many areas of science, including medicine, economics, and the social sciences. A variety of theoretical properties of these methods have been proven, but empirical evaluation remains a challenge, largely due to the lack of observational data sets for which treatment effect is known. We describe and analyze observational sampling from randomized controlled trials (OSRCT), a method for evaluating causal inference methods using data from randomized controlled trials (RCTs). This method can be used to create constructed observational data sets with corresponding unbiased estimates of treatment effect, substantially increasing the number of data sets available for evaluating causal inference methods. We show that, in expectation, OSRCT creates data sets that are equivalent to those produced by randomly sampling from empirical data sets in which all potential outcomes are available. We then perform a large-scale evaluation of seven causal inference methods over 37 data sets, drawn from RCTs, as well as simulators, real-world computational systems, and observational data sets augmented with a synthetic response variable. We find notable performance differences when comparing across data from different sources, demonstrating the importance of using data from a variety of sources when evaluating any …

Good generalization performance across a wide variety of domains caused by many external and internal factors is the fundamental goal of any machine learning algorithm. This paper theoretically proves that the choice of loss function matters for improving the generalization performance of deep learning-based systems. By deriving the generalization error bound for deep neural models trained by stochastic gradient descent, we pinpoint the characteristics of the loss function that is linked to the generalization error and can therefore be used for guiding the loss function selection process. In summary, our main statement in this paper is: choose a stable loss function, generalize better. Focusing on human age estimation from the face which is a challenging topic in computer vision, we then propose a novel loss function for this learning problem. We theoretically prove that the proposed loss function achieves stronger stability, and consequently a tighter generalization error bound, compared to the other common loss functions for this problem. We have supported our findings theoretically, and demonstrated the merits of the guidance process experimentally, achieving significant improvements.

We consider a popular family of constrained optimization problems arising in machine learning that involve optimizing a non-decomposable evaluation metric with a certain thresholded form, while constraining another metric of interest. Examples of such problems include optimizing false negative rate at a fixed false positive rate, optimizing precision at a fixed recall, optimizing the area under the precision-recall or ROC curves, etc. Our key idea is to formulate a rate-constrained optimization that expresses the threshold parameter as a function of the model parameters via the Implicit Function theorem. We show how the resulting optimization problem can be solved using standard gradient based methods. Experiments on benchmark datasets demonstrate the effectiveness of our proposed method over existing state-of-the-art approaches for these problems.

Consider a prosthetic arm, learning to adapt to its user's control signals. We propose \emph{Interaction-Grounded Learning} for this novel setting, in which a learner's goal is to interact with the environment with no grounding or explicit reward to optimize its policies. Such a problem evades common RL solutions which require an explicit reward. The learning agent observes a multidimensional \emph{context vector}, takes an \emph{action}, and then observes a multidimensional \emph{feedback vector}. This multidimensional feedback vector has \emph{no} explicit reward information. In order to succeed, the algorithm must learn how to evaluate the feedback vector to discover a latent reward signal, with which it can ground its policies without supervision. We show that in an Interaction-Grounded Learning setting, with certain natural assumptions, a learner can discover the latent reward and ground its policy for successful interaction. We provide theoretical guarantees and a proof-of-concept empirical evaluation to demonstrate the effectiveness of our proposed approach.

Landmark codes underpin reliable physical layer communication, e.g., Reed-Muller, BCH, Convolution, Turbo, LDPC, and Polar codes: each is a linear code and represents a mathematical breakthrough. The impact on humanity is huge: each of these codes has been used in global wireless communication standards (satellite, WiFi, cellular). Reliability of communication over the classical additive white Gaussian noise (AWGN) channel enables benchmarking and ranking of the different codes. In this paper, we construct KO codes, a computationally efficient family of deep-learning driven (encoder, decoder) pairs that outperform the state-of-the-art reliability performance on the standardized AWGN channel. KO codes beat state-of-the-art Reed-Muller and Polar codes, under the low-complexity successive cancellation decoding, in the challenging short-to-medium block length regime on the AWGN channel. We show that the gains of KO codes are primarily due to the nonlinear mapping of information bits directly to transmit symbols (bypassing modulation) and yet possess an efficient, high-performance decoder. The key technical innovation that renders this possible is design of a novel family of neural architectures inspired by the computation tree of the {\bf K}ronecker {\bf O}peration (KO) central to Reed-Muller and Polar codes. These architectures pave way for the discovery of a much richer class of hitherto …

A key problem in program synthesis is searching over the large space of possible programs. Human programmers might decide the high-level structure of the desired program before thinking about the details; motivated by this intuition, we consider two-level search for program synthesis, in which the synthesizer first generates a plan, a sequence of symbols that describes the desired program at a high level, before generating the program. We propose to learn representations of programs that can act as plans to organize such a two-level search. Discrete latent codes are appealing for this purpose, and can be learned by applying recent work on discrete autoencoders. Based on these insights, we introduce the Latent Programmer (LP), a program synthesis method that first predicts a discrete latent code from input/output examples, and then generates the program in the target language. We evaluate the LP on two domains, demonstrating that it yields an improvement in accuracy, especially on longer programs for which search is most difficult.

Intersection over union (IoU) score, also named Jaccard Index, is one of the most fundamental evaluation methods in machine learning. The original IoU computation cannot provide non-zero gradients and thus cannot be directly optimized by nowadays deep learning methods. Several recent works generalized IoU for bounding box regression, but they are not straightforward to adapt for pixelwise prediction. In particular, the original IoU fails to provide effective gradients for the non-overlapping and location-deviation cases, which results in performance plateau. In this paper, we propose PixIoU, a generalized IoU for pixelwise prediction that is sensitive to the distance for non-overlapping cases and the locations in prediction. We provide proofs that PixIoU holds many nice properties as the original IoU. To optimize the PixIoU, we also propose a loss function that is proved to be submodular, hence we can apply the Lov\'asz functions, the efficient surrogates for submodular functions for learning this loss. Experimental results show consistent performance improvements by learning PixIoU over the original IoU for several different pixelwise prediction tasks on Pascal VOC, VOT-2020 and Cityscapes.

We study a fundamental problem in computational chemistry known as molecular conformation generation, trying to predict stable 3D structures from 2D molecular graphs. Existing machine learning approaches usually first predict distances between atoms and then generate a 3D structure satisfying the distances, where noise in predicted distances may induce extra errors during 3D coordinate generation. Inspired by the traditional force field methods for molecular dynamics simulation, in this paper, we propose a novel approach called ConfGF by directly estimating the gradient fields of the log density of atomic coordinates. The estimated gradient fields allow directly generating stable conformations via Langevin dynamics. However, the problem is very challenging as the gradient fields are roto-translation equivariant. We notice that estimating the gradient fields of atomic coordinates can be translated to estimating the gradient fields of interatomic distances, and hence develop a novel algorithm based on recent score-based generative models to effectively estimate these gradients. Experimental results across multiple tasks show that ConfGF outperforms previous state-of-the-art baselines by a significant margin.

In single-item auction design, it is well known due to Cremer and McLean that when bidders’ valuations are drawn from a correlated prior distribution, the auctioneer can extract full social surplus as revenue. However, in most real-world applications, the prior is usually unknown and can only be learned from historical data. In this work, we investigate the robustness of the optimal auction with correlated valuations via sample complexity analysis. We prove upper and lower bounds on the number of samples from the unknown prior required to learn a (1-epsilon)-approximately optimal auction. Our results reinforce the common belief that optimal correlated auctions are sensitive to the distribution parameters and hard to learn unless the prior distribution is well-behaved.

Machine learning models are often deployed in different settings than they were trained and validated on, posing a challenge to practitioners who wish to predict how well the deployed model will perform on a target distribution. If an unlabeled sample from the target distribution is available, along with a labeled sample from a possibly different source distribution, standard approaches such as importance weighting can be applied to estimate performance on the target. However, importance weighting struggles when the source and target distributions have non-overlapping support or are high-dimensional. Taking inspiration from fields such as epidemiology and polling, we develop Mandoline, a new evaluation framework that mitigates these issues. Our key insight is that practitioners may have prior knowledge about the ways in which the distribution shifts, which we can use to better guide the importance weighting procedure. Specifically, users write simple "slicing functions" – noisy, potentially correlated binary functions intended to capture possible axes of distribution shift – to compute reweighted performance estimates. We further describe a density ratio estimation framework for the slices and show how its estimation error scales with slice quality and dataset size. Empirical validation on NLP and vision tasks shows that Mandoline can estimate performance …

In multi-dimensional classification (MDC), there are multiple class variables in the output space with each of them corresponding to one heterogeneous class space. Due to the heterogeneity of class spaces, it is quite challenging to consider the dependencies among class variables when learning from MDC examples. In this paper, we propose a novel MDC approach named SLEM which learns the predictive model in an encoded label space instead of the original heterogeneous one. Specifically, SLEM works in an encoding-training-decoding framework. In the encoding phase, each class vector is mapped into a real-valued one via three cascaded operations including pairwise grouping, one-hot conversion and sparse linear encoding. In the training phase, a multi-output regression model is learned within the encoded label space. In the decoding phase, the predicted class vector is obtained by adapting orthogonal matching pursuit over outputs of the learned multi-output regression model. Experimental results clearly validate the superiority of SLEM against state-of-the-art MDC approaches.

Transfer learning is essential when sufficient data comes from the source domain, with scarce labeled data from the target domain. We develop estimators that achieve minimax linear risk for linear regression problems under distribution shift. Our algorithms cover different transfer learning settings including covariate shift and model shift. We also consider when data are generated from either linear or general nonlinear models. We show that linear minimax estimators are within an absolute constant of the minimax risk even among nonlinear estimators for various source/target distributions.

Reliably predicting the products of chemical reactions presents a fundamental challenge in synthetic chemistry. Existing machine learning approaches typically produce a reaction product by sequentially forming its subparts or intermediate molecules. Such autoregressive methods, however, not only require a pre-defined order for the incremental construction but preclude the use of parallel decoding for efficient computation. To address these issues, we devise a non-autoregressive learning paradigm that predicts reaction in one shot. Leveraging the fact that chemical reactions can be described as a redistribution of electrons in molecules, we formulate a reaction as an arbitrary electron flow and predict it with a novel multi-pointer decoding network. Experiments on the USPTO-MIT dataset show that our approach has established a new state-of-the-art top-1 accuracy and achieves at least 27 times inference speedup over the state-of-the-art methods. Also, our predictions are easier for chemists to interpret owing to predicting the electron flows.

We provide a unifying view of a large family of previous imitation learning algorithms through the lens of moment matching. At its core, our classification scheme is based on whether the learner attempts to match (1) reward or (2) action-value moments of the expert's behavior, with each option leading to differing algorithmic approaches. By considering adversarially chosen divergences between learner and expert behavior, we are able to derive bounds on policy performance that apply for all algorithms in each of these classes, the first to our knowledge. We also introduce the notion of moment recoverability, implicit in many previous analyses of imitation learning, which allows us to cleanly delineate how well each algorithmic family is able to mitigate compounding errors. We derive three novel algorithm templates (AdVIL, AdRIL, and DAeQuIL) with strong guarantees, simple implementation, and competitive empirical performance.

Neural networks trained via gradient descent with random initialization and without any regularization enjoy good generalization performance in practice despite being highly overparametrized. A promising direction to explain this phenomenon is to study how initialization and overparametrization affect convergence and implicit bias of training algorithms. In this paper, we present a novel analysis of single-hidden-layer linear networks trained under gradient flow, which connects initialization, optimization, and overparametrization. Firstly, we show that the squared loss converges exponentially to its optimum at a rate that depends on the level of imbalance of the initialization. Secondly, we show that proper initialization constrains the dynamics of the network parameters to lie within an invariant set. In turn, minimizing the loss over this set leads to the min-norm solution. Finally, we show that large hidden layer width, together with (properly scaled) random initialization, ensures proximity to such an invariant set during training, allowing us to derive a novel non-asymptotic upper-bound on the distance between the trained network and the min-norm solution.

We consider learning to optimize a classification metric defined by a black-box function of the confusion matrix. Such black-box learning settings are ubiquitous, for example, when the learner only has query access to the metric of interest, or in noisy-label and domain adaptation applications where the learner must evaluate the metric via performance evaluation using a small validation sample. Our approach is to adaptively learn example weights on the training dataset such that the resulting weighted objective best approximates the metric on the validation sample. We show how to model and estimate the example weights and use them to iteratively post-shift a pre-trained class probability estimator to construct a classifier. We also analyze the resulting procedure's statistical properties. Experiments on various label noise, domain shift, and fair classification setups confirm that our proposal compares favorably to the state-of-the-art baselines for each application.

We tackle the problem of conditioning probabilistic programs on distributions of observable variables. Probabilistic programs are usually conditioned on samples from the joint data distribution, which we refer to as deterministic conditioning. However, in many real-life scenarios, the observations are given as marginal distributions, summary statistics, or samplers. Conventional probabilistic programming systems lack adequate means for modeling and inference in such scenarios. We propose a generalization of deterministic conditioning to stochastic conditioning, that is, conditioning on the marginal distribution of a variable taking a particular form. To this end, we first define the formal notion of stochastic conditioning and discuss its key properties. We then show how to perform inference in the presence of stochastic conditioning. We demonstrate potential usage of stochastic conditioning on several case studies which involve various kinds of stochastic conditioning and are difficult to solve otherwise. Although we present stochastic conditioning in the context of probabilistic programming, our formalization is general and applicable to other settings.

Online allocation problems with resource constraints have a rich history in computer science and operations research. In this paper, we introduce the regularized online allocation problem, a variant that includes a non-linear regularizer acting on the total resource consumption. In this problem, requests repeatedly arrive over time and, for each request, a decision maker needs to take an action that generates a reward and consumes resources. The objective is to simultaneously maximize total rewards and the value of the regularizer subject to the resource constraints. Our primary motivation is the online allocation of internet advertisements wherein firms seek to maximize additive objectives such as the revenue or efficiency of the allocation. By introducing a regularizer, firms can account for the fairness of the allocation or, alternatively, punish under-delivery of advertisements---two common desiderata in internet advertising markets. We design an algorithm when arrivals are drawn independently from a distribution that is unknown to the decision maker. Our algorithm is simple, fast, and attains the optimal order of sub-linear regret compared to the optimal allocation with the benefit of hindsight. Numerical experiments confirm the effectiveness of the proposed algorithm and of the regularizers in an internet advertising application.

We study exploration in stochastic multi-armed bandits when we have access to a divisible resource that can be allocated in varying amounts to arm pulls. We focus in particular on the allocation of distributed computing resources, where we may obtain results faster by allocating more resources per pull, but might have reduced throughput due to nonlinear scaling. For example, in simulation-based scientific studies, an expensive simulation can be sped up by running it on multiple cores. This speed-up however, is partly offset by the communication among cores, which results in lower throughput than if fewer cores were allocated to run more trials in parallel. In this paper, we explore these trade-offs in two settings. First, in a fixed confidence setting, we need to find the best arm with a given target success probability as quickly as possible. We propose an algorithm which trades off between information accumulation and throughput and show that the time taken can be upper bounded by the solution of a dynamic program whose inputs are the gaps between the sub-optimal and optimal arms. We also prove a matching hardness result. Second, we present an algorithm for a fixed deadline setting, where we are given a time …

Spatio-temporal forecasting has numerous applications in analyzing wireless, traffic, and financial networks. Many classical statistical models often fall short in handling the complexity and high non-linearity present in time-series data. Recent advances in deep learning allow for better modelling of spatial and temporal dependencies. While most of these models focus on obtaining accurate point forecasts, they do not characterize the prediction uncertainty. In this work, we consider the time-series data as a random realization from a nonlinear state-space model and target Bayesian inference of the hidden states for probabilistic forecasting. We use particle flow as the tool for approximating the posterior distribution of the states, as it is shown to be highly effective in complex, high-dimensional settings. Thorough experimentation on several real world time-series datasets demonstrates that our approach provides better characterization of uncertainty while maintaining comparable accuracy to the state-of-the-art point forecasting methods.

Many sequential decision problems involve finding a policy that maximizes total reward while obeying safety constraints. Although much recent research has focused on the development of safe reinforcement learning (RL) algorithms that produce a safe policy after training, ensuring safety during training as well remains an open problem. A fundamental challenge is performing exploration while still satisfying constraints in an unknown Markov decision process (MDP). In this work, we address this problem for the chance-constrained setting.We propose a new algorithm, SAILR, that uses an intervention mechanism based on advantage functions to keep the agent safe throughout training and optimizes the agent's policy using off-the-shelf RL algorithms designed for unconstrained MDPs. Our method comes with strong guarantees on safety during "both" training and deployment (i.e., after training and without the intervention mechanism) and policy performance compared to the optimal safety-constrained policy. In our experiments, we show that SAILR violates constraints far less during training than standard safe RL and constrained MDP approaches and converges to a well-performing policy that can be deployed safely without intervention. Our code is available at https://github.com/nolanwagener/safe_rl.

Smooth dynamics interrupted by discontinuities are known as hybrid systems and arise commonly in nature. Latent ODEs allow for powerful representation of irregularly sampled time series but are not designed to capture trajectories arising from hybrid systems. Here, we propose the Latent Segmented ODE (LatSegODE), which uses Latent ODEs to perform reconstruction and changepoint detection within hybrid trajectories featuring jump discontinuities and switching dynamical modes. Where it is possible to train a Latent ODE on the smooth dynamical flows between discontinuities, we apply the pruned exact linear time (PELT) algorithm to detect changepoints where latent dynamics restart, thereby maximizing the joint probability of a piece-wise continuous latent dynamical representation. We propose usage of the marginal likelihood as a score function for PELT, circumventing the need for model-complexity-based penalization. The LatSegODE outperforms baselines in reconstructive and segmentation tasks including synthetic data sets of sine waves, Lotka Volterra dynamics, and UCI Character Trajectories.

There has been recently a significant boost to machine learning with distributed data, in particular with the success of federated learning. A common and very challenging setting is that of vertical or feature partitioned data, when multiple data providers hold different features about common entities. In general, training needs to be preceded by record linkage (RL), a step that finds the correspondence between the observations of the datasets. RL is prone to mistakes in the real world. Despite the importance of the problem, there has been so far no formal assessment of the way in which RL errors impact learning models. Work in the area either use heuristics or assume that the optimal RL is known in advance. In this paper, we provide the first assessment of the problem for supervised learning. For wide sets of losses, we provide technical conditions under which the classifier learned after noisy RL converges (with the data size) to the best classifier that would be learned from mistake-free RL. This yields new insights on the way the pipeline RL + ML operates, from the role of large margin classification on dampening the impact of RL mistakes to clues on how to further optimize RL …

Despite their overwhelming capacity to overfit, deep neural networks trained by specific optimization algorithms tend to generalize relatively well to unseen data. Recently, researchers explained it by investigating the implicit bias of optimization algorithms. A remarkable progress is the work (Lyu & Li, 2019), which proves gradient descent (GD) maximizes the margin of homogeneous deep neural networks. Except the first-order optimization algorithms like GD, adaptive algorithms such as AdaGrad, RMSProp and Adam are popular owing to their rapid training process. Mean-while, numerous works have provided empirical evidence that adaptive methods may suffer from poor generalization performance. However, theoretical explanation for the generalization of adaptive optimization algorithms is still lacking. In this paper, we study the implicit bias of adaptive optimization algorithms on homogeneous neural networks. In particular, we study the convergent direction of parameters when they are optimizing the logistic loss. We prove that the convergent direction of Adam and RMSProp is the same as GD, while for AdaGrad, the convergent direction depends on the adaptive conditioner. Technically, we provide a unified framework to analyze convergent direction of adaptive optimization algorithms by constructing novel and nontrivial adaptive gradient flow and surrogate margin. The theoretical findings explain the superiority on generalization …

The success of minimax learning problems of generative adversarial networks (GANs) has been observed to depend on the minimax optimization algorithm used for their training. This dependence is commonly attributed to the convergence speed and robustness properties of the underlying optimization algorithm. In this paper, we show that the optimization algorithm also plays a key role in the generalization performance of the trained minimax model. To this end, we analyze the generalization properties of standard gradient descent ascent (GDA) and proximal point method (PPM) algorithms through the lens of algorithmic stability as defined by Bousquet & Elisseeff, 2002 under both convex-concave and nonconvex-nonconcave minimax settings. While the GDA algorithm is not guaranteed to have a vanishing excess risk in convex-concave problems, we show the PPM algorithm enjoys a bounded excess risk in the same setup. For nonconvex-nonconcave problems, we compare the generalization performance of stochastic GDA and GDmax algorithms where the latter fully solves the maximization subproblem at every iteration. Our generalization analysis suggests the superiority of GDA provided that the minimization and maximization subproblems are solved simultaneously with similar learning rates. We discuss several numerical results indicating the role of optimization algorithms in the generalization of learned minimax models.

A discriminatively trained neural net classifier can fit the training data perfectly if all information about its input other than class membership has been discarded prior to the output layer. Surprisingly, past research has discovered that some extraneous visual detail remains in the unnormalized logits. This finding is based on inversion techniques that map deep embeddings back to images. We explore this phenomenon further using a novel synthesis of methods, yielding a feedforward inversion model that produces remarkably high fidelity reconstructions, qualitatively superior to those of past efforts. When applied to an adversarially robust classifier model, the reconstructions contain sufficient local detail and global structure that they might be confused with the original image in a quick glance, and the object category can clearly be gleaned from the reconstruction. Our approach is based on BigGAN (Brock, 2019), with conditioning on logits instead of one-hot class labels. We use our reconstruction model as a tool for exploring the nature of representations, including: the influence of model architecture and training objectives (specifically robust losses), the forms of invariance that networks achieve, representational differences between correctly and incorrectly classified images, and the effects of manipulating logits and images. We believe that our method …

32% of all global deaths in the world are caused by cardiovascular diseases. Early detection, especially for patients with ischemia or cardiac arrhythmia, is crucial. To reduce the time between symptoms onset and treatment, wearable ECG sensors were developed to allow for the recording of the full 12-lead ECG signal at home. However, if even a single lead is not correctly positioned on the body that lead becomes corrupted, making automatic diagnosis on the basis of the full signal impossible. In this work, we present a methodology to reconstruct missing or noisy leads using the theory of Koopman Operators. Given a dataset consisting of full 12-lead ECGs, we learn a dynamical system describing the evolution of the 12 individual signals together in time. The Koopman theory indicates that there exists a high-dimensional embedding space in which the operator which propagates from one time instant to the next is linear. We therefore learn both the mapping to this embedding space, as well as the corresponding linear operator. Armed with this representation, we are able to impute missing leads by solving a least squares system in the embedding space, which can be achieved efficiently due to the sparse structure of the system. …

Feedforward computation, such as evaluating a neural network or sampling from an autoregressive model, is ubiquitous in machine learning. The sequential nature of feedforward computation, however, requires a strict order of execution and cannot be easily accelerated with parallel computing. To enable parallelization, we frame the task of feedforward computation as solving a system of nonlinear equations. We then propose to find the solution using a Jacobi or Gauss-Seidel fixed-point iteration method, as well as hybrid methods of both. Crucially, Jacobi updates operate independently on each equation and can be executed in parallel. Our method is guaranteed to give exactly the same values as the original feedforward computation with a reduced (or equal) number of parallelizable iterations, and hence reduced time given sufficient parallel computing power. Experimentally, we demonstrate the effectiveness of our approach in accelerating (i) backpropagation of RNNs, (ii) evaluation of DenseNets, and (iii) autoregressive sampling of MADE and PixelCNN++, with speedup factors between 2.1 and 26 under various settings.

For machine learning systems to be reliable, we must understand their performance in unseen, out- of-distribution environments. In this paper, we empirically show that out-of-distribution performance is strongly correlated with in-distribution performance for a wide range of models and distribution shifts. Specifically, we demonstrate strong correlations between in-distribution and out-of- distribution performance on variants of CIFAR- 10 & ImageNet, a synthetic pose estimation task derived from YCB objects, FMoW-WILDS satellite imagery classification, and wildlife classification in iWildCam-WILDS. The correlation holds across model architectures, hyperparameters, training set size, and training duration, and is more precise than what is expected from existing domain adaptation theory. To complete the picture, we also investigate cases where the correlation is weaker, for instance some synthetic distribution shifts from CIFAR-10-C and the tissue classification dataset Camelyon17-WILDS. Finally, we provide a candidate theory based on a Gaussian data model that shows how changes in the data covariance arising from distribution shift can affect the observed correlations.

A common workflow in single-cell RNA-seq analysis is to project the data to a latent space, cluster the cells in that space, and identify sets of marker genes that explain the differences among the discovered clusters. A primary drawback to this three-step procedure is that each step is carried out independently, thereby neglecting the effects of the nonlinear embedding and inter-gene dependencies on the selection of marker genes. Here we propose an integrated deep learning framework, Adversarial Clustering Explanation (ACE), that bundles all three steps into a single workflow. The method thus moves away from the notion of "marker genes" to instead identify a panel of explanatory genes. This panel may include genes that are not only enriched but also depleted relative to other cell types, as well as genes that exhibit differences between closely related cell types. Empirically, we demonstrate that ACE is able to identify gene panels that are both highly discriminative and nonredundant, and we demonstrate the applicability of ACE to an image recognition task.

In this work, we develop linear bandit algorithms that automatically adapt to different environments. By plugging a novel loss estimator into the optimization problem that characterizes the instance-optimal strategy, our first algorithm not only achieves nearly instance-optimal regret in stochastic environments, but also works in corrupted environments with additional regret being the amount of corruption, while the state-of-the-art (Li et al., 2019) achieves neither instance-optimality nor the optimal dependence on the corruption amount. Moreover, by equipping this algorithm with an adversarial component and carefully-designed testings, our second algorithm additionally enjoys minimax-optimal regret in completely adversarial environments, which is the first of this kind to our knowledge. Finally, all our guarantees hold with high probability, while existing instance-optimal guarantees only hold in expectation.

Computationally efficient contextual bandits are often based on estimating a predictive model of rewards given contexts and arms using past data. However, when the reward model is not well-specified, the bandit algorithm may incur unexpected regret, so recent work has focused on algorithms that are robust to misspecification. We propose a simple family of contextual bandit algorithms that adapt to misspecification error by reverting to a good safe policy when there is evidence that misspecification is causing a regret increase. Our algorithm requires only an offline regression oracle to ensure regret guarantees that gracefully degrade in terms of a measure of the average misspecification level. Compared to prior work, we attain similar regret guarantees, but we do no rely on a master algorithm, and do not require more robust oracles like online or constrained regression oracles (e.g., Foster et al. (2020), Krishnamurthy et al. (2020)). This allows us to design algorithms for more general function approximation classes.

In real-world applications, data often come in a growing manner, where the data volume and the number of classes may increase dynamically. This will bring a critical challenge for learning: given the increasing data volume or the number of classes, one has to instantaneously adjust the neural model capacity to obtain promising performance. Existing methods either ignore the growing nature of data or seek to independently search an optimal architecture for a given dataset, and thus are incapable of promptly adjusting the architectures for the changed data. To address this, we present a neural architecture adaptation method, namely Adaptation eXpert (AdaXpert), to efficiently adjust previous architectures on the growing data. Specifically, we introduce an architecture adjuster to generate a suitable architecture for each data snapshot, based on the previous architecture and the different extent between current and previous data distributions. Furthermore, we propose an adaptation condition to determine the necessity of adjustment, thereby avoiding unnecessary and time-consuming adjustments. Extensive experiments on two growth scenarios (increasing data volume and number of classes) demonstrate the effectiveness of the proposed method.

A landmark challenge for AI is to learn flexible, powerful representations from small numbers of examples. On an important class of tasks, hypotheses in the form of programs provide extreme generalization capabilities from surprisingly few examples. However, whereas large natural few-shot learning image benchmarks have spurred progress in meta-learning for deep networks, there is no comparably big, natural program-synthesis dataset that can play a similar role. This is because, whereas images are relatively easy to label from internet meta-data or annotated by non-experts, generating meaningful input-output examples for program induction has proven hard to scale. In this work, we propose a new way of leveraging unit tests and natural inputs for small programs as meaningful input-output examples for each sub-program of the overall program. This allows us to create a large-scale naturalistic few-shot program-induction benchmark and propose new challenges in this domain. The evaluation of multiple program induction and synthesis algorithms points to shortcomings of current methods and suggests multiple avenues for future work.

In batched multi-armed bandit problems, the learner can adaptively pull arms and adjust strategy in batches. In many real applications, not only the regret but also the batch complexity need to be optimized. Existing batched bandit algorithms usually assume that the time horizon T is known in advance. However, many applications involve an unpredictable stopping time. In this paper, we study the anytime batched multi-armed bandit problem. We propose an anytime algorithm that achieves the asymptotically optimal regret for exponential families of reward distributions with O(\log \log T \ilog^{\alpha} (T)) \footnote{Notation \ilog^{\alpha} (T) is the result of iteratively applying the logarithm function on T for \alpha times, e.g., \ilog^{3} (T)=\log\log\log T.} batches, where $\alpha\in O_{T}(1). Moreover, we prove that for any constant c>0, no algorithm can achieve the asymptotically optimal regret within c\log\log T batches.

When reasoning about strategic behavior in a machine learning context it is tempting to combine standard microfoundations of rational agents with the statistical decision theory underlying classification. In this work, we argue that a direct combination of these ingredients leads to brittle solution concepts of limited descriptive and prescriptive value. First, we show that rational agents with perfect information produce discontinuities in the aggregate response to a decision rule that we often do not observe empirically. Second, when any positive fraction of agents is not perfectly strategic, desirable stable points---where the classifier is optimal for the data it entails---no longer exist. Third, optimal decision rules under standard microfoundations maximize a measure of negative externality known as social burden within a broad class of assumptions about agent behavior. Recognizing these limitations we explore alternatives to standard microfoundations for binary classification. We describe desiderata that help navigate the space of possible assumptions about agent responses, and we then propose the noisy response model. Inspired by smoothed analysis and empirical observations, noisy response incorporates imperfection in the agent responses, which we show mitigates the limitations of standard microfoundations. Our model retains analytical tractability, leads to more robust insights about stable points, and imposes …

Structured output prediction problems (e.g., sequential tagging, hierarchical multi-class classification) often involve constraints over the output space. These constraints interact with the learned models to filter infeasible solutions and facilitate in building an accountable system. However, despite constraints are useful, they are often based on hand-crafted rules. This raises a question -- can we mine constraints and rules from data based on a learning algorithm?

In this paper, we present a general framework for mining constraints from data. In particular, we consider the inference in structured output prediction as an integer linear programming (ILP) problem. Then, given the coefficients of the objective function and the corresponding solution, we mine the underlying constraints by estimating the outer and inner polytopes of the feasible set. We verify the proposed constraint mining algorithm in various synthetic and real-world applications and demonstrate that the proposed approach successfully identifies the feasible set at scale. 
In particular, we show that our approach can learn to solve 9x9 Sudoku puzzles and minimal spanning tree problems from examples without providing the underlying rules. Our algorithm can also integrate with a neural network model to learn the hierarchical label structure of a multi-label classification task. Besides, we provide theoretical …

0-1 knapsack is of fundamental importance across many fields. In this paper, we present a game-theoretic method to solve 0-1 knapsack problems (KPs) where the number of items (products) is large and the values of items are not predetermined but decided by an external value assignment function (e.g., a neural network in our case) during the optimization process. While existing papers are interested in predicting solutions with neural networks for classical KPs whose objective functions are mostly linear functions, we are interested in solving KPs whose objective functions are neural networks. In other words, we choose a subset of items that maximize the sum of the values predicted by neural networks. Its key challenge is how to optimize the neural network-based non-linear KP objective with a budget constraint. Our solution is inspired by game-theoretic approaches in deep learning, e.g., generative adversarial networks. After formally defining our two-player game, we develop an adaptive gradient ascent method to solve it. In our experiments, our method successfully solves two neural network-based non-linear KPs and conventional linear KPs with 1 million items.

We study the approximation properties of convolutional architectures applied to time series modelling, which can be formulated mathematically as a functional approximation problem. In the recurrent setting, recent results reveal an intricate connection between approximation efficiency and memory structures in the data generation process. In this paper, we derive parallel results for convolutional architectures, with WaveNet being a prime example. Our results reveal that in this new setting, approximation efficiency is not only characterised by memory, but also additional fine structures in the target relationship. This leads to a novel definition of spectrum-based regularity that measures the complexity of temporal relationships under the convolutional approximation scheme. These analyses provide a foundation to understand the differences between architectural choices for time series modelling and can give theoretically grounded guidance for practical applications.

Gaussian noise injections (GNIs) are a family of simple and widely-used regularisation methods for training neural networks, where one injects additive or multiplicative Gaussian noise to the network activations at every iteration of the optimisation algorithm, which is typically chosen as stochastic gradient descent (SGD). In this paper, we focus on the so-called implicit effect' of GNIs, which is the effect of the injected noise on the dynamics of SGD. We show that this effect induces an \emph{asymmetric heavy-tailed noise} on SGD gradient updates. In order to model this modified dynamics, we first develop a Langevin-like stochastic differential equation that is driven by a general family of \emph{asymmetric} heavy-tailed noise. Using this model we then formally prove that GNIs induce animplicit bias', which varies depending on the heaviness of the tails and the level of asymmetry. Our empirical results confirm that different types of neural networks trained with GNIs are well-modelled by the proposed dynamics and that the implicit effect of these injections induces a bias that degrades the performance of networks.

This paper quantifies the uncertainty of prediction risk for the min-norm least squares estimator in high-dimensional linear regression models. We establish the asymptotic normality of prediction risk when both the sample size and the number of features tend to infinity. Based on the newly established central limit theorems(CLTs), we derive the confidence intervals of the prediction risk under various scenarios. Our results demonstrate the sample-wise non-monotonicity of the prediction risk and confirm ``more data hurt" phenomenon. Furthermore, the width of confidence intervals indicates that over-parameterization would enlarge the randomness of prediction performance.

Understanding generalization and estimation error of estimators for simple models such as linear and generalized linear models has attracted a lot of attention recently. This is in part due to an interesting observation made in machine learning community that highly over-parameterized neural networks achieve zero training error, and yet they are able to generalize well over the test samples. This phenomenon is captured by the so called double descent curve, where the generalization error starts decreasing again after the interpolation threshold. A series of recent works tried to explain such phenomenon for simple models. In this work, we analyze the asymptotics of estimation error in ridge estimators for convolutional linear models. These convolutional inverse problems, also known as deconvolution, naturally arise in different fields such as seismology, imaging, and acoustics among others. Our results hold for a large class of input distributions that include i.i.d. features as a special case. We derive exact formulae for estimation error of ridge estimators that hold in a certain high-dimensional regime. We show the double descent phenomenon in our experiments for convolutional models and show that our theoretical results match the experiments.

The performance of neural networks depends on precise relationships between four distinct ingredients: the architecture, the loss function, the statistical structure of inputs, and the ground truth target function. Much theoretical work has focused on understanding the role of the first two ingredients under highly simplified models of random uncorrelated data and target functions. In contrast, performance likely relies on a conspiracy between the statistical structure of the input distribution and the structure of the function to be learned.
To understand this better we revisit ridge regression in high dimensions, which corresponds to an exceedingly simple architecture and loss function, but we analyze its performance under arbitrary correlations between input features and the target function.
We find a rich mathematical structure that includes: (1) a dramatic reduction in sample complexity when the target function aligns with data anisotropy; (2) the existence of multiple descent curves; (3) a sequence of phase transitions in the performance, loss landscape, and optimal regularization as a function of the amount of data that explains the first two effects.

We introduce a new graphical bilinear bandit problem where a learner (or a \emph{central entity}) allocates arms to the nodes of a graph and observes for each edge a noisy bilinear reward representing the interaction between the two end nodes. We study the best arm identification problem in which the learner wants to find the graph allocation maximizing the sum of the bilinear rewards. By efficiently exploiting the geometry of this bandit problem, we propose a \emph{decentralized} allocation strategy based on random sampling with theoretical guarantees. In particular, we characterize the influence of the graph structure (e.g. star, complete or circle) on the convergence rate and propose empirical experiments that confirm this dependency.

We consider repair tasks: given a critic (e.g., compiler) that assesses the quality of an input, the goal is to train a fixer that converts a bad example (e.g., code with syntax errors) into a good one (e.g., code with no errors). Existing works create training data consisting of (bad, good) pairs by corrupting good examples using heuristics (e.g., dropping tokens). However, fixers trained on this synthetically-generated data do not extrapolate well to the real distribution of bad inputs. To bridge this gap, we propose a new training approach, Break-It-Fix-It (BIFI), which has two key ideas: (i) we use the critic to check a fixer's output on real bad inputs and add good (fixed) outputs to the training data, and (ii) we train a breaker to generate realistic bad code from good code. Based on these ideas, we iteratively update the breaker and the fixer while using them in conjunction to generate more paired data. We evaluate BIFI on two code repair datasets: GitHub-Python, a new dataset we introduce where the goal is to repair Python code with AST parse errors; and DeepFix, where the goal is to repair C code with compiler errors. BIFI outperforms existing methods, obtaining 90.5% …

Can models with particular structure avoid being biased towards spurious correlation in out-of-distribution (OOD) generalization? Peters et al. (2016) provides a positive answer for linear cases. In this paper, we use a functional modular probing method to analyze deep model structures under OOD setting. We demonstrate that even in biased models (which focus on spurious correlation) there still exist unbiased functional subnetworks. Furthermore, we articulate and confirm the functional lottery ticket hypothesis: the full network contains a subnetwork with proper structure that can achieve better OOD performance. We then propose Modular Risk Minimization to solve the subnetwork selection problem. Our algorithm learns the functional structure from a given dataset, and can be combined with any other OOD regularization methods. Experiments on various OOD generalization tasks corroborate the effectiveness of our method.

The early phase of training a deep neural network has a dramatic effect on the local curvature of the loss function. For instance, using a small learning rate does not guarantee stable optimization because the optimization trajectory has a tendency to steer towards regions of the loss surface with increasing local curvature. We ask whether this tendency is connected to the widely observed phenomenon that the choice of the learning rate strongly influences generalization. We first show that stochastic gradient descent (SGD) implicitly penalizes the trace of the Fisher Information Matrix (FIM), a measure of the local curvature, from the start of training. We argue it is an implicit regularizer in SGD by showing that explicitly penalizing the trace of the FIM can significantly improve generalization. We highlight that poor final generalization coincides with the trace of the FIM attaining a large value early in training, to which we refer as catastrophic Fisher explosion. Finally, to gain insight into the regularization effect of penalizing the trace of the FIM, we show that it limits memorization by reducing the learning speed of examples with noisy labels more than that of the examples with clean labels.

Distributed computing has been a prominent solution to efficiently process massive datasets in parallel. However, the existence of stragglers is one of the major concerns that slows down the overall speed of distributed computing. To deal with this problem, we consider a distributed matrix multiplication scenario where a master assigns multiple tasks to each worker to exploit stragglers' computing ability (which is typically wasted in conventional distributed computing). We propose Chebyshev polynomial codes, which can achieve order-wise improvement in encoding complexity at the master and communication load in distributed matrix multiplication using task entanglement. The key idea of task entanglement is to reduce the number of encoded matrices for multiple tasks assigned to each worker by intertwining encoded matrices. We experimentally demonstrate that, in cloud environments, Chebyshev polynomial codes can provide significant reduction in overall processing time in distributed computing for matrix multiplication, which is a key computational component in modern deep learning.

Recent work has considered natural variations of the {\em multi-armed bandit} problem, where the reward distribution of each arm is a special function of the time passed since its last pulling. In this direction, a simple (yet widely applicable) model is that of {\em blocking bandits}, where an arm becomes unavailable for a deterministic number of rounds after each play. In this work, we extend the above model in two directions: (i) We consider the general combinatorial setting where more than one arms can be played at each round, subject to feasibility constraints. (ii) We allow the blocking time of each arm to be stochastic. We first study the computational/unconditional hardness of the above setting and identify the necessary conditions for the problem to become tractable (even in an approximate sense). Based on these conditions, we provide a tight analysis of the approximation guarantee of a natural greedy heuristic that always plays the maximum expected reward feasible subset among the available (non-blocked) arms. When the arms' expected rewards are unknown, we adapt the above heuristic into a bandit algorithm, based on UCB, for which we provide sublinear (approximate) regret guarantees, matching the theoretical lower bounds in the limiting case of …

A core element in decision-making under uncertainty is the feedback on the quality of the performed actions. However, in many applications, such feedback is restricted. For example, in recommendation systems, repeatedly asking the user to provide feedback on the quality of recommendations will annoy them. In this work, we formalize decision-making problems with querying budget, where there is a (possibly time-dependent) hard limit on the number of reward queries allowed. Specifically, we focus on multi-armed bandits, linear contextual bandits, and reinforcement learning problems. We start by analyzing the performance of `greedy' algorithms that query a reward whenever they can. We show that in fully stochastic settings, doing so performs surprisingly well, but in the presence of any adversity, this might lead to linear regret. To overcome this issue, we propose the Confidence-Budget Matching (CBM) principle that queries rewards when the confidence intervals are wider than the inverse square root of the available budget. We analyze the performance of CBM based algorithms in different settings and show that it performs well in the presence of adversity in the contexts, initial states, and budgets.

We develop a method to construct distribution-free prediction intervals for dynamic time-series, called \Verb|EnbPI| that wraps around any bootstrap ensemble estimator to construct sequential prediction intervals. \Verb|EnbPI| is closely related to the conformal prediction (CP) framework but does not require data exchangeability. Theoretically, these intervals attain finite-sample, \textit{approximately valid} marginal coverage for broad classes of regression functions and time-series with strongly mixing stochastic errors. Computationally, \Verb|EnbPI| avoids overfitting and requires neither data-splitting nor training multiple ensemble estimators; it efficiently aggregates bootstrap estimators that have been trained. In general, \Verb|EnbPI| is easy to implement, scalable to producing arbitrarily many prediction intervals sequentially, and well-suited to a wide range of regression functions. We perform extensive real-data analyses to demonstrate its effectiveness.

Decentralized training of deep learning models enables on-device learning over networks, as well as efficient scaling to large compute clusters. Experiments in earlier works reveal that, even in a data-center setup, decentralized training often suffers from the degradation in the quality of the model: the training and test performance of models trained in a decentralized fashion is in general worse than that of models trained in a centralized fashion, and this performance drop is impacted by parameters such as network size, communication topology and data partitioning. We identify the changing consensus distance between devices as a key parameter to explain the gap between centralized and decentralized training. We show in theory that when the training consensus distance is lower than a critical quantity, decentralized training converges as fast as the centralized counterpart. We empirically validate that the relation between generalization performance and consensus distance is consistent with this theoretical observation. Our empirical insights allow the principled design of better decentralized training schemes that mitigate the performance drop. To this end, we provide practical training guidelines and exemplify its effectiveness on the data-center setup as the important first step.

Multivariate Hawkes processes (MHPs) are widely used in a variety of fields to model the occurrence of causally related discrete events in continuous time. Most state-of-the-art approaches address the problem of learning MHPs from perfect traces without noise. In practice, the process through which events are collected might introduce noise in the timestamps. In this work, we address the problem of learning the causal structure of MHPs when the observed timestamps of events are subject to random and unknown shifts, also known as random translations. We prove that the cumulants of MHPs are invariant to random translations, and therefore can be used to learn their underlying causal structure. Furthermore, we empirically characterize the effect of random translations on state-of-the-art learning methods. We show that maximum likelihood-based estimators are brittle, while cumulant-based estimators remain stable even in the presence of significant time shifts.

Deep learning for graph matching (GM) has emerged as an important research topic due to its superior performance over traditional methods and insights it provides for solving other combinatorial problems on graph. While recent deep methods for GM extensively investigated effective node/edge feature learning or downstream GM solvers given such learned features, there is little existing work questioning if the fixed connectivity/topology typically constructed using heuristics (e.g., Delaunay or k-nearest) is indeed suitable for GM. From a learning perspective, we argue that the fixed topology may restrict the model capacity and thus potentially hinder the performance. To address this, we propose to learn the (distribution of) latent topology, which can better support the downstream GM task. We devise two latent graph generation procedures, one deterministic and one generative. Particularly, the generative procedure emphasizes the across-graph consistency and thus can be viewed as a matching-guided co-generative model. Our methods deliver superior performance over previous state-of-the-arts on public benchmarks, hence supporting our hypothesis.

Diffusion source identification on networks is a problem of fundamental importance in a broad class of applications, including controlling the spreading of rumors on social media, identifying a computer virus over cyber networks, or identifying the disease center during epidemiology. Though this problem has received significant recent attention, most known approaches are well-studied in only very restrictive settings and lack theoretical guarantees for more realistic networks. We introduce a statistical framework for the study of this problem and develop a confidence set inference approach inspired by hypothesis testing. Our method efficiently produces a small subset of nodes, which provably covers the source node with any pre-specified confidence level without restrictive assumptions on network structures. To our knowledge, this is the first diffusion source identification method with a practically useful theoretical guarantee on general networks. We demonstrate our approach via extensive synthetic experiments on well-known random network models, a large data set of real-world networks as well as a mobility network between cities concerning the COVID-19 spreading in January 2020.

Incorporating graph side information into recommender systems has been widely used to better predict ratings, but relatively few works have focused on theoretical guarantees. Ahn et al. (2018) firstly characterized the optimal sample complexity in the presence of graph side information, but the results are limited due to strict, unrealistic assumptions made on the unknown latent preference matrix and the structure of user clusters. In this work, we propose a new model in which 1) the unknown latent preference matrix can have any discrete values, and 2) users can be clustered into multiple clusters, thereby relaxing the assumptions made in prior work. Under this new model, we fully characterize the optimal sample complexity and develop a computationally-efficient algorithm that matches the optimal sample complexity. Our algorithm is robust to model errors and outperforms the existing algorithms in terms of prediction performance on both synthetic and real data.

In this paper, we introduce a new perspective on training deep neural networks capable of state-of-the-art performance without the need for the expensive over-parameterization by proposing the concept of In-Time Over-Parameterization (ITOP) in sparse training. By starting from a random sparse network and continuously exploring sparse connectivities during training, we can perform an Over-Parameterization over the course of training, closing the gap in the expressibility between sparse training and dense training. We further use ITOP to understand the underlying mechanism of Dynamic Sparse Training (DST) and discover that the benefits of DST come from its ability to consider across time all possible parameters when searching for the optimal sparse connectivity. As long as sufficient parameters have been reliably explored, DST can outperform the dense neural network by a large margin. We present a series of experiments to support our conjecture and achieve the state-of-the-art sparse training performance with ResNet-50 on ImageNet. More impressively, ITOP achieves dominant performance over the overparameterization-based sparse methods at extreme sparsities. When trained with ResNet-34 on CIFAR-100, ITOP can match the performance of the dense model at an extreme sparsity 98%.

We propose a framework for model selection by combining base algorithms in stochastic bandits and reinforcement learning. We require a candidate regret bound for each base algorithm that may or may not hold. We select base algorithms to play in each round using a ``balancing condition'' on the candidate regret bounds. Our approach simultaneously recovers previous worst-case regret bounds, while also obtaining much smaller regret in natural scenarios when some base learners significantly exceed their candidate bounds. Our framework is relevant in many settings, including linear bandits and MDPs with nested function classes, linear bandits with unknown misspecification, and tuning confidence parameters of algorithms such as LinUCB. Moreover, unlike recent efforts in model selection for linear stochastic bandits, our approach can be extended to consider adversarial rather than stochastic contexts.

This paper presents a novel approach for hierarchical time series forecasting that produces coherent, probabilistic forecasts without requiring any explicit post-processing reconciliation. Unlike the state-of-the-art, the proposed method simultaneously learns from all time series in the hierarchy and incorporates the reconciliation step into a single trainable model. This is achieved by applying the reparameterization trick and casting reconciliation as an optimization problem with a closed-form solution. These model features make end-to-end learning of hierarchical forecasts possible, while accomplishing the challenging task of generating forecasts that are both probabilistic and coherent. Importantly, our approach also accommodates general aggregation constraints including grouped and temporal hierarchies. An extensive empirical evaluation on real-world hierarchical datasets demonstrates the advantages of the proposed approach over the state-of-the-art.

Several practical applications of reinforcement learning involve an agent learning from past data without the possibility of further exploration. Often these applications require us to 1) identify a near optimal policy or to 2) estimate the value of a target policy. For both tasks we derive exponential information-theoretic lower bounds in discounted infinite horizon MDPs with a linear function representation for the action value function even if 1) realizability holds, 2) the batch algorithm observes the exact reward and transition functions, and 3) the batch algorithm is given the best a priori data distribution for the problem class. Our work introduces a new `oracle + batch algorithm' framework to prove lower bounds that hold for every distribution. The work shows an exponential separation between batch and online reinforcement learning.

Federated Learning (FL) is an emerging learning scheme that allows different distributed clients to train deep neural networks together without data sharing. Neural networks have become popular due to their unprecedented success. To the best of our knowledge, the theoretical guarantees of FL concerning neural networks with explicit forms and multi-step updates are unexplored. Nevertheless, training analysis of neural networks in FL is non-trivial for two reasons: first, the objective loss function we are optimizing is non-smooth and non-convex, and second, we are even not updating in the gradient direction. Existing convergence results for gradient descent-based methods heavily rely on the fact that the gradient direction is used for updating. The current paper presents a new class of convergence analysis for FL, Federated Neural Tangent Kernel (FL-NTK), which corresponds to overparamterized ReLU neural networks trained by gradient descent in FL and is inspired by the analysis in Neural Tangent Kernel (NTK). Theoretically, FL-NTK converges to a global-optimal solution at a linear rate with properly tuned learning parameters. Furthermore, with proper distributional assumptions, FL-NTK can also achieve good generalization. The proposed theoretical analysis scheme can be generalized to more complex neural networks.

Designing novel protein sequences for a desired 3D topological fold is a fundamental yet non-trivial task in protein engineering. Challenges exist due to the complex sequence--fold relationship, as well as the difficulties to capture the diversity of the sequences (therefore structures and functions) within a fold. To overcome these challenges, we propose Fold2Seq, a novel transformer-based generative framework for designing protein sequences conditioned on a specific target fold. To model the complex sequence--structure relationship, Fold2Seq jointly learns a sequence embedding using a transformer and a fold embedding from the density of secondary structural elements in 3D voxels. On test sets with single, high-resolution and complete structure inputs for individual folds, our experiments demonstrate improved or comparable performance of Fold2Seq in terms of speed, coverage, and reliability for sequence design, when compared to existing state-of-the-art methods that include data-driven deep generative models and physics-based RosettaDesign. The unique advantages of fold-based Fold2Seq, in comparison to a structure-based deep model and RosettaDesign, become more evident on three additional real-world challenges originating from low-quality, incomplete, or ambiguous input structures. Source code and data are available at https://github.com/IBM/fold2seq.

The safe operation of physical systems typically relies on high-quality models. Since a continuous stream of data is generated during run-time, such models are often obtained through the application of Gaussian process regression because it provides guarantees on the prediction error. Due to its high computational complexity, Gaussian process regression must be used offline on batches of data, which prevents applications, where a fast adaptation through online learning is necessary to ensure safety. In order to overcome this issue, we propose the LoG-GP. It achieves a logarithmic update and prediction complexity in the number of training points through the aggregation of locally active Gaussian process models. Under weak assumptions on the aggregation scheme, it inherits safety guarantees from exact Gaussian process regression. These theoretical advantages are exemplarily exploited in the design of a safe and data-efficient, online-learning control policy. The efficiency and performance of the proposed real-time learning approach is demonstrated in a comparison to state-of-the-art methods.