mtybilly/Instruct2DS huggingface dataset:
Online Control of the False Coverage Rate and False Sign Rate
Authors: Weinstein, Asaf and Ramdas, Aaditya
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: The reproducibility debate has caused a renewed interest in changing how one reports uncertainty, from $p$-value for testing a null hypothesis to a confidence interval (CI) for the corresponding parameter. When CIs for multiple selected parameters are being reported, the analog of the false discovery rate (FDR) is the false coverage rate (FCR), which is the expected ratio of number of reported CIs failing to cover their respective parameters to the total number of reported CIs. Here, we consider the general problem of FCR control in the online setting, where one encounters an infinite sequence of fixed unknown parameters ordered by time. We propose a novel solution to the problem which only requires the scientist to be able to construct marginal CIs. As special cases, our framework yields algorithms for online FDR control and online sign-classification procedures that control the false sign rate (FSR). All of our methodology applies equally well to prediction intervals, having particular implications for selective conformal inference.
Batch Stationary Distribution Estimation
Authors: Wen, Junfeng and Dai, Bo and Li, Lihong and Schuurmans, Dale
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: We consider the problem of approximating the stationary distribution of an ergodic Markov chain given a set of sampled transitions. Classical simulation-based approaches assume access to the underlying process so that trajectories of sufficient length can be gathered to approximate stationary sampling. Instead, we consider an alternative setting where a \emphfixed set of transitions has been collected beforehand, by a separate, possibly unknown procedure. The goal is still to estimate properties of the stationary distribution, but without additional access to the underlying system. We propose a consistent estimator that is based on recovering a correction ratio function over the given data. In particular, we develop a variational power method (VPM) that provides provably consistent estimates under general conditions. In addition to unifying a number of existing approaches from different subfields, we also find that VPM yields significantly better estimates across a range of problems, including queueing, stochastic differential equations, post-processing MCMC, and off-policy evaluation.
Domain Aggregation Networks for Multi-Source Domain Adaptation
Authors: Wen, Junfeng and Greiner, Russell and Schuurmans, Dale
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: In many real-world applications, we want to exploit multiple source datasets to build a model for a different but related target dataset. Despite the recent empirical success, most existing research has used ad-hoc methods to combine multiple sources, leading to a gap between theory and practice. In this paper, we develop a finite-sample generalization bound based on domain discrepancy and accordingly propose a theoretically justified optimization procedure. Our algorithm, Domain AggRegation Network (DARN), can automatically and dynamically balance between including more data to increase effective sample size and excluding irrelevant data to avoid negative effects during training. We find that DARN can significantly outperform the state-of-the-art alternatives on multiple real-world tasks, including digit/object recognition and sentiment analysis.
Towards Understanding the Regularization of Adversarial Robustness on Neural Networks
Authors: Wen, Yuxin and Li, Shuai and Jia, Kui
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: The problem of adversarial examples has shown that modern Neural Network (NN) models could be rather fragile. Among the more established techniques to solve the problem, one is to require the model to be \emph$ε$-adversarially robust (AR); that is, to require the model not to change predicted labels when any given input examples are perturbed within a certain range. However, it is observed that such methods would lead to standard performance degradation, i.e., the degradation on natural examples. In this work, we study the degradation through the regularization perspective. We identify quantities from generalization analysis of NNs; with the identified quantities we empirically find that AR is achieved by regularizing/biasing NNs towards less confident solutions by making the changes in the feature space (induced by changes in the instance space) of most layers smoother uniformly in all directions; so to a certain extent, it prevents sudden change in prediction w.r.t. perturbations. However, the end result of such smoothing concentrates samples around decision boundaries, resulting in less confident solutions, and leads to worse standard performance. Our studies suggest that one might consider ways that build AR into NNs in a gentler way to avoid the problematic regularization.
Amortised Learning by Wake-Sleep
Authors: Wenliang, Li and Moskovitz, Theodore and Kanagawa, Heishiro and Sahani, Maneesh
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Models that employ latent variables to capture structure in observed data lie at the heart of many current unsupervised learning algorithms, but exact maximum-likelihood learning for powerful and flexible latent-variable models is almost always intractable. Thus, state-of-the-art approaches either abandon the maximum-likelihood framework entirely, or else rely on a variety of variational approximations to the posterior distribution over the latents. Here, we propose an alternative approach that we call amortised learning. Rather than computing an approximation to the posterior over latents, we use a wake-sleep Monte-Carlo strategy to learn a function that directly estimates the maximum-likelihood parameter updates. Amortised learning is possible whenever samples of latents and observations can be simulated from the generative model, treating the model as a “black box”. We demonstrate its effectiveness on a wide range of complex models, including those with latents that are discrete or supported on non-Euclidean spaces.
How Good is the Bayes Posterior in Deep Neural Networks Really?
Authors: Wenzel, Florian and Roth, Kevin and Veeling, Bastiaan and Swiatkowski, Jakub and Tran, Linh and Mandt, Stephan and Snoek, Jasper and Salimans, Tim and Jenatton, Rodolphe and Nowozin, Sebastian
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: During the past five years the Bayesian deep learning community has developed increasingly accurate and efficient approximate inference procedures that allow for Bayesian inference in deep neural networks. However, despite this algorithmic progress and the promise of improved uncertainty quantification and sample efficiency there are—as of early 2020—no publicized deployments of Bayesian neural networks in industrial practice. In this work we cast doubt on the current understanding of Bayes posteriors in popular deep neural networks: we demonstrate through careful MCMC sampling that the posterior predictive induced by the Bayes posterior yields systematically worse predictions when compared to simpler methods including point estimates obtained from SGD. Furthermore, we demonstrate that predictive performance is improved significantly through the use of a “cold posterior” that overcounts evidence. Such cold posteriors sharply deviate from the Bayesian paradigm but are commonly used as heuristic in Bayesian deep learning papers. We put forward several hypotheses that could explain cold posteriors and evaluate the hypotheses through experiments. Our work questions the goal of accurate posterior approximations in Bayesian deep learning: If the true Bayes posterior is poor, what is the use of more accurate approximations? Instead, we argue that it is timely to focus on understanding the origin of cold posteriors.
Predictive Sampling with Forecasting Autoregressive Models
Authors: Wiggers, Auke and Hoogeboom, Emiel
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Autoregressive models (ARMs) currently hold state-of-the-art performance in likelihood-based modeling of image and audio data. Generally, neural network based ARMs are designed to allow fast inference, but sampling from these models is impractically slow. In this paper, we introduce the predictive sampling algorithm: a procedure that exploits the fast inference property of ARMs in order to speed up sampling, while keeping the model intact. We propose two variations of predictive sampling, namely sampling with ARM fixed-point iteration and learned forecasting modules. Their effectiveness is demonstrated in two settings: i) explicit likelihood modeling on binary MNIST, SVHN and CIFAR10, and ii) discrete latent modeling in an autoencoder trained on SVHN, CIFAR10 and Imagenet32. Empirically, we show considerable improvements over baselines in number of ARM inference calls and sampling speed.
State Space Expectation Propagation: Efficient Inference Schemes for Temporal Gaussian Processes
Authors: Wilkinson, William and Chang, Paul and Andersen, Michael and Solin, Arno
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: We formulate approximate Bayesian inference in non-conjugate temporal and spatio-temporal Gaussian process models as a simple parameter update rule applied during Kalman smoothing. This viewpoint encompasses most inference schemes, including expectation propagation (EP), the classical (Extended, Unscented, etc.) Kalman smoothers, and variational inference. We provide a unifying perspective on these algorithms, showing how replacing the power EP moment matching step with linearisation recovers the classical smoothers. EP provides some benefits over the traditional methods via introduction of the so-called cavity distribution, and we combine these benefits with the computational efficiency of linearisation, providing extensive empirical analysis demonstrating the efficacy of various algorithms under this unifying framework. We provide a fast implementation of all methods in JAX.
Efficient nonparametric statistical inference on population feature importance using Shapley values
Authors: Williamson, Brian and Feng, Jean
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: The true population-level importance of a variable in a prediction task provides useful knowledge about the underlying data-generating mechanism and can help in deciding which measurements to collect in subsequent experiments. Valid statistical inference on this importance is a key component in understanding the population of interest. We present a computationally efficient procedure for estimating and obtaining valid statistical inference on the \textbfShapley \textbfPopulation \textbfVariable \textbfImportance \textbfMeasure (SPVIM). Although the computational complexity of the true SPVIM scales exponentially with the number of variables, we propose an estimator based on randomly sampling only $Θ(n)$ feature subsets given $n$ observations. We prove that our estimator converges at an asymptotically optimal rate. Moreover, by deriving the asymptotic distribution of our estimator, we construct valid confidence intervals and hypothesis tests. Our procedure has good finite-sample performance in simulations, and for an in-hospital mortality prediction task produces similar variable importance estimates when different machine learning algorithms are applied.
Efficiently sampling functions from Gaussian process posteriors
Authors: Wilson, James and Borovitskiy, Viacheslav and Terenin, Alexander and Mostowsky, Peter and Deisenroth, Marc
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Gaussian processes are the gold standard for many real-world modeling problems, especially in cases where a model’s success hinges upon its ability to faithfully represent predictive uncertainty. These problems typically exist as parts of larger frameworks, wherein quantities of interest are ultimately defined by integrating over posterior distributions. These quantities are frequently intractable, motivating the use of Monte Carlo methods. Despite substantial progress in scaling up Gaussian processes to large training sets, methods for accurately generating draws from their posterior distributions still scale cubically in the number of test locations. We identify a decomposition of Gaussian processes that naturally lends itself to scalable sampling by separating out the prior from the data. Building off of this factorization, we propose an easy-to-use and general-purpose approach for fast posterior sampling, which seamlessly pairs with sparse approximations to afford scalability both during training and at test time. In a series of experiments designed to test competing sampling schemes’ statistical properties and practical ramifications, we demonstrate how decoupled sample paths accurately represent Gaussian process posteriors at a fraction of the usual cost.
Learning to Rank Learning Curves
Authors: Wistuba, Martin and Pedapati, Tejaswini
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Many automated machine learning methods, such as those for hyperparameter and neural architecture optimization, are computationally expensive because they involve training many different model configurations. In this work, we present a new method that saves computational budget by terminating poor configurations early on in the training. In contrast to existing methods, we consider this task as a ranking and transfer learning problem. We qualitatively show that by optimizing a pairwise ranking loss and leveraging learning curves from other data sets, our model is able to effectively rank learning curves without having to observe many or very long learning curves. We further demonstrate that our method can be used to accelerate a neural architecture search by a factor of up to 100 without a significant performance degradation of the discovered architecture. In further experiments we analyze the quality of ranking, the influence of different model components as well as the predictive behavior of the model.
Causal Inference using Gaussian Processes with Structured Latent Confounders
Authors: Witty, Sam and Takatsu, Kenta and Jensen, David and Mansinghka, Vikash
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Latent confounders—unobserved variables that influence both treatment and outcome—can bias estimates of causal effects. In some cases, these confounders are shared across observations, e.g. all students taking a course are influenced by the course’s difficulty in addition to any educational interventions they receive individually. This paper shows how to semiparametrically model latent confounders that have this structure and thereby improve estimates of causal effects. The key innovations are a hierarchical Bayesian model, Gaussian processes with structured latent confounders (GP-SLC), and a Monte Carlo inference algorithm for this model based on elliptical slice sampling. GP-SLC provides principled Bayesian uncertainty estimates of individual treatment effect with minimal assumptions about the functional forms relating confounders, covariates, treatment, and outcome. Finally, this paper shows GP-SLC is competitive with or more accurate than widely used causal inference techniques on three benchmark datasets, including the Infant Health and Development Program and a dataset showing the effect of changing temperatures on state-wide energy consumption across New England.
Near Input Sparsity Time Kernel Embeddings via Adaptive Sampling
Authors: Woodruff, David and Zandieh, Amir
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: To accelerate kernel methods, we propose a near input sparsity time method for sampling the high-dimensional space implicitly defined by a kernel transformation. Our main contribution is an importance sampling method for subsampling the feature space of a degree $q$ tensoring of data points in almost input sparsity time, improving the recent oblivious sketching of (Ahle et al., 2020) by a factor of $q^5/2/ε^2$. This leads to a subspace embedding for the polynomial kernel as well as the Gaussian kernel with a target dimension that is only linearly dependent on the statistical dimension of the kernel and in time which is only linearly dependent on the sparsity of the input dataset. We show how our subspace embedding bounds imply new statistical guarantees for kernel ridge regression. Furthermore, we empirically show that in large-scale regression tasks, our algorithm outperforms state-of-the-art kernel approximation methods.
Is Local SGD Better than Minibatch SGD?
Authors: Woodworth, Blake and Patel, Kumar Kshitij and Stich, Sebastian and Dai, Zhen and Bullins, Brian and Mcmahan, Brendan and Shamir, Ohad and Srebro, Nathan
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: We study local SGD (also known as parallel SGD and federated SGD), a natural and frequently used distributed optimization method. Its theoretical foundations are currently lacking and we highlight how all existing error guarantees in the convex setting are dominated by a simple baseline, minibatch SGD. (1) For quadratic objectives we prove that local SGD strictly dominates minibatch SGD and that accelerated local SGD is minmax optimal for quadratics; (2) For general convex objectives we provide the first guarantee that at least \emphsometimes improves over minibatch SGD, but our guarantee does not always improve over, nor even match, minibatch SGD; (3) We show that indeed local SGD does \emphnot dominate minibatch SGD by presenting a lower bound on the performance of local SGD that is worse than the minibatch SGD guarantee.
Obtaining Adjustable Regularization for Free via Iterate Averaging
Authors: Wu, Jingfeng and Braverman, Vladimir and Yang, Lin
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Regularization for optimization is a crucial technique to avoid overfitting in machine learning. In order to obtain the best performance, we usually train a model by tuning the regularization parameters. It becomes costly, however, when a single round of training takes significant amount of time. Very recently, Neu and Rosasco show that if we run stochastic gradient descent (SGD) on linear regression problems, then by averaging the SGD iterates properly, we obtain a regularized solution. It left open whether the same phenomenon can be achieved for other optimization problems and algorithms. In this paper, we establish an averaging scheme that provably converts the iterates of SGD on an arbitrary strongly convex and smooth objective function to its regularized counterpart with an adjustable regularization parameter. Our approaches can be used for accelerated and preconditioned optimization methods as well. We further show that the same methods work empirically on more general optimization objectives including neural networks. In sum, we obtain adjustable regularization for free for a large class of optimization problems and resolve an open question raised by Neu and Rosasco.
DeltaGrad: Rapid retraining of machine learning models
Authors: Wu, Yinjun and Dobriban, Edgar and Davidson, Susan
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Machine learning models are not static and may need to be retrained on slightly changed datasets, for instance, with the addition or deletion of a set of data points. This has many applications, including privacy, robustness, bias reduction, and uncertainty quantifcation. However, it is expensive to retrain models from scratch. To address this problem, we propose the DeltaGrad algorithm for rapid retraining machine learning models based on information cached during the training phase. We provide both theoretical and empirical support for the effectiveness of DeltaGrad, and show that it compares favorably to the state of the art.
On the Noisy Gradient Descent that Generalizes as SGD
Authors: Wu, Jingfeng and Hu, Wenqing and Xiong, Haoyi and Huan, Jun and Braverman, Vladimir and Zhu, Zhanxing
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: The gradient noise of SGD is considered to play a central role in the observed strong generalization abilities of deep learning. While past studies confirm that the magnitude and the covariance structure of gradient noise are critical for regularization, it remains unclear whether or not the class of noise distributions is important. In this work we provide negative results by showing that noises in classes different from the SGD noise can also effectively regularize gradient descent. Our finding is based on a novel observation on the structure of the SGD noise: it is the multiplication of the gradient matrix and a sampling noise that arises from the mini-batch sampling procedure. Moreover, the sampling noises unify two kinds of gradient regularizing noises that belong to the Gaussian class: the one using (scaled) Fisher as covariance and the one using the gradient covariance of SGD as covariance. Finally, thanks to the flexibility of choosing noise class, an algorithm is proposed to perform noisy gradient descent that generalizes well, the variant of which even benefits large batch SGD training without hurting generalization.
Stronger and Faster Wasserstein Adversarial Attacks
Authors: Wu, Kaiwen and Wang, Allen and Yu, Yaoliang
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Deep models, while being extremely flexible and accurate, are surprisingly vulnerable to “small, imperceptible” perturbations known as adversarial attacks. While the majority of existing attacks focus on measuring perturbations under the $\ell_p$ metric, Wasserstein distance, which takes geometry in pixel space into account, has long been known to be a suitable metric for measuring image quality and has recently risen as a compelling alternative to the $\ell_p$ metric in adversarial attacks. However, constructing an effective attack under the Wasserstein metric is computationally much more challenging and calls for better optimization algorithms. We address this gap in two ways: (a) we develop an exact yet efficient projection operator to enable a stronger projected gradient attack; (b) we show that the Frank-Wolfe method equipped with a suitable linear minimization oracle works extremely fast under Wasserstein constraints. Our algorithms not only converge faster but also generate much stronger attacks. For instance, we decrease the accuracy of a residual network on CIFAR-10 to $3.4%$ within a Wasserstein perturbation ball of radius $0.005$, in contrast to $65.6%$ using the previous Wasserstein attack based on an \emphapproximate projection operator. Furthermore, employing our stronger attacks in adversarial training significantly improves the robustness of adversarially trained models.
Sequence Generation with Mixed Representations
Authors: Wu, Lijun and Xie, Shufang and Xia, Yingce and Fan, Yang and Lai, Jian-Huang and Qin, Tao and Liu, Tieyan
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Tokenization is the first step of many natural language processing (NLP) tasks and plays an important role for neural NLP models. Tokenizaton method such as byte-pair encoding (BPE), which can greatly reduce the large vocabulary and deal with out-of-vocabulary words, has shown to be effective and is widely adopted for sequence generation tasks. While various tokenization methods exist, there is no common acknowledgement which is the best. In this work, we propose to leverage the mixed representations from different tokenization methods for sequence generation tasks, in order to boost the model performance with unique characteristics and advantages of individual tokenization methods. Specifically, we introduce a new model architecture to incorporate mixed representations and a co-teaching algorithm to better utilize the diversity of different tokenization methods. Our approach achieves significant improvements on neural machine translation (NMT) tasks with six language pairs (e.g., English$łeftrightarrow$German, English$łeftrightarrow$Romanian), as well as an abstractive summarization task.
Adversarial Robustness via Runtime Masking and Cleansing
Authors: Wu, Yi-Hsuan and Yuan, Chia-Hung and Wu, Shan-Hung
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Deep neural networks are shown to be vulnerable to adversarial attacks. This motivates robust learning techniques, such as the adversarial training, whose goal is to learn a network that is robust against adversarial attacks. However, the sample complexity of robust learning can be significantly larger than that of “standard” learning. In this paper, we propose improving the adversarial robustness of a network by leveraging the potentially large test data seen at runtime. We devise a new defense method, called runtime masking and cleansing (RMC), that adapts the network at runtime before making a prediction to dynamically mask network gradients and cleanse the model of the non-robust features inevitably learned during the training process due to the size limit of the training set. We conduct experiments on real-world datasets and the results demonstrate the effectiveness of RMC empirically.
On the Generalization Effects of Linear Transformations in Data Augmentation
Authors: Wu, Sen and Zhang, Hongyang and Valiant, Gregory and Re, Christopher
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Data augmentation is a powerful technique to improve performance in applications such as image and text classification tasks. Yet, there is little rigorous understanding of why and how various augmentations work. In this work, we consider a family of linear transformations and study their effects on the ridge estimator in an over-parametrized linear regression setting. First, we show that transformations which preserve the labels of the data can improve estimation by enlarging the span of the training data. Second, we show that transformations which mix data can improve estimation by playing a regularization effect. Finally, we validate our theoretical insights on MNIST. Based on the insights, we propose an augmentation scheme that searches over the space of transformations by how \emphuncertain the model is about the transformed data. We validate our proposed scheme on image and text datasets. For example, our method outperforms RandAugment by 1.24% on CIFAR-100 using Wide-ResNet-28-10. Furthermore, we achieve comparable accuracy to the SoTA Adversarial AutoAugment on CIFAR datasets.
Amortized Population Gibbs Samplers with Neural Sufficient Statistics
Authors: Wu, Hao and Zimmermann, Heiko and Sennesh, Eli and Le, Tuan Anh and Van De Meent, Jan-Willem
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: We develop amortized population Gibbs (APG) samplers, a class of scalable methods that frame structured variational inference as adaptive importance sampling. APG samplers construct high-dimensional proposals by iterating over updates to lower-dimensional blocks of variables. We train each conditional proposal by minimizing the inclusive KL divergence with respect to the conditional posterior. To appropriately account for the size of the input data, we develop a new parameterization in terms of neural sufficient statistics. Experiments show that APG samplers can be used to train highly-structured deep generative models in an unsupervised manner, and achieve substantial improvements in inference accuracy relative to standard autoencoding variational methods.
Continuous Graph Neural Networks
Authors: Xhonneux, Louis-Pascal and Qu, Meng and Tang, Jian
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: This paper builds on the connection between graph neural networks and traditional dynamical systems. We propose continuous graph neural networks (CGNN), which generalise existing graph neural networks with discrete dynamics in that they can be viewed as a specific discretisation scheme. The key idea is how to characterise the continuous dynamics of node representations, i.e. the derivatives of node representations, w.r.t. time.Inspired by existing diffusion-based methods on graphs (e.g. PageRank and epidemic models on social networks), we define the derivatives as a combination of the current node representations,the representations of neighbors, and the initial values of the nodes. We propose and analyse two possible dynamics on graphs—including each dimension of node representations (a.k.a. the feature channel) change independently or interact with each other—both with theoretical justification. The proposed continuous graph neural net-works are robust to over-smoothing and hence allow us to build deeper networks, which in turn are able to capture the long-range dependencies between nodes. Experimental results on the task of node classification demonstrate the effectiveness of our proposed approach over competitive baselines.
A Flexible Framework for Nonparametric Graphical Modeling that Accommodates Machine Learning
Authors: Xiang, Yunhua and Simon, Noah
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Graphical modeling has been broadly useful for exploring the dependence structure among features in a dataset. However, the strength of graphical modeling hinges on our ability to encode and estimate conditional dependencies. In particular, commonly used measures such as partial correlation are only meaningful under strongly parametric (in this case, multivariate Gaussian) assumptions. These assumptions are unverifiable, and there is often little reason to believe they hold in practice. In this paper, we instead consider 3 non-parametric measures of conditional dependence. These measures are meaningful without structural assumptions on the multivariate distribution of the data. In addition, we show that for 2 of these measures there are simple, strong plug-in estimators that require only the estimation of a conditional mean. These plug-in estimators (1) are asymptotically linear and non-parametrically efficient, (2) allow incorporation of flexible machine learning techniques for conditional mean estimation, and (3) enable the construction of valid Wald-type confidence intervals. In addition, by leveraging the influence function of these estimators, one can obtain intervals with simultaneous coverage guarantees for all pairs of features.
Generative Flows with Matrix Exponential
Authors: Xiao, Changyi and Liu, Ligang
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Generative flows models enjoy the properties of tractable exact likelihood and efficient sampling, which are composed of a sequence of invertible functions. In this paper, we incorporate matrix exponential into generative flows. Matrix exponential is a map from matrices to invertible matrices, this property is suitable for generative flows. Based on matrix exponential, we propose matrix exponential coupling layers that are a general case of affine coupling layers and matrix exponential invertible 1 x 1 convolutions that do not collapse during training. And we modify the networks architecture to make training stable and significantly speed up the training process. Our experiments show that our model achieves great performance on density estimation amongst generative flows models.
Disentangling Trainability and Generalization in Deep Neural Networks
Authors: Xiao, Lechao and Pennington, Jeffrey and Schoenholz, Samuel
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: A longstanding goal in the theory of deep learning is to characterize the conditions under which a given neural network architecture will be trainable, and if so, how well it might generalize to unseen data. In this work, we provide such a characterization in the limit of very wide and very deep networks, for which the analysis simplifies considerably. For wide networks, the trajectory under gradient descent is governed by the Neural Tangent Kernel (NTK), and for deep networks the NTK itself maintains only weak data dependence. By analyzing the spectrum of the NTK, we formulate necessary conditions for trainability and generalization across a range of architectures, including Fully Connected Networks (FCNs) and Convolutional Neural Networks (CNNs). We identify large regions of hyperparameter space for which networks can memorize the training set but completely fail to generalize. We find that CNNs without global average pooling behave almost identically to FCNs, but that CNNs with pooling have markedly different and often better generalization performance. These theoretical results are corroborated experimentally on CIFAR10 for a variety of network architectures. We include a \hrefhttps://colab.research.google.com/github/google/neural-tangents/blob/master/notebooks/disentangling_trainability_and_generalization.ipynbcolab notebook that reproduces the essential results of the paper.
Optimally Solving Two-Agent Decentralized POMDPs Under One-Sided Information Sharing
Authors: Xie, Yuxuan and Dibangoye, Jilles and Buffet, Olivier
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Optimally solving decentralized partially observable Markov decision processes under either full or no information sharing received significant attention in recent years. However, little is known about how partial information sharing affects existing theory and algorithms. This paper addresses this question for a team of two agents, with one-sided information sharing—ıe both agents have imperfect information about the state of the world, but only one has access to what the other sees and does. From the perspective of a central planner, we show that the original problem can be reformulated into an equivalent information-state Markov decision process and solved as such. Besides, we prove that the optimal value function exhibits a specific form of uniform continuity. We also present a heuristic search algorithm utilizing this property and providing the first results for this family of problems.
Maximum-and-Concatenation Networks
Authors: Xie, Xingyu and Kong, Hao and Wu, Jianlong and Zhang, Wayne and Liu, Guangcan and Lin, Zhouchen
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: While successful in many fields, deep neural networks (DNNs) still suffer from some open problems such as bad local minima and unsatisfactory generalization performance. In this work, we propose a novel architecture called Maximum-and-Concatenation Networks (MCN) to try eliminating bad local minima and improving generalization ability as well. Remarkably, we prove that MCN has a very nice property; that is, every local minimum of an (l+1)-layer MCN can be better than, at least as good as, the global minima of the network consisting of its first l layers. In other words, by increasing the network depth, MCN can autonomously improve its local minima’s goodness, what is more, it is easy to plug MCN into an existing deep model to make it also have this property. Finally, under mild conditions, we show that MCN can approximate certain continuous function arbitrarily well with high efficiency; that is, the covering number of MCN is much smaller than most existing DNNs such as deep ReLU. Based on this, we further provide a tight generalization bound to guarantee the inference ability of MCN when dealing with testing samples.
Zeno++: Robust Fully Asynchronous SGD
Authors: Xie, Cong and Koyejo, Sanmi and Gupta, Indranil
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: We propose Zeno++, a new robust asynchronous Stochastic Gradient Descent(SGD) procedure, intended to tolerate Byzantine failures of workers. In contrast to previous work, Zeno++ removes several unrealistic restrictions on worker-server communication, now allowing for fully asynchronous updates from anonymous workers, for arbitrarily stale worker updates, and for the possibility of an unbounded number of Byzantine workers. The key idea is to estimate the descent of the loss value after the candidate gradient is applied, where large descent values indicate that the update results in optimization progress. We prove the convergence of Zeno++ for non-convex problems under Byzantine failures. Experimental results show that Zeno++ outperforms existing Byzantine-tolerant asynchronous SGD algorithms.
Lower Complexity Bounds for Finite-Sum Convex-Concave Minimax Optimization Problems
Authors: Xie, Guangzeng and Luo, Luo and Lian, Yijiang and Zhang, Zhihua
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: This paper studies the lower bound complexity for minimax optimization problem whose objective function is the average of $n$ individual smooth convex-concave functions. We consider the algorithm which gets access to gradient and proximal oracle for each individual component. For the strongly-convex-strongly-concave case, we prove such an algorithm can not reach an $ɛ$-suboptimal point in fewer than $Ømegałeft((n+ąppa)łog(1/ɛ)i̊ght)$ iterations, where $\p̨pa$ is the condition number of the objective function. This lower bound matches the upper bound of the existing incremental first-order oracle algorithm stochastic variance-reduced extragradient. We develop a novel construction to show the above result, which partitions the tridiagonal matrix of classical examples into $n$ groups. This construction is friendly to the analysis of incremental gradient and proximal oracle and we also extend the analysis to general convex-concave cases.
On the Number of Linear Regions of Convolutional Neural Networks
Authors: Xiong, Huan and Huang, Lei and Yu, Mengyang and Liu, Li and Zhu, Fan and Shao, Ling
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: One fundamental problem in deep learning is understanding the outstanding performance of deep Neural Networks (NNs) in practice. One explanation for the superiority of NNs is that they can realize a large class of complicated functions, i.e., they have powerful expressivity. The expressivity of a ReLU NN can be quantified by the maximal number of linear regions it can separate its input space into. In this paper, we provide several mathematical results needed for studying the linear regions of CNNs, and use them to derive the maximal and average numbers of linear regions for one-layer ReLU CNNs. Furthermore, we obtain upper and lower bounds for the number of linear regions of multi-layer ReLU CNNs. Our results suggest that deeper CNNs have more powerful expressivity than their shallow counterparts, while CNNs have more expressivity than fully-connected NNs per parameter.
On Layer Normalization in the Transformer Architecture
Authors: Xiong, Ruibin and Yang, Yunchang and He, Di and Zheng, Kai and Zheng, Shuxin and Xing, Chen and Zhang, Huishuai and Lan, Yanyan and Wang, Liwei and Liu, Tieyan
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: The Transformer is widely used in natural language processing tasks. To train a Transformer however, one usually needs a carefully designed learning rate warm-up stage, which is shown to be crucial to the final performance but will slow down the optimization and bring more hyper-parameter tunings. In this paper, we first study theoretically why the learning rate warm-up stage is essential and show that the location of layer normalization matters. Specifically, we prove with mean field theory that at initialization, for the original-designed Post-LN Transformer, which places the layer normalization between the residual blocks, the expected gradients of the parameters near the output layer are large. Therefore, using a large learning rate on those gradients makes the training unstable. The warm-up stage is practically helpful for avoiding this problem. On the other hand, our theory also shows that if the layer normalization is put inside the residual blocks (recently proposed as Pre-LN Transformer), the gradients are well-behaved at initialization. This motivates us to remove the warm-up stage for the training of Pre-LN Transformers. We show in our experiments that Pre-LN Transformers without the warm-up stage can reach comparable results with baselines while requiring significantly less training time and hyper-parameter tuning on a wide range of applications.
On Variational Learning of Controllable Representations for Text without Supervision
Authors: Xu, Peng and Cheung, Jackie Chi Kit and Cao, Yanshuai
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: The variational autoencoder (VAE) can learn the manifold of natural images on certain datasets, as evidenced by meaningful interpolating or extrapolating in the continuous latent space. However, on discrete data such as text, it is unclear if unsupervised learning can discover similar latent space that allows controllable manipulation. In this work, we find that sequence VAEs trained on text fail to properly decode when the latent codes are manipulated, because the modified codes often land in holes or vacant regions in the aggregated posterior latent space, where the decoding network fails to generalize. Both as a validation of the explanation and as a fix to the problem, we propose to constrain the posterior mean to a learned probability simplex, and performs manipulation within this simplex. Our proposed method mitigates the latent vacancy problem and achieves the first success in unsupervised learning of controllable representations for text. Empirically, our method outperforms unsupervised baselines and strong supervised approaches on text style transfer, and is capable of performing more flexible fine-grained control over text generation than existing methods.
Class-Weighted Classification: Trade-offs and Robust Approaches
Authors: Xu, Ziyu and Dan, Chen and Khim, Justin and Ravikumar, Pradeep
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: We consider imbalanced classification, the problem in which a label may have low marginal probability relative to other labels, by weighting losses according to the correct class. First, we examine the convergence rates of the expected excess weighted risk of plug-in classifiers where the weighting for the plug-in classifier and the risk may be different. This leads to irreducible errors that do not converge to the weighted Bayes risk, which motivates our consideration of robust risks. We define a robust risk that minimizes risk over a set of weightings, show excess risk bounds for this problem, and demonstrate that particular choices of the weighting set leads to a special instance of conditional value at risk (CVaR) from stochastic programming, which we call label conditional value at risk (LCVaR). Additionally, we generalize this weighting to derive a new robust risk problem that we call label heterogeneous conditional value at risk (LHCVaR). Finally, we empirically demonstrate the efficacy of LCVaR and LHCVaR on improving class conditional risks.
A Finite-Time Analysis of Q-Learning with Neural Network Function Approximation
Authors: Xu, Pan and Gu, Quanquan
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Q-learning with neural network function approximation (neural Q-learning for short) is among the most prevalent deep reinforcement learning algorithms. Despite its empirical success, the non-asymptotic convergence rate of neural Q-learning remains virtually unknown. In this paper, we present a finite-time analysis of a neural Q-learning algorithm, where the data are generated from a Markov decision process, and the action-value function is approximated by a deep ReLU neural network. We prove that neural Q-learning finds the optimal policy with an $O(1/\sqrtT)$ convergence rate if the neural function approximator is sufficiently overparameterized, where $T$ is the number of iterations. To our best knowledge, our result is the first finite-time analysis of neural Q-learning under non-i.i.d. data assumption.
Understanding and Stabilizing GANs’ Training Dynamics Using Control Theory
Authors: Xu, Kun and Li, Chongxuan and Zhu, Jun and Zhang, Bo
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Generative adversarial networks (GANs) are effective in generating realistic images but the training is often unstable. There are existing efforts that model the training dynamics of GANs in the parameter space but the analysis cannot directly motivate practically effective stabilizing methods. To this end, we present a conceptually novel perspective from control theory to directly model the dynamics of GANs in the frequency domain and provide simple yet effective methods to stabilize GAN’s training. We first analyze the training dynamic of a prototypical Dirac GAN and adopt the widely-used closed-loop control (CLC) to improve its stability. We then extend CLC to stabilize the training dynamic of normal GANs, which can be implemented as an L2 regularizer on the output of the discriminator. Empirical results show that our method can effectively stabilize the training and obtain state-of-the-art performance on data generation tasks.
Learning Autoencoders with Relational Regularization
Authors: Xu, Hongteng and Luo, Dixin and Henao, Ricardo and Shah, Svati and Carin, Lawrence
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: We propose a new algorithmic framework for learning autoencoders of data distributions. In this framework, we minimize the discrepancy between the model distribution and the target one, with relational regularization on learnable latent prior. This regularization penalizes the fused Gromov-Wasserstein (FGW) distance between the latent prior and its corresponding posterior, which allows us to learn a structured prior distribution associated with the generative model in a flexible way. Moreover, it helps us co-train multiple autoencoders even if they are with heterogeneous architectures and incomparable latent spaces. We implement the framework with two scalable algorithms, making it applicable for both probabilistic and deterministic autoencoders. Our relational regularized autoencoder (RAE) outperforms existing methods, e.g., variational autoencoder, Wasserstein autoencoder, and their variants, on generating images. Additionally, our relational co-training strategy of autoencoders achieves encouraging results in both synthesis and real-world multi-view learning tasks.