本博客致力於整理出ICML 2019接收的所有論文，包括題目、作者、摘要等重要信息，能夠方便廣大讀者迅速找到自己領域相關的論文。
相關論文代碼、附錄可參考ICML 2019
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Title: AReS and MaRS - Adversarial and MMD-Minimizing Regression for SDEs
Author: Gabriele Abbati, Philippe Wenk, Michael A. Osborne, Andreas Krause, Bernhard Schölkopf, Stefan Bauer
Abstract: Stochastic differential equations are an important modeling class in many disciplines. Consequently, there exist many methods relying on various discretization and numerical integration schemes. In this paper, we propose a novel, probabilistic model for estimating the drift and diffusion given noisy observations of the underlying stochastic system. Using state-of-the-art adversarial and moment matching inference techniques, we avoid the discretization schemes of classical approaches. This leads to significant improvements in parameter accuracy and robustness given random initial guesses. On four established benchmark systems, we compare the performance of our algorithms to state-of-the-art solutions based on extended Kalman filtering and Gaussian processes.
Title: Dynamic Weights in Multi-Objective Deep Reinforcement Learning
Author: Axel Abels, Diederik Roijers, Tom Lenaerts, Ann Nowé, Denis Steckelmacher
Abstract: Many real world decision problems are characterized by multiple conflicting objectives which must be balanced based on their relative importance. In the dynamic weights setting the relative importance changes over time and specialized algorithms that deal with such change, such as the tabular Reinforcement Learning (RL) algorithm by Natarajan & Tadepalli (2005), are required. However, this earlier work is not feasible for RL settings that necessitate the use of function approximators. We generalize across weight changes and high-dimensional inputs by proposing a multi-objective Q-network whose outputs are conditioned on the relative importance of objectives, and introduce Diverse Experience Replay (DER) to counter the inherent non-stationarity of the dynamic weights setting. We perform an extensive experimental evaluation and compare our methods to adapted algorithms from Deep Multi-Task/Multi-Objective RL and show that our proposed network in combination with DER dominates these adapted algorithms across weight change scenarios and problem domains.
Title: MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing
Author: Sami Abu-El-Haija, Bryan Perozzi, Amol Kapoor, Nazanin Alipourfard, Kristina Lerman, Hrayr Harutyunyan, Greg Ver Steeg, Aram Galstyan
Abstract: Existing popular methods for semi-supervised learning with Graph Neural Networks (such as the Graph Convolutional Network) provably cannot learn a general class of neighborhood mixing relationships. To address this weakness, we propose a new model, MixHop, that can learn these relationships, including difference operators, by repeatedly mixing feature representations of neighbors at various distances. MixHop requires no additional memory or computational complexity, and outperforms on challenging baselines. In addition, we propose sparsity regularization that allows us to visualize how the network prioritizes neighborhood information across different graph datasets. Our analysis of the learned architectures reveals that neighborhood mixing varies per datasets.
Comments: Graph Neural Networks
Title: Communication-Constrained Inference and the Role of Shared Randomness
Author: Jayadev Acharya, Clement Canonne, Himanshu Tyagi
Abstract: A central server needs to perform statistical inference based on samples that are distributed over multiple users who can each send a message of limited length to the center. We study problems of distribution learning and identity testing in this distributed inference setting and examine the role of shared randomness as a resource. We propose a general purpose simulate-and-infer strategy that uses only private-coin communication protocols and is sample-optimal for distribution learning. This general strategy turns out to be sample-optimal even for distribution testing among private-coin protocols. Interestingly, we propose a public-coin protocol that outperforms simulate-and-infer for distribution testing and is, in fact, sample-optimal. Underlying our public-coin protocol is a random hash that when applied to the samples minimally contracts the chi-squared distance of their distribution from the uniform distribution.
Title: Distributed Learning with Sublinear Communication
Author: Jayadev Acharya, Chris De Sa, Dylan Foster, Karthik Sridharan
Abstract: In distributed statistical learning, samples are split across machines and a learner wishes to use minimal communication to learn as well as if the examples were on a single machine. This model has received substantial interest in machine learning due to its scalability and potential for parallel speedup. However, in high-dimensional settings, where the number examples is smaller than the number of features (“dimension”), the speedup afforded by distributed learning may be overshadowed by the cost of communicating a single example. This paper investigates the following question: When is it possible to learn a -dimensional model in the distributed setting with total communication sublinear in ? Starting with a negative result, we show that for learning -bounded or sparse linear models, no algorithm can obtain optimal error until communication is linear in dimension. Our main result is that that by slightly relaxing the standard boundedness assumptions for linear models, we can obtain distributed algorithms that enjoy optimal error with communication logarithmic in dimension. This result is based on a family of algorithms that combine mirror descent with randomized sparsification/quantization of iterates, and extends to the general stochastic convex optimization model.
Title: Communication Complexity in Locally Private Distribution Estimation and Heavy Hitters
Author: Jayadev Acharya, Ziteng Sun
Abstract: We consider the problems of distribution estimation, and heavy hitter (frequency) estimation under privacy, and communication constraints. While the constraints have been studied separately, optimal schemes for one are sub-optimal for the other. We propose a sample-optimal -locally differentially private (LDP) scheme for distribution estimation, where each user communicates one bit, and requires public randomness. We also show that Hadamard Response, a recently proposed scheme for -LDP distribution estimation is also utility-optimal for heavy hitters estimation. Our final result shows that unlike distribution estimation, without public randomness, any utilityoptimal heavy hitter estimation algorithm must require bits of communication per user.
Title: Learning Models from Data with Measurement Error: Tackling Underreporting
Author: Roy Adams, Yuelong Ji, Xiaobin Wang, Suchi Saria
Abstract: Measurement error in observational datasets can lead to systematic bias in inferences based on these datasets. As studies based on observational data are increasingly used to inform decisions with real-world impact, it is critical that we develop a robust set of techniques for analyzing and adjusting for these biases. In this paper we present a method for estimating the distribution of an outcome given a binary exposure that is subject to underreporting. Our method is based on a missing data view of the measurement error problem, where the true exposure is treated as a latent variable that is marginalized out of a joint model. We prove three different conditions under which the outcome distribution can still be identified from data containing only errorprone observations of the exposure. We demonstrate this method on synthetic data and analyze its sensitivity to near violations of the identifiability conditions. Finally, we use this method to estimate the effects of maternal smoking and heroin use during pregnancy on childhood obesity, two import problems from public health. Using the proposed method, we estimate these effects using only subject-reported drug use data and refine the range of estimates generated by a sensitivity analysis-based approach. Further, the estimates produced by our method are consistent with existing literature on both the effects of maternal smoking and the rate at which subjects underreport smoking.
Title: TibGM: A Transferable and Information-Based Graphical Model Approach for Reinforcement Learning
Author: Tameem Adel, Adrian Weller
Abstract: One of the challenges to reinforcement learning (RL) is scalable transferability among complex tasks. Incorporating a graphical model (GM), along with the rich family of related methods, as a basis for RL frameworks provides potential to address issues such as transferability, generalisation and exploration. Here we propose a flexible GM-based RL framework which leverages efficient inference procedures to enhance generalisation and transfer power. In our proposed transferable and information-based graphical model framework ‘TibGM’, we show the equivalence between our mutual information-based objective in the GM, and an RL consolidated objective consisting of a standard reward maximisation target and a generalisation/transfer objective. In settings where there is a sparse or deceptive reward signal, our TibGM framework is flexible enough to incorporate exploration bonuses depicting intrinsic rewards. We empirically verify improved performance and exploration power.
Title: PAC Learnability of Node Functions in Networked Dynamical Systems
Author: Abhijin Adiga, Chris J Kuhlman, Madhav Marathe, S Ravi, Anil Vullikanti
Abstract: We consider the PAC learnability of the functions at the nodes of a discrete networked dynamical system, assuming that the underlying network is known. We provide tight bounds on the sample complexity of learning threshold functions. We establish a computational intractability result for efficient PAC learning of such functions. We develop efficient consistent learners when the number of negative examples is small. Using synthetic and real-world networks, we experimentally study how the network structure and sample complexity influence the quality of inference.
Title: Static Automatic Batching In TensorFlow
Author: Ashish Agarwal
Abstract: Dynamic neural networks are becoming increasingly common, and yet it is hard to implement them efficiently. On-the-fly operation batching for such models is sub-optimal and suffers from run time overheads, while writing manually batched versions can be hard and error-prone. To address this, we extend TensorFlow with , a parallel-for loop optimized using static loop vectorization. With , users can express computation using nested loops and conditional constructs, but get performance resembling that of a manually batched version. Benchmarks demonstrate speedups of one to two orders of magnitude on a range of tasks, from Jacobian computation, to auto-batching Graph Neural Networks.
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Title: Efficient Full-Matrix Adaptive Regularization
Author: Naman Agarwal, Brian Bullins, Xinyi Chen, Elad Hazan, Karan Singh, Cyril Zhang, Yi Zhang
Abstract: Adaptive regularization methods pre-multiply a descent direction by a preconditioning matrix. Due to the large number of parameters of machine learning problems, full-matrix preconditioning methods are prohibitively expensive. We show how to modify full-matrix adaptive regularization in order to make it practical and effective. We also provide a novel theoretical analysis for adaptive regularization in optimization settings. The core of our algorithm, termed GGT, consists of the efficient computation of the inverse square root of a low-rank matrix. Our preliminary experiments show improved iteration-wise convergence rates across synthetic tasks and standard deep learning benchmarks, and that the more carefullypreconditioned steps sometimes lead to a better solution.
Title: Online Control with Adversarial Disturbances
Author: Naman Agarwal, Brian Bullins, Elad Hazan, Sham Kakade, Karan Singh
Abstract: We study the control of linear dynamical systems with adversarial disturbances, as opposed to statistical noise. We present an efficient algorithm that achieves nearly-tight regret bounds in this setting. Our result generalizes upon previous work in two main aspects: the algorithm can accommodate adversarial noise in the dynamics, and can handle general convex costs.
Title: Fair Regression: Quantitative Definitions and Reduction-Based Algorithms
Author: Alekh Agarwal, Miroslav Dudik, Zhiwei Steven Wu
Abstract: In this paper, we study the prediction of a realvalued target, such as a risk score or recidivism rate, while guaranteeing a quantitative notion of fairness with respect to a protected attribute such as gender or race. We call this class of problems . We propose general schemes for fair regression under two notions of fairness: (1) statistical parity, which asks that the prediction be statistically independent of the protected attribute, and (2) bounded group loss, which asks that the prediction error restricted to any protected group remain below some pre-determined level. While we only study these two notions of fairness, our schemes are applicable to arbitrary Lipschitzcontinuous losses, and so they encompass leastsquares regression, logistic regression, quantile regression, and many other tasks. Our schemes only require access to standard risk minimization algorithms (such as standard classification or least-squares regression) while providing theoretical guarantees on the optimality and fairness of the obtained solutions. In addition to analyzing theoretical properties of our schemes, we empirically demonstrate their ability to uncover fairness–accuracy frontiers on several standard datasets.
Title: Learning to Generalize from Sparse and Underspecified Rewards
Author: Rishabh Agarwal, Chen Liang, Dale Schuurmans, Mohammad Norouzi
Abstract: We consider the problem of learning from sparse and underspecified rewards, where an agent receives a complex input, such as a natural language instruction, and needs to generate a complex response, such as an action sequence, while only receiving binary success-failure feedback. Such success-failure rewards are often underspecified: they do not distinguish between purposeful and accidental success. Generalization from underspecified rewards hinges on discounting spurious trajectories that attain accidental success, while learning from sparse feedback requires effective exploration. We address exploration by using a mode covering direction of KL divergence to collect a diverse set of successful trajectories, followed by a mode seeking KL divergence to train a robust policy. We propose Meta Reward Learning (MeRL) to construct an auxiliary reward function that provides more refined feedback for learning. The parameters of the auxiliary reward function are optimized with respect to the validation performance of a trained policy. The MeRL approach outperforms an alternative method for reward learning based on Bayesian Optimization, and achieves the state-of-the-art on weakly-supervised semantic parsing. It improves previous work by 1.2% and 2.4% on WIKITABLEQUESTIONS and WIKISQL datasets respectively.
Title: The Kernel Interaction Trick: Fast Bayesian Discovery of Pairwise Interactions in High Dimensions
Author: Raj Agrawal, Brian Trippe, Jonathan Huggins, Tamara Broderick
Abstract: Discovering interaction effects on a response of interest is a fundamental problem faced in biology, medicine, economics, and many other scientific disciplines. In theory, Bayesian methods for discovering pairwise interactions enjoy many benefits such as coherent uncertainty quantification, the ability to incorporate background knowledge, and desirable shrinkage properties. In practice, however, Bayesian methods are often computationally intractable for even moderatedimensional problems. Our key insight is that many hierarchical models of practical interest admit a particular Gaussian process (GP) representation; the GP allows us to capture the posterior with a vector of kernel hyper-parameters rather than interactions and main effects. With the implicit representation, we can run Markov chain Monte Carlo (MCMC) over model hyperparameters in time and memory linear in p per iteration. We focus on sparsity-inducing models and show on datasets with a variety of covariate behaviors that our method: (1) reduces runtime by orders of magnitude over naive applications of MCMC, (2) provides lower Type I and Type II error relative to state-of-the-art LASSO-based approaches, and (3) offers improved computational scaling in high dimensions relative to existing Bayesian and LASSO-based approaches.
Title: Understanding the Impact of Entropy on Policy Optimization
Author: Zafarali Ahmed, Nicolas Le Roux, Mohammad Norouzi, Dale Schuurmans
Abstract: Entropy regularization is commonly used to improve policy optimization in reinforcement learning. It is believed to help with by encouraging the selection of more stochastic policies. In this work, we analyze this claim usingm new visualizations of the optimization landscape based on randomly perturbing the loss function. We first show that even with access to the exact gradient, policy optimization is difficult due to the geometry of the objective function. We then qualitatively show that in some environments, a policy with higher entropy can make the optimization landscape smoother, thereby connecting local optima and enabling the use of larger learning rates. This paper presents new tools for understanding the optimization landscape, shows that policy entropy serves as a regularizer, and highlights the challenge of designing general-purpose policy optimization algorithms.
Title: Fairwashing: the risk of rationalization
Author: Ulrich Aivodji, Hiromi Arai, Olivier Fortineau, Sébastien Gambs, Satoshi Hara, Alain Tapp
Abstract: Black-box explanation is the problem of explaining how a machine learning model – whose internal logic is hidden to the auditor and generally complex – produces its outcomes. Current approaches for solving this problem include model explanation, outcome explanation as well as model inspection. While these techniques can be beneficial by providing interpretability, they can be used in a negative manner to perform fairwashing, which we define as promoting the false perception that a machine learning model respects some ethical values. In particular, we demonstrate that it is possible to systematically rationalize decisions taken by an unfair black-box model using the model explanation as well as the outcome explanation approaches with a given fairness metric. Our solution, LaundryML, is based on a regularized rule list enumeration algorithm whose objective is to search for fair rule lists approximating an unfair black-box model. We empirically evaluate our rationalization technique on black-box models trained on real-world datasets and show that one can obtain rule lists with high fidelity to the black-box model while being considerably less unfair at the same time.
Title: Adaptive Stochastic Natural Gradient Method for One-Shot Neural Architecture Search
Author: Youhei Akimoto, Shinichi Shirakawa, Nozomu Yoshinari, Kento Uchida, Shota Saito, Kouhei Nishida
Abstract: High sensitivity of neural architecture search (NAS) methods against their input such as stepsize (i.e., learning rate) and search space prevents practitioners from applying them out-of-the-box to their own problems, albeit its purpose is to automate a part of tuning process. Aiming at a fast, robust, and widely-applicable NAS, we develop a generic optimization framework for NAS. We turn a coupled optimization of connection weights and neural architecture into a differentiable optimization by means of stochastic relaxation. It accepts arbitrary search space (widely-applicable) and enables to employ a gradient-based simultaneous optimization of weights and architecture (fast). We propose a stochastic natural gradient method with an adaptive step-size mechanism built upon our theoretical investigation (robust). Despite its simplicity and no problem-dependent parameter tuning, our method exhibited near state-of-theart performances with low computational budgets both on image classification and inpainting tasks.
Title: Projections for Approximate Policy Iteration Algorithms
Author: Riad Akrour, Joni Pajarinen, Jan Peters, Gerhard Neumann
Abstract: Approximate policy iteration is a class of reinforcement learning (RL) algorithms where the policy is encoded using a function approximator and which has been especially prominent in RL with continuous action spaces. In this class of RL algorithms, ensuring increase of the policy return during policy update often requires to constrain the change in action distribution. Several approximations exist in the literature to solve thi constrained policy update problem. In this paper, we propose to improve over such solutions by introducing a set of projections that transform the constrained problem into an unconstrained one which is then solved by standard gradient descent. Using these projections, we empirically demonstrate that our approach can improve the policy update solution and the control over exploration of existing approximate policy iteration algorithms.
Title: Validating Causal Inference Models via Influence Functions
Author: Ahmed Alaa, Mihaela Van Der Schaar
Abstract: The problem of estimating causal effects of treatments from observational data falls beyond the realm of supervised learning — because counterfactual data is inaccessible, we can never observe the true causal effects. In the absence of “supervision”, how can we evaluate the performance of causal inference methods? In this paper, we use influence functions — the functional derivatives of a loss function — to develop a model validation procedure that estimates the estimation error of causal inference methods. Our procedure utilizes a Taylor-like expansion to approximate the loss function of a method on a given dataset in terms of the influence functions of its loss on a “synthesized”, proximal dataset with known causal effects. Under minimal regularity assumptions, we show that our procedure is -consistent and efficient. Experiments on 77 benchmark datasets show that using our procedure, we can accurately predict the comparative performances of state-of-the-art causal inference methods applied to a given observational study.
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Title: Multi-objective training of Generative Adversarial Networks with multiple discriminators
Author: Isabela Albuquerque, Joao Monteiro, Thang Doan, Breandan Considine, Tiago Falk, Ioannis Mitliagkas
Abstract: Recent literature has demonstrated promising results for training Generative Adversarial Networks by employing a set of discriminators, in contrast to the traditional game involving one generator against a single adversary. Such methods perform single-objective optimization on some simple consolidation of the losses, e.g. an arithmetic average. In this work, we revisit the multiple-discriminator setting by framing the simultaneous minimization of losses provided by different models as a multi-objective optimization problem. Specifically, we evaluate the performance of multiple gradient descent and the hypervolume maximization algorithm on a number of different datasets. Moreover, we argue that the previously proposed methods and hypervolume maximization can all be seen as variations of multiple gradient descent in which the update direction can be computed efficiently. Our results indicate that hypervolume maximization presents a better compromise between sample quality and computational cost than previous methods.
Title: Graph Element Networks: adaptive, structured computation and memory
Author: Ferran Alet, Adarsh Keshav Jeewajee, Maria Bauza Villalonga, Alberto Rodriguez, Tomas Lozano-Perez, Leslie Kaelbling
Abstract: We explore the use of graph neural networks (GNNs) to model spatial processes in which there is no graphical structure. Similar to , we assign nodes of a GNN to spatial locations and use a computational process defined on the graph to model the relationship between an initial function defined over a space and a resulting function in the same space. We use GNNs as a computational substrate, and show that the locations of the nodes in space as well as their connectivity can be optimized to focus on the most complex parts of the space. Moreover, this representational strategy allows the learned inputoutput relationship to generalize over the size of the underlying space and run the same model at different levels of precision, trading computation for accuracy. We demonstrate this method on a traditional PDE problem, a physical prediction problem from robotics, and learning to predict scene images from novel viewpoints.
Comments: Graph Neural Networks
Title: Analogies Explained: Towards Understanding Word Embeddings
Author: Carl Allen, Timothy Hospedales
Abstract: Word embeddings generated by neural network methods such as (W2V) are well known
to exhibit seemingly linear behaviour, e.g. the embeddings of analogy “woman is to queen as man is to king” approximately describe a parallelogram. This property is particularly intriguing since the embeddings are not trained to achieve it. Several explanations have been proposed, but each introduces assumptions that do not hold in practice. We derive a probabilistically grounded definition of that we re-interpret as , a mathematical description of “ is to ”. From these concepts we prove existence of linear relationships between W2V-type embeddings that underlie the analogical phenomenon, identifying explicit error terms.
Title: Infinite Mixture Prototypes for Few-shot Learning
Author: Kelsey Allen, Evan Shelhamer, Hanul Shin, Joshua Tenenbaum
Abstract: We propose infinite mixture prototypes to adaptively represent both simple and complex data distributions for few-shot learning. Infinite mixture prototypes combine deep representation learning with Bayesian nonparametrics, representing each class by a set of clusters, unlike existing prototypical methods that represent each class by a single cluster. By inferring the number of clusters, infinite mixture prototypes interpolate between nearest neighbor and prototypical representations in a learned feature space, which improves accuracy and robustness in the few-shot regime. We show the importance of adaptive capacity for capturing complex data distributions such as super-classes (like alphabets in character recognition), with 10-25% absolute accuracy improvements over prototypical networks, while still maintaining or improving accuracy on standard few-shot learning benchmarks. By clustering labeled and unlabeled data with the same rule, infinite mixture prototypes achieve state-of-the-art semi-supervised accuracy, and can perform purely unsupervised clustering, unlike existing fully- and semi-supervised prototypical methods.
Comments: Clustering
Title: A Convergence Theory for Deep Learning via Over-Parameterization
Author: Zeyuan Allen-Zhu, Yuanzhi Li, Zhao Song
Abstract: Deep neural networks (DNNs) have demonstrated dominating performance in many fields; since AlexNet, networks used in practice are going wider and deeper. On the theoretical side, a long line of works have been focusing on why we can train neural networks when there is only one hidden layer. The theory of multi-layer networks remains unsettled. In this work, we prove simple algorithms such as stochastic gradient descent (SGD) can find on the training objective of DNNs in . We only make two assumptions: the inputs do not degenerate and the network is over-parameterized. The latter means the number of hidden neurons is sufficiently large: in , the number of DNN layers and in , the number of training samples. As concrete examples, starting from randomly initialized weights, we show that SGD attains 100% training accuracy in classification tasks, or minimizes regression loss in linear convergence speed , with running time polynomial in and . Our theory applies to the widely-used but non-smooth ReLU activation, and to any smooth and possibly non-convex loss functions. In terms of network architectures, our theory at least applies to fully-connected neural networks, convolutional neural networks (CNN), and residual neural networks (ResNet).
Title: Asynchronous Batch Bayesian Optimisation with Improved Local Penalisation
Author: Ahsan Alvi, Binxin Ru, Jan-Peter Calliess, Stephen Roberts, Michael A. Osborne
Abstract: Batch Bayesian optimisation (BO) has been successfully applied to hyperparameter tuning using parallel computing, but it is wasteful of resources: workers that complete jobs ahead of others are left idle. We address this problem by developing an approach, Penalising Locally for Asynchronous Bayesian Optimisation on k workers (PLAyBOOK), for asynchronous parallel BO. We demonstrate empirically the efficacy of PLAyBOOK and its variants on synthetic tasks and a real-world problem. We undertake a comparison between synchronous and asynchronous BO, and show that asynchronous BO often outperforms synchronous batch BO in both wall-clock time and number of function evaluations.
Title: Bounding User Contributions: A Bias-Variance Trade-off in Differential Privacy
Author: Kareem Amin, Alex Kulesza, Andres Munoz, Sergei Vassilvtiskii
Abstract: Differentially private learning algorithms protect individual participants in the training dataset by guaranteeing that their presence does not significantly change the resulting model. In order to make this promise, such algorithms need to know the maximum contribution that can be made by a single user: the more data an individual can contribute, the more noise will need to be added to protect them. While most existing analyses assume that the maximum contribution is known and fixed in advance—indeed, it is often assumed that each user contributes only a single example— we argue that in practice there is a meaningful choice to be made. On the one hand, if we allow users to contribute large amounts of data, we may end up adding excessive noise to protect a few outliers, even when the majority contribute only modestly. On the other hand, limiting users to small contributions keeps noise levels low at the cost of potentially discarding significant amounts of excess data, thus introducing bias. Here, we characterize this trade-off for an empirical risk minimization setting, showing that in general there is a “sweet spot” that depends on measurable properties of the dataset, but that there is also a concrete cost to privacy that cannot be avoided simply by collecting more data.
Title: Explaining Deep Neural Networks with a Polynomial Time Algorithm for Shapley Value Approximation
Author: Marco Ancona, Cengiz Oztireli, Markus Gross
Abstract: The problem of explaining the behavior of deep neural networks has recently gained a lot of attention. While several attribution methods have been proposed, most come without strong theoretical foundations, which raises questions about their reliability. On the other hand, the literature on cooperative game theory suggests Shapley values as a unique way of assigning relevance scores such that certain desirable properties are satisfied. Unfortunately, the exact evaluation of Shapley values is prohibitively expensive, exponential in the number of input features. In this work, by leveraging recent results on uncertainty propagation, we propose a novel, polynomial-time approximation of Shapley values in deep neural networks. We show that our method produces significantly better approximations of Shapley values than existing state-of-the-art attribution methods.
Title: Scaling Up Ordinal Embedding: A Landmark Approach
Author: Jesse Anderton, Javed Aslam
Abstract: Ordinal Embedding is the problem of placing objects into to satisfy constraints like “object is closer to than to .” It can accommodate data that embeddings from features or distances cannot, but is a more difficult problem. We propose a novel landmark-based method as a partial solution. At small to medium scales, we present a novel combination of existing methods with some new theoretical justification. For very large values of optimizing over an entire embedding breaks down, so we propose a novel method which first embeds a subset of objects and then embeds the remaining objects independently and in parallel. We prove a distance error bound for our method in terms of and that it has time complexity, and show empirically that it is able to produce high quality embeddings in a fraction of the time needed for any published method.
Title: Sorting Out Lipschitz Function Approximation
Author: Cem Anil, James Lucas, Roger Grosse
Abstract: Training neural networks under a strict Lipschitz constraint is useful for provable adversarial robustness, generalization bounds, interpretable gradients, and Wasserstein distance estimation. By the composition property of Lipschitz functions, it suffices to ensure that each individual affine transformation or nonlinear activation is 1-Lipschitz. The challenge is to do this while maintaining the expressive power. We identify a necessary property for such an architecture: each of the layers must preserve the gradient norm during backpropagation. Based on this, we propose to combine a gradient norm preserving activation function, GroupSort, with norm-constrained weight matrices. We show that norm-constrained GroupSort architectures are universal Lipschitz function approximators. Empirically, we show that normconstrained GroupSort networks achieve tighter estimates of Wasserstein distance than their ReLU counterparts and can achieve provable adversarial robustness guarantees with little cost to accuracy.
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Title: Sparse Multi-Channel Variational Autoencoder for the Joint Analysis of Heterogeneous Data
Author: Luigi Antelmi, Nicholas Ayache, Philippe Robert, Marco Lorenzi
Abstract: Interpretable modeling of heterogeneous data channels is essential in medical applications, for example when jointly analyzing clinical scores and medical images. Variational Autoencoders (VAE) are powerful generative models that learn representations of complex data. The flexibility of VAE may come at the expense of lack of interpretability in describing the joint relationship between heterogeneous data. To tackle this problem, in this work we extend the variational framework of VAE to bring parsimony and interpretability when jointly account for latent relationships across multiple channels. In the latent space, this is achieved by constraining the variational distribution of each channel to a common target prior. Parsimonious latent representations are enforced by variational dropout. Experiments on synthetic data show that our model correctly identifies the prescribed latent dimensions and data relationships across multiple testing scenarios. When applied to imaging and clinical data, our method allows to identify the joint effect of age and pathology in describing clinical condition in a large scale clinical cohort.
Title: Unsupervised Label Noise Modeling and Loss Correction
Author: Eric Arazo, Diego Ortego, Paul Albert, Noel O’Connor, Kevin Mcguinness
Abstract: Despite being robust to small amounts of label noise, convolutional neural networks trained with stochastic gradient methods have been shown to easily fit random labels. When there are a mixture of correct and mislabelled targets, networks tend to fit the former before the latter. This suggests using a suitable two-component mixture model as an unsupervised generative model of sample loss values during training to allow online estimation of the probability that a sample is mislabelled. Specifically, we propose a beta mixture to estimate this probability and correct the loss by relying on the network prediction (the so-called bootstrapping loss). We further adapt augmentation to drive our approach a step further. Experiments on CIFAR10/100 and TinyImageNet demonstrate a robustness to label noise that substantially outperforms recent state-of-the-art. Source code is available at https://git.io/fjsvE and Appendix at https://arxiv.org/abs/1904.11238.
Title: Fine-Grained Analysis of Optimization and Generalization for Overparameterized Two-Layer Neural Networks
Author: Sanjeev Arora, Simon Du, Wei Hu, Zhiyuan Li, Ruosong Wang
Abstract: Recent works have cast some light on the mystery of why deep nets fit any data and generalize despite being very overparametrized. This paper analyzes training and generalization for a simple 2-layer ReLU net with random initialization, and provides the following improvements over recent works: (i) Using a tighter characterization of training speed than recent papers, an explanation for why training a neural net with random labels leads to slower training, as originally observed in [Zhang et al. ICLR’17]. (ii) Generalization bound independent of network size, using a data-dependent complexity measure. Our measure distinguishes clearly between random labels and true labels on MNIST and CIFAR, as shown by experiments. Moreover, recent papers require sample complexity to increase (slowly) with the size, while our sample complexity is completely independent of the network size. (iii) Learnability of a broad class of smooth functions by 2-layer ReLU nets trained via gradient descent. The key idea is to track dynamics of training and generalization via properties of a related kernel.
Title: Distributed Weighted Matching via Randomized Composable Coresets
Author: Sepehr Assadi, Mohammadhossein Bateni, Vahab Mirrokni
Abstract: Maximum weight matching is one of the most fundamental combinatorial optimization problems with a wide range of applications in data mining and bioinformatics. Developing distributed weighted matching algorithms is challenging due to the sequential nature of efficient algorithms for this problem. In this paper, we develop a simple distributed algorithm for the problem on general graphs with approximation guarantee of that (nearly) that of the sequential algorithm. A key advantage of this algorithm is that it can be easily implemented in only two rounds of computation in modern parallel computation frameworks such as MapReduce. We also demonstrate the efficiency of our algorithm in practice on various graphs (some with half a trillion edges) by achieving objective values always close to what is achievable in the centralized setting.
Title: Stochastic Gradient Push for Distributed Deep Learning
Author: Mahmoud Assran, Nicolas Loizou, Nicolas Ballas, Mike Rabbat
Abstract: Distributed data-parallel algorithms aim to accelerate the training of deep neural networks by parallelizing the computation of large mini-batch gradient updates across multiple nodes. Approaches that synchronize nodes using exact distributed averaging (e.g., via ALLREDUCE) are sensitive to stragglers and communication delays. The PUSHSUM gossip algorithm is robust to these issues, but only performs approximate distributed averaging. This paper studies Stochastic Gradient Push (SGP), which combines PUSHSUM with stochastic gradient updates. We prove that SGP converges to a stationary point of smooth, nonconvex objectives at the same sub-linear rate as SGD, and that all nodes achieve consensus. We empirically validate the performance of SGP on image classification (ResNet-50, ImageNet) and machine translation (Transformer, WMT’16 EnDe) workloads.
Title: Bayesian Optimization of Composite Functions
Author: Raul Astudillo, Peter Frazier
Abstract: We consider optimization of objective functions, i.e., of the form , where is a black-box derivative-free expensiveto-evaluate function with vector-valued outputs, and is a cheap-to-evaluate real-valued function. While these problems can be solved with standard Bayesian optimization, we propose a novel approach that exploits the composite structure of the objective function to substantially improve sampling efficiency. Our approach models using a multi-output Gaussian process and chooses where to sample using the expected improvement evaluated on the implied non-Gaussian posterior on , which we call expected improvement for composite functions (EI-CF). Although EI-CF cannot be computed in closed form, we provide a novel stochastic gradient estimator that allows its efficient maximization. We also show that our approach is asymptotically consistent, i.e., that it recovers a globally optimal solution as sampling effort grows to infinity, generalizing previous convergence results for classical expected improvement. Numerical experiments show that our approach dramatically outperforms standard Bayesian optimization benchmarks, reducing simple regret by several orders of magnitude.
Title: Linear-Complexity Data-Parallel Earth Mover’s Distance Approximations
Author: Kubilay Atasu, Thomas Mittelholzer
Abstract: The Earth Mover’s Distance (EMD) is a stateof-the art metric for comparing discrete probability distributions, but its high distinguishability comes at a high cost in computational complexity. Even though linear-complexity approximation algorithms have been proposed to improve its scalability, these algorithms are either limited to vector spaces with only a few dimensions or they become ineffective when the degree of overlap between the probability distributions is high. We propose novel approximation algorithms that overcome both of these limitations, yet still achieve linear time complexity. All our algorithms are data parallel, and thus, we take advantage of massively parallel computing engines, such as Graphics Processing Units (GPUs). On the popular text-based 20 Newsgroups dataset, the new algorithms are four orders of magnitude faster than a multi-threaded CPU implementation of Word Mover’s Distance and match its nearest-neighbors-search accuracy. On MNIST images, the new algorithms are four orders of magnitude faster than a GPU implementation of the Sinkhorn’s algorithm while offering a slightly higher nearest-neighbors-search accuracy.
Title: Benefits and Pitfalls of the Exponential Mechanism with Applications to Hilbert Spaces and Functional PCA
Author: Jordan Awan, Ana Kenney, Matthew Reimherr, Aleksandra Slavković
Abstract: The exponential mechanism is a fundamental tool of Differential Privacy (DP) due to its strong privacy guarantees and flexibility. We study its extension to settings with summaries based on infinite dimensional outputs such as with functional data analysis, shape analysis, and nonparametric statistics. We show that the mechanism must be designed with respect to a specific base measure over the output space, such as a Gaussian process. We provide a positive result that establishes a Central Limit Theorem for the exponential mechanism quite broadly. We also provide a negative result, showing that the magnitude of noise introduced for privacy is asymptotically non-negligible relative to the statistical estimation error. We develop an -DP mechanism for functional principal component analysis, applicable in separable Hilbert spaces, and demonstrate its performance via simulations and applications to two datasets.
Title: Feature Grouping as a Stochastic Regularizer for High-Dimensional Structured Data
Author: Sergul Aydore, Bertrand Thirion, Gael Varoquaux
Abstract: In many applications where collecting data is expensive, for example neuroscience or medical imaging, the sample size is typically small compared to the feature dimension. These datasets call for intelligent regularization that exploits known structure, such as correlations between the features arising from the measurement device. However, existing structured regularizers need specially crafted solvers, which are difficult to apply to complex models. We propose a new regularizer specifically designed to leverage structure in the data in a way that can be applied efficiently to complex models. Our approach relies on feature grouping, using a fast clustering algorithm inside a stochastic gradient descent loop: given a family of feature groupings that capture feature covariations, we randomly select these groups at each iteration. Experiments on two real-world datasets demonstrate that the proposed approach produces models that generalize better than those trained with conventional regularizers, and also improves convergence speed, and has a linear computational cost.
Title: Beyond the Chinese Restaurant and Pitman-Yor processes: Statistical Models with double power-law behavior
Author: Fadhel Ayed, Juho Lee, Francois Caron
Abstract: Bayesian nonparametric approaches, in particular the Pitman-Yor process and the associated twoparameter Chinese Restaurant process, have been successfully used in applications where the data exhibit a power-law behavior. Examples include natural language processing, natural images or networks. There is also growing empirical evidence suggesting that some datasets exhibit a tworegime power-law behavior: one regime for small frequencies, and a second regime, with a different exponent, for high frequencies. In this paper, we introduce a class of completely random measures which are doubly regularly-varying. Contrary to the Pitman-Yor process, we show that when completely random measures in this class are normalized to obtain random probability measures and associated random partitions, such partitions exhibit a double power-law behavior. We present two general constructions and discuss in particular two models within this class: the beta prime process (Broderick et al. (2015, 2018) and a novel process called generalized BFRY process. We derive efficient Markov chain Monte Carlo algorithms to estimate the parameters of these models. Finally, we show that the proposed models provide a better fit than the Pitman-Yor process on various datasets.
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Title: Scalable Fair Clustering
Author: Arturs Backurs, Piotr Indyk, Krzysztof Onak, Baruch Schieber, Ali Vakilian, Tal Wagner
Abstract: We study the fair variant of the classic -median problem introduced by Chierichetti et al. (Chierichetti et al., 2017) in which the points are colored, and the goal is to minimize the same average distance objective as in the standard -median problem while ensuring that all clusters have an “approximately equal” number of points of each color. Chierichetti et al. proposed a twophase algorithm for fair -clustering. In the first step, the pointset is partitioned into subsets called fairlets that satisfy the fairness requirement and approximately preserve the -median objective. In the second step, fairlets are merged into clusters by one of the existing -median algorithms. The running time of this algorithm is dominated by the first step, which takes super-quadratic time. In this paper, we present a practical approximate fairlet decomposition algorithm that runs in nearly linear time.
Comments: Clustering
Title: Entropic GANs meet VAEs: A Statistical Approach to Compute Sample Likelihoods in GANs
Author: Yogesh Balaji, Hamed Hassani, Rama Chellappa, Soheil Feizi
Abstract: Building on the success of deep learning, two modern approaches to learn a probability model from the data are Generative Adversarial Networks (GANs) and Variational AutoEncoders (VAEs). VAEs consider an explicit probability model for the data and compute a generative distribution by maximizing a variational lower-bound on the log-likelihood function. GANs, however, compute a generative model by minimizing a distance between observed and generated probability distributions without considering an explicit model for the observed data. The lack of having explicit probability models in GANs prohibits computation of sample likelihoods in their frameworks and limits their use in statistical inference problems. In this work, we resolve this issue by constructing an explicit probability model that can be used to compute sample likelihood statistics in GANs. In particular, we prove that under this probability model, a family of Wasserstein GANs with an entropy regularization can be viewed as a generative model that maximizes a variational lower-bound on average sample log likelihoods, an approach that VAEs are based on. This result makes a principled connection between two modern generative models, namely GANs and VAEs. In addition to the aforementioned theoretical results, we compute likelihood statistics for GANs trained on Gaussian, MNIST, SVHN, CIFAR-10 and LSUN datasets. Our numerical results validate the proposed theory.
Title: Provable Guarantees for Gradient-Based Meta-Learning
Author: Maria-Florina Balcan, Mikhail Khodak, Ameet Talwalkar
Abstract: We study the problem of meta-learning through the lens of online convex optimization, developing a meta-algorithm bridging the gap between popular gradient-based meta-learning and classical regularization-based multi-task transfer methods. Our method is the first to simultaneously satisfy good sample efficiency guarantees in the convex setting, with generalization bounds that improve with task-similarity, while also being computationally scalable to modern deep learning architectures and the many-task setting. Despite its simplicity, the algorithm matches, up to a constant factor, a lower bound on the performance of any such parameter-transfer method under natural task similarity assumptions. We use experiments in both convex and deep learning settings to verify and demonstrate the applicability of our theory.
Title: Open-ended learning in symmetric zero-sum games
Author: David Balduzzi, Marta Garnelo, Yoram Bachrach, Wojciech Czarnecki, Julien Perolat, Max Jaderberg, Thore Graepel
Abstract: Zero-sum games such as chess and poker are, abstractly, functions that evaluate pairs of agents, for example labeling them ‘winner’ and ‘loser’. If the game is approximately transitive, then selfplay generates sequences of agents of increasing strength. However, nontransitive games, such as rock-paper-scissors, can exhibit strategic cycles, and there is no longer a clear objective – we want agents to increase in strength, but against whom is unclear. In this paper, we introduce a geometric framework for formulating agent objectives in zero-sum games, in order to construct adaptive sequences of objectives that yield openended learning. The framework allows us to reason about population performance in nontransitive games, and enables the development of a new algorithm (rectified Nash response,) that uses game-theoretic niching to construct diverse populations of effective agents, producing a stronger set of agents than existing algorithms. We apply to two highly nontransitive resource allocation games and find that consistently outperforms the existing alternatives.
Title: Concrete Autoencoders: Differentiable Feature Selection and Reconstruction
Author: Muhammed Fatih Balın, Abubakar Abid, James Zou
Abstract: We introduce the concrete autoencoder, an endto-end differentiable method for global feature selection, which efficiently identifies a subset of the most informative features and simultaneously learns a neural network to reconstruct the input data from the selected features. Our method is unsupervised, and is based on using a concrete selector layer as the encoder and using a standard neural network as the decoder. During the training phase, the temperature of the concrete selector layer is gradually decreased, which encourages a user-specified number of discrete features to be learned; during test time, the selected features can be used with the decoder network to reconstruct the remaining input features. We evaluate concrete autoencoders on a variety of datasets, where they significantly outperform state-of-theart methods for feature selection and data reconstruction. In particular, on a large-scale gene expression dataset, the concrete autoencoder selects a small subset of genes whose expression levels can be used to impute the expression levels of the remaining genes; in doing so, it improves on the current widely-used expert-curated L1000 landmark genes, potentially reducing measurement costs by 20%. The concrete autoencoder can be implemented by adding just a few lines of code to a standard autoencoder, and the code for the algorithm and experiments is publicly available.
Title: HOList: An Environment for Machine Learning of Higher Order Logic Theorem Proving
Author: Kshitij Bansal, Sarah Loos, Markus Rabe, Christian Szegedy, Stewart Wilcox
Abstract: We present an environment, benchmark, and deep learning driven automated theorem prover for higher-order logic. Higher-order interactive theorem provers enable the formalization of arbitrary mathematical theories and thereby present an interesting, open-ended challenge for deep learning. We provide an open-source framework based on the HOL Light theorem prover that can be used as a reinforcement learning environment. HOL Light comes with a broad coverage of basic mathematical theorems on calculus and the formal proof of the Kepler conjecture, from which we derive a challenging benchmark for automated reasoning. We also present a deep reinforcement learning driven automated theorem prover, DeepHOL, with strong initial results on this benchmark.
Title: Structured agents for physical construction
Author: Victor Bapst, Alvaro Sanchez-Gonzalez, Carl Doersch, Kimberly Stachenfeld, Pushmeet Kohli, Peter Battaglia, Jessica Hamrick
Abstract: Physical construction—the ability to compose objects, subject to physical dynamics, to serve some function—is fundamental to human intelligence. We introduce a suite of challenging physical construction tasks inspired by how children play with blocks, such as matching a target configuration, stacking blocks to connect objects together, and creating shelter-like structures over target objects. We examine how a range of deep reinforcement learning agents fare on these challenges, and introduce several new approaches which provide superior performance. Our results show that agents which use structured representations (e.g., objects and scene graphs) and structured policies (e.g., object-centric actions) outperform those which use less structured representations, and generalize better beyond their training when asked to reason about larger scenes. Model-based agents which use Monte-Carlo Tree Search also outperform strictly model-free agents in our most challenging construction problems. We conclude that approaches which combine structured representations and reasoning with powerful learning are a key path toward agents that possess rich intuitive physics, scene understanding, and planning.
Title: Learning to Route in Similarity Graphs
Author: Dmitry Baranchuk, Dmitry Persiyanov, Anton Sinitsin, Artem Babenko
Abstract: Recently similarity graphs became the leading paradigm for efficient nearest neighbor search, outperforming traditional tree-based and LSHbased methods. Similarity graphs perform the search via greedy routing: a query traverses the graph and in each vertex moves to the adjacent vertex that is the closest to this query. In practice, similarity graphs are often susceptible to local minima, when queries do not reach its nearest neighbors, getting stuck in suboptimal vertices. In this paper we propose to learn the routing function that overcomes local minima via incorporating information about the graph global structure. In particular, we augment the vertices of a given graph with additional representations that are learned to provide the optimal routing from the start vertex to the query nearest neighbor. By thorough experiments, we demonstrate that the proposed learnable routing successfully diminishes the local minima problem and significantly improves the overall search performance.
Title: A Personalized Affective Memory Model for Improving Emotion Recognition
Author: Pablo Barros, German Parisi, Stefan Wermter
Abstract: Recent models of emotion recognition strongly rely on supervised deep learning solutions for the distinction of general emotion expressions. However, they are not reliable when recognizing online and personalized facial expressions, e.g., for person-specific affective understanding. In this paper, we present a neural model based on a conditional adversarial autoencoder to learn how to represent and edit general emotion expressions. We then propose Grow-When-Required networks as personalized affective memories to learn individualized aspects of emotion expressions. Our model achieves state-of-the-art performance on emotion recognition when evaluated on in-the-wild datasets. Furthermore, our experiments include ablation studies and neural visualizations in order to explain the behavior of our model.
Title: Scale-free adaptive planning for deterministic dynamics & discounted rewards
Author: Peter Bartlett, Victor Gabillon, Jennifer Healey, Michal Valko
Abstract: We address the problem of planning in an environment with deterministic dynamics and stochastic discounted rewards under a limited numerical budget where the ranges of both rewards and noise are unknown. We introduce PlaTγPOOS, an adaptive, robust, and efficient alternative to the OLOP (open-loop optimistic planning) algorithm. Whereas OLOP requires a priori knowledge of the ranges of both rewards and noise, PlaTγPOOS dynamically adapts its behavior to both. This allows PlaTγPOOS to be immune to two vulnerabilities of OLOP: failure when given underestimated ranges of noise and rewards and inefficiency when these are overestimated. PlaTγPOOS additionally adapts to the global smoothness of the value function. PlaTγPOOS acts in a provably more efficient manner vs. OLOP when OLOP is given an overestimated reward and show that in the case of no noise, PlaTγPOOS learns exponentially faster.
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Title: Pareto Optimal Streaming Unsupervised Classification
Author: Soumya Basu, Steven Gutstein, Brent Lance, Sanjay Shakkottai
Abstract: We study an online and streaming unsupervised classification system. Our setting consists of a collection of classifiers (with unknown confusion matrices) each of which can classify one sample per unit time, and which are accessed by a stream of unlabeled samples. Each sample is dispatched to one or more classifiers, and depending on the labels collected from these classifiers, may be sent to other classifiers to collect additional labels. The labels are continually aggregated. Once the aggregated label has high enough accuracy (pre-specified threshold for accuracy) or the sample is sent to all the classifiers, the now labeled sample is ejected from the system. For any given pre-specified accuracy threshold, the objective is to sustain the maximum possible sample arrival rate, such that the number of samples in memory does not grow unbounded. In this paper, we characterize the Pareto-optimal region of accuracy and arrival rate, and develop an algorithm that can operate at any point within this region. Our algorithm uses queueing-based routing and scheduling approaches combined with a novel online tensor decomposition method to learn the hidden parameters, to Pareto-optimality guarantees. We finally verify our theoretical results through simulations on two ensembles formed using AlexNet, VGG, and ResNet deep image classifiers.
Title: Categorical Feature Compression via Submodular Optimization
Author: Mohammadhossein Bateni, Lin Chen, Hossein Esfandiari, Thomas Fu, Vahab Mirrokni, Afshin Rostamizadeh
Abstract: In the era of big data, learning from categorical features with very large vocabularies (e.g., 28 million for the Criteo click prediction dataset) has become a practical challenge for machine learning researchers and practitioners. We design a highly-scalable vocabulary compression algorithm that seeks to maximize the mutual information between the compressed categorical feature and the target binary labels and we furthermore show that its solution is guaranteed to be within a factor of the global optimal solution. To achieve this, we introduce a novel reparametrization of the mutual information objective, which we prove is submodular, and design a data structure to query the submodular function in
amortized time (where is the input vocabulary size). Our complete algorithm is shown to operate in time. Additionally, we design a distributed implementation in which the query data structure is decomposed across machines such that each machine only requires space, while still preserving the approximation guarantee and using only logarithmic rounds of computation. We also provide analysis of simple alternative heuristic compression methods to demonstrate they cannot achieve any approximation guarantee. Using the large-scale Criteo learning task, we demonstrate better performance in retaining mutual information and also verify competitive learning performance compared to other baseline methods.
Title: Noise2Self: Blind Denoising by Self-Supervision
Author: Joshua Batson, Loic Royer
Abstract: We propose a general framework for denoising high-dimensional measurements which requires no prior on the signal, no estimate of the noise, and no clean training data. The only assumption is that the noise exhibits statistical independence across different dimensions of the measurement, while the true signal exhibits some correlation. For a broad class of functions (“-invariant”), it is then possible to estimate the performance of a denoiser from noisy data alone. This allows us to calibrate -invariant versions of any parameterised denoising algorithm, from the single hyperparameter of a median filter to the millions of weights of a deep neural network. We demonstrate this on natural image and microscopy data, where we exploit noise independence between pixels, and on single-cell gene expression data, where we exploit independence between detections of individual molecules. This framework generalizes recent work on training neural nets from noisy images and on cross-validation for matrix factorization.
Title: Efficient optimization of loops and limits with randomized telescoping sums
Author: Alex Beatson, Ryan P Adams
Abstract: We consider optimization problems in which the objective requires an inner loop with many steps or is the limit of a sequence of increasingly costly approximations. Meta-learning, training recurrent neural networks, and optimization of the solutions to differential equations are all examples of optimization problems with this character. In such problems, it can be expensive to compute the objective function value and its gradient, but truncating the loop or using less accurate approximations can induce biases that damage the overall solution. We propose randomized telescope (RT) gradient estimators, which represent the objective as the sum of a telescoping series and sample linear combinations of terms to provide cheap unbiased gradient estimates. We identify conditions under which RT estimators achieve optimization convergence rates independent of the length of the loop or the required accuracy of the approximation. We also derive a method for tuning RT estimators online to maximize a lower bound on the expected decrease in loss per unit of computation. We evaluate our adaptive RT estimators on a range of applications including meta-optimization of learning rates, variational inference of ODE parameters, and training an LSTM to model long sequences.
Title: Recurrent Kalman Networks: Factorized Inference in High-Dimensional Deep Feature Spaces
Author: Philipp Becker, Harit Pandya, Gregor Gebhardt, Cheng Zhao, C. James Taylor, Gerhard Neumann
Abstract: In order to integrate uncertainty estimates into deep time-series modelling, Kalman Filters (KFs) (Kalman et al., 1960) have been integrated with deep learning models, however, such approaches typically rely on approximate inference techniques such as variational inference which makes learning more complex and often less scalable due to approximation errors. We propose a new deep approach to Kalman filtering which can be learned directly in an end-to-end manner using backpropagation without additional approximations. Our approach uses a high-dimensional factorized latent state representation for which the Kalman updates simplify to scalar operations and thus avoids hard to backpropagate, computationally heavy and potentially unstable matrix inversions. Moreover, we use locally linear dynamic models to efficiently propagate the latent state to the next time step. The resulting network architecture, which we call Recurrent Kalman Network (RKN), can be used for any time-series data, similar to a LSTM (Hochreiter & Schmidhuber, 1997) but uses an explicit representation of uncertainty. As shown by our experiments, the RKN obtains much more accurate uncertainty estimates than an LSTM or Gated Recurrent Units (GRUs) (Cho et al., 2014) while also showing a slightly improved prediction performance and outperforms various recent generative models on an image imputation task.
Title: Switching Linear Dynamics for Variational Bayes Filtering
Author: Philip Becker-Ehmck, Jan Peters, Patrick Van Der Smagt
Abstract: System identification of complex and nonlinear systems is a central problem for model predictive control and model-based reinforcement learning. Despite their complexity, such systems can often be approximated well by a set of linear dynamical systems if broken into appropriate subsequences. This mechanism not only helps us find good approximations of dynamics, but also gives us deeper insight into the underlying system. Leveraging Bayesian inference, Variational Autoencoders and Concrete relaxations, we show how to learn a richer and more meaningful state space, e.g. encoding joint constraints and collisions with walls in a maze, from partial and highdimensional observations. This representation translates into a gain of accuracy of learned dynamics showcased on various simulated tasks.
Title: Active Learning for Probabilistic Structured Prediction of Cuts and Matchings
Author: Sima Behpour, Anqi Liu, Brian Ziebart
Abstract: Active learning methods, like uncertainty sampling, combined with probabilistic prediction techniques have achieved success in various problems like image classification and text classification. For more complex multivariate prediction tasks, the relationships between labels play an important role in designing structured classifiers with better performance. However, computational time complexity limits prevalent probabilistic methods from effectively supporting active learning. Specifically, while non-probabilistic methods based on structured support vector machines can be tractably applied to predicting cuts and bipartite matchings, conditional random fields are intractable for these structures. We propose an adversarial approach for active learning with structured prediction domains that is tractable for cuts and matching. We evaluate this approach algorithmically in two important structured prediction problems: multi-label classification and object tracking in videos. We demonstrate better accuracy and computational efficiency for our proposed method.
Title: Invertible Residual Networks
Author: Jens Behrmann, Will Grathwohl, Ricky T. Q. Chen, David Duvenaud, Joern-Henrik Jacobsen
Abstract: We show that standard ResNet architectures can be made invertible, allowing the same model to be used for classification, density estimation, and generation. Typically, enforcing invertibility requires partitioning dimensions or restricting network architectures. In contrast, our approach only requires adding a simple normalization step during training, already available in standard frameworks. Invertible ResNets define a generative model which can be trained by maximum likelihood on unlabeled data. To compute likelihoods, we introduce a tractable approximation to the Jacobian log-determinant of a residual block. Our empirical evaluation shows that invertible ResNets perform competitively with both stateof-the-art image classifiers and flow-based generative models, something that has not been previously achieved with a single architecture.
Title: Greedy Layerwise Learning Can Scale To ImageNet
Author: Eugene Belilovsky, Michael Eickenberg, Edouard Oyallon
Abstract: Shallow supervised 1-hidden layer neural networks have a number of favorable properties that make them easier to interpret, analyze, and optimize than their deep counterparts, but lack their representational power. Here we use 1-hidden layer learning problems to sequentially build deep networks layer by layer, which can inherit properties from shallow networks. Contrary to previous approaches using shallow networks, we focus on problems where deep learning is reported as critical for success. We thus study CNNs on image classification tasks using the large-scale ImageNet dataset and the CIFAR-10 dataset. Using a simple set of ideas for architecture and training we find that solving sequential 1-hidden-layer auxiliary problems lead to a CNN that exceeds AlexNet performance on ImageNet. Extending this training methodology to construct individual layers by solving 2-and-3-hidden layer auxiliary problems, we obtain an 11-layer network that exceeds several members of the VGG model family on ImageNet, and can train a VGG-11 model to the same accuracy as end-to-end learning. To our knowledge, this is the first competitive alternative to end-to-end training of CNNs that can scale to ImageNet. We illustrate several interesting properties of these models and conduct a range of experiments to study the properties this training induces on the intermediate representations.
Title: Overcoming Multi-model Forgetting
Author: Yassine Benyahia, Kaicheng Yu, Kamil Bennani Smires, Martin Jaggi, Anthony C. Davison, Mathieu Salzmann, Claudiu Musat
Abstract: We identify a phenomenon, which we refer to as multi-model forgetting, that occurs when sequentially training multiple deep networks with partially-shared parameters; the performance of previously-trained models degrades as one optimizes a subsequent one, due to the overwriting of shared parameters. To overcome this, we introduce a statistically-justified weight plasticity loss that regularizes the learning of a model’s shared parameters according to their importance for the previous models, and demonstrate its effectiveness when training two models sequentially and for neural architecture search. Adding weight plasticity in neural architecture search preserves the best models to the end of the search and yields improved results in both natural language processing and computer vision tasks.
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Title: Optimal Kronecker-Sum Approximation of Real Time Recurrent Learning
Author: Frederik Benzing, Marcelo Matheus Gauy, Asier Mujika, Anders Martinsson, Angelika Steger
Abstract: One of the central goals of Recurrent Neural Networks (RNNs) is to learn long-term dependencies in sequential data. Nevertheless, the most popular training method, Truncated Backpropagation through Time (TBPTT), categorically forbids learning dependencies beyond the truncation horizon. In contrast, the online training algorithm Real Time Recurrent Learning (RTRL) provides untruncated gradients, with the disadvantage of impractically large computational costs. Recently published approaches reduce these costs by providing noisy approximations of RTRL. We present a new approximation algorithm of RTRL, Optimal Kronecker-Sum Approximation (OK). We prove that OK is optimal for a class of approximations of RTRL, which includes all approaches published so far. Additionally, we show that OK has empirically negligible noise: Unlike previous algorithms it matches TBPTT in a real world task (character-level Penn TreeBank) and can exploit online parameter updates to outperform TBPTT in a synthetic string memorization task. Code available at GitHub.
Title: Adversarially Learned Representations for Information Obfuscation and Inference
Author: Martin Bertran, Natalia Martinez, Afroditi Papadaki, Qiang Qiu, Miguel Rodrigues, Galen Reeves, Guillermo Sapiro
Abstract: Data collection and sharing are pervasive aspects of modern society. This process can either be voluntary, as in the case of a person taking a facial image to unlock his/her phone, or incidental, such as traffic cameras collecting videos on pedestrians. An undesirable side effect of these processes is that shared data can carry information about attributes that users might consider as sensitive, even when such information is of limited use for the task. It is therefore desirable for both data collectors and users to design procedures that minimize sensitive information leakage. Balancing the competing objectives of providing meaningful individualized service levels and inference while obfuscating sensitive information is still an open problem. In this work, we take an information theoretic approach that is implemented as an unconstrained adversarial game between Deep Neural Networks in a principled, data-driven manner. This approach enables us to learn domain-preserving stochastic transformations that maintain performance on existing algorithms while minimizing sensitive information leakage.
Title: Bandit Multiclass Linear Classification: Efficient Algorithms for the Separable Case
Author: Alina Beygelzimer, David Pal, Balazs Szorenyi, Devanathan Thiruvenkatachari, Chen-Yu Wei, Chicheng Zhang
Abstract: We study the problem of efficient online multiclass linear classification with bandit feedback, where all examples belong to one of classes and lie in the -dimensional Euclidean space. Previous works have left open the challenge of designing efficient algorithms with finite mistake bounds when the data is linearly separable by a margin . In this work, we take a first step towards this problem. We consider two notions of linear separability, strong and weak. 1. Under the strong linear separability condition, we design an efficient algorithm that achieves a near-optimal mistake bound of . 2. Under the more challenging weak linear separability condition, we design an efficient algorithm with a mistake bound of . Our algorithm is based on kernel Perceptron and is inspired by the work of Klivans & Servedio (2008) on improperly learning intersection of halfspaces.
Title: Analyzing Federated Learning through an Adversarial Lens
Author: Arjun Nitin Bhagoji, Supriyo Chakraborty, Prateek Mittal, Seraphin Calo
Abstract: Federated learning distributes model training among a multitude of agents, who, guided by privacy concerns, perform training using their local data but share only model parameter updates, for iterative aggregation at the server to train an overall global model. In this work, we explore how the federated learning setting gives rise to a new threat, namely model poisoning, different from traditional data poisoning. Model poisoning is carried out by an adversary controlling a small number of malicious agents (usually 1) with the aim of causing the global model to misclassify a set of chosen inputs with high confidence. We explore a number of attack strategies for deep neural networks, starting with targeted model poisoning using boosting of the malicious agent’s update to overcome the effects of other agents. We also propose two critical notions of stealth to detect malicious updates. We bypass these by including them in the adversarial objective to carry out stealthy model poisoning. We improve attack stealth with the use of an alternating minimization strategy which alternately optimizes for stealth and the adversarial objective. We also empirically demonstrate that Byzantine-resilient aggregation strategies are not robust to our attacks. Our results show that effective and stealthy model poisoning attacks are possible, highlighting vulnerabilities in the federated learning setting.
Title: Optimal Continuous DR-Submodular Maximization and Applications to Provable Mean Field Inference
Author: Yatao Bian, Joachim Buhmann, Andreas Krause
Abstract: Mean field inference in probabilistic models is generally a highly nonconvex problem. Existing optimization methods, e.g., coordinate ascent algorithms, typically only find local optima. In this work we propose provable mean field methods for probabilistic log-submodular models and its posterior agreement (PA) with strong approximation guarantees. The main algorithmic technique is a new Double Greedy scheme, termed DR-DoubleGreedy, for continuous DR-submodular maximization with boxconstraints. This one-pass algorithm achieves the optimal 1/2 approximation ratio, which may be of independent interest. We validate the superior performance of our algorithms with baseline results on both synthetic and real-world datasets.
Title: More Efficient Off-Policy Evaluation through Regularized Targeted Learning
Author: Aurelien Bibaut, Ivana Malenica, Nikos Vlassis, Mark Van Der Laan
Abstract: We study the problem of off-policy evaluation (OPE) in Reinforcement Learning (RL), where the aim is to estimate the performance of a new policy given historical data that may have been generated by a different policy, or policies. In particular, we introduce a novel doubly-robust estimator for the OPE problem in RL, based on the Targeted Maximum Likelihood Estimation principle from the statistical causal inference literature. We also introduce several variance reduction techniques that lead to impressive performance gains in offpolicy evaluation. We show empirically that our estimator uniformly wins over existing off-policy evaluation methods across multiple RL environments and various levels of model misspecification. Finally, we further the existing theoretical analysis of estimators for the RL off-policy estimation problem by showing their rate of convergence and characterizing their asymptotic distribution.
Title: A Kernel Perspective for Regularizing Deep Neural Networks
Author: Alberto Bietti, Grégoire Mialon, Dexiong Chen, Julien Mairal
Abstract: We propose a new point of view for regularizing deep neural networks by using the norm of a reproducing kernel Hilbert space (RKHS). Even though this norm cannot be computed, it admits upper and lower approximations leading to various practical strategies. Specifically, this perspective (i) provides a common umbrella for many existing regularization principles, including spectral norm and gradient penalties, or adversarial training, (ii) leads to new effective regularization penalties, and (iii) suggests hybrid strategies combining lower and upper bounds to get better approximations of the RKHS norm. We experimentally show this approach to be effective when learning on small datasets, or to obtain adversarially robust models.
Title: Rethinking Lossy Compression: The Rate-Distortion-Perception Tradeoff
Author: Yochai Blau, Tomer Michaeli
Abstract: Lossy compression algorithms are typically designed and analyzed through the lens of Shannon’s rate-distortion theory, where the goal is to achieve the lowest possible distortion (e.g., low MSE or high SSIM) at any given bit rate. However, in recent years, it has become increasingly accepted that “low distortion” is not a synonym for “high perceptual quality”, and in fact optimization of one often comes at the expense of the other. In light of this understanding, it is natural to seek for a generalization of rate-distortion theory which takes perceptual quality into account. In this paper, we adopt the mathematical definition of perceptual quality recently proposed by Blau & Michaeli (2018), and use it to study the three-way tradeoff between rate, distortion, and perception. We show that restricting the perceptual quality to be high, generally leads to an elevation of the rate-distortion curve, thus necessitating a sacrifice in either rate or distortion. We prove several fundamental properties of this triple-tradeoff, calculate it in closed form for a Bernoulli source, and illustrate it visually on a toy MNIST example.
Title: Correlated bandits or: How to minimize mean-squared error online
Author: Vinay Praneeth Boda, Prashanth L.A.
Abstract: While the objective in traditional multi-armed bandit problems is to find the arm with the highest mean, in many settings, finding an arm that best captures information about other arms is of interest. This objective, however, requires learning the underlying correlation structure and not just the means of the arms. Sensors placement for industrial surveillance and cellular network monitoring are a few applications, where the underlying correlation structure plays an important role. Motivated by such applications, we formulate the correlated bandit problem, where the objective is to find the arm with the lowest mean-squared error (MSE) in estimating all the arms. To this end, we derive first an MSE estimator, based on sample variances and covariances, and show that our estimator exponentially concentrates around the true MSE. Under a best-arm identification framework, we propose a successive rejects type algorithm and provide bounds on the probability of error in identifying the best arm. Using minmax theory, we also derive fundamental performance limits for the correlated bandit problem.
Title: Adversarial Attacks on Node Embeddings via Graph Poisoning
Author: Aleksandar Bojchevski, Stephan Günnemann
Abstract: The goal of network representation learning is to learn low-dimensional node embeddings that capture the graph structure and are useful for solving downstream tasks. However, despite the proliferation of such methods, there is currently no study of their robustness to adversarial attacks. We provide the first adversarial vulnerability analysis on the widely used family of methods based on random walks. We derive efficient adversarial perturbations that poison the network structure and have a negative effect on both the quality of the embeddings and the downstream tasks. We further show that our attacks are transferable since they generalize to many models and are successful even when the attacker is restricted.
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Title: Online Variance Reduction with Mixtures
Author: Zalán Borsos, Sebastian Curi, Kfir Yehuda Levy, Andreas Krause
Abstract: Adaptive importance sampling for stochastic optimization is a promising approach that offers improved convergence through variance reduction. In this work, we propose a new framework for variance reduction that enables the use of mixtures over predefined sampling distributions, which can naturally encode prior knowledge about the data. While these sampling distributions are fixed, the mixture weights are adapted during the optimization process. We propose VRM, a novel and efficient adaptive scheme that asymptotically recovers the best mixture weights in hindsight and can also accommodate sampling distributions over sets of points. We empirically demonstrate the versatility of VRM in a range of applications.
Title: Compositional Fairness Constraints for Graph Embeddings
Author: Avishek Bose, William Hamilton
Abstract: Learning high-quality node embeddings is a key building block for machine learning models that operate on graph data, such as social networks and recommender systems. However, existing graph embedding techniques are unable to cope with fairness constraints, e.g., ensuring that the learned representations do not correlate with certain attributes, such as age or gender. Here, we introduce an adversarial framework to enforce fairness constraints on graph embeddings. Our approach is compositional—meaning that it can flexibly accommodate different combinations of fairness constraints during inference. For instance, in the context of social recommendations, our framework would allow one user to request that their recommendations are invariant to both their age and gender, while also allowing another user to request invariance to just their age. Experiments on standard knowledge graph and recommender system benchmarks highlight the utility of our proposed framework.
Title: Unreproducible Research is Reproducible
Author: Xavier Bouthillier, César Laurent, Pascal Vincent
Abstract: The apparent contradiction in the title is a wordplay on the different meanings attributed to the word reproducible across different scientific fields. What we imply is that unreproducible findings can be built upon reproducible methods. Without denying the importance of facilitating the reproduction of methods, we deem important to reassert that reproduction of findings is a fundamental step of the scientific inquiry. We argue that the commendable quest towards easy deterministic reproducibility of methods and numerical results should not have us forget the even more important necessity of ensuring the reproducibility of empirical findings and conclusions by properly accounting for essential sources of variations. We provide experiments to exemplify the brittleness of current common practice in the evaluation of models in the field of deep learning, showing that even if the results could be reproduced, a slightly different experiment would not support the findings. We hope to help clarify the distinction between exploratory and empirical research in the field of deep learning and believe more energy should be devoted to proper empirical research in our community. This work is an attempt to promote the use of more rigorous and diversified methodologies. It is not an attempt to impose a new methodology and it is not a critique on the nature of exploratory research.
Title: Blended Conditonal Gradients
Author: Gábor Braun, Sebastian Pokutta, Dan Tu, Stephen Wright
Abstract: We present a blended conditional gradient approach for minimizing a smooth convex function over a polytope , combining the Frank–Wolfe algorithm (also called conditional gradient) with gradient-based steps, different from away steps and pairwise steps, but still achieving linear convergence for strongly convex functions, along with good practical performance. Our approach retains all favorable properties of conditional gradient algorithms, notably avoidance of projections onto and maintenance of iterates as sparse convex combinations of a limited number of extreme points of . The algorithm is lazy, making use of inexpensive inexact solutions of the linear programming subproblem that characterizes the conditional gradient approach. It decreases measures of optimality rapidly, both in the number of iterations and in wall-clock time, outperforming even the lazy conditional gradient algorithms of (Braun et al., 2017). We also present a streamlined version of the algorithm that applies when is the probability simplex.
Title: Coresets for Ordered Weighted Clustering
Author: Vladimir Braverman, Shaofeng H.-C. Jiang, Robert Krauthgamer, Xuan Wu
Abstract: We design coresets for ORDERED -MEDIAN, a generalization of classical clustering problems such as -MEDIAN and -CENTER. Its objective function is defined via the Ordered Weighted Averaging (OWA) paradigm of Yager (1988), where data points are weighted according to a predefined weight vector, but in order of their contribution to the objective (distance from the centers). A powerful data-reduction technique, called a coreset, is to summarize a point set in into a small (weighted) point set , such that for every set of potential centers, the objective value of the coreset approximates that of within factor . When there are multiple objectives (weights), the above standard coreset might have limited usefulness, whereas in a simultaneous coreset, the above approximation holds for all weights (in addition to all centers). Our main result is a construction of a simultaneous coreset of size for ORDERED -MEDIAN. We validate our algorithm on a real geographical data set, and we find our coreset leads to a massive speedup of clustering computations, while maintaining high accuracy for a range of weights.
Comments: Clustering
Title: Target Tracking for Contextual Bandits: Application to Demand Side Management
Author: Margaux Brégère, Pierre Gaillard, Yannig Goude, Gilles Stoltz
Abstract: We propose a contextual-bandit approach for demand side management by offering price incentives. More precisely, a target mean consumption is set at each round and the mean consumption is modeled as a complex function of the distribution of prices sent and of some contextual variables such as the temperature, weather, and so on. The performance of our strategies is measured in quadratic losses through a regret criterion. We offer upper bounds on this regret (up to polylogarithmic terms)—and even faster rates under stronger assumptions—for strategies inspired by standard strategies for contextual bandits (like LinUCB, see Li et al., 2010). Simulations on a real data set gathered by UK Power Networks, in which price incentives were offered, show that our strategies are effective and may indeed manage demand response by suitably picking the price levels.
Title: Active Manifolds: A non-linear analogue to Active Subspaces
Author: Robert Bridges, Anthony Gruber, Christopher Felder, Miki Verma, Chelsey Hoff
Abstract: We present an approach to analyze functions that addresses limitations present in the Active Subspaces (AS) method of Constantine et al. (2015; 2014). Under appropriate hypotheses, our Active Manifolds (AM) method identifies a 1-D curve in the domain (the active manifold) on which nearly all values of the unknown function are attained, and which can be exploited for approximation or analysis, especially when is large (high-dimensional input space). We provide theorems justifying our AM technique and an algorithm permitting functional approximation and sensitivity analysis. Using accessible, low-dimensional functions as initial examples, we show AM reduces approximation error by an order of magnitude compared to AS, at the expense of more computation. Following this, we revisit the sensitivity analysis by Glaws et al. (2017), who apply AS to analyze a magnetohydrodynamic power generator model, and compare the performance of AM on the same data. Our analysis provides detailed information not captured by AS, exhibiting the influence of each parameter individually along an active manifold. Overall, AM represents a novel technique for analyzing functional models with benefits including: reducing -dimensional analysis to a 1-D analogue, permitting more accurate regression than AS (at more computational expense), enabling more informative sensitivity analysis, and granting accessible visualizations (2-D plots) of parameter sensitivity along the AM.
Title: Conditioning by adaptive sampling for robust design
Author: David Brookes, Hahnbeom Park, Jennifer Listgarten
Abstract: We present a method for design problems wherein the goal is to maximize or specify the value of one or more properties of interest (e. g., maximizing the fluorescence of a protein). We assume access to black box, stochastic “oracle” predictive functions, each of which maps from design space to a distribution over properties of interest. Because many state-of-the-art predictive models are known to suffer from pathologies, especially for data far from the training distribution, the design problem is different from directly optimizing the oracles. Herein, we propose a method to solve this problem that uses model-based adaptive sampling to estimate a distribution over the design space, conditioned on the desired properties.
Title: Extrapolating Beyond Suboptimal Demonstrations via Inverse Reinforcement Learning from Observations
Author: Daniel Brown, Wonjoon Goo, Prabhat Nagarajan, Scott Niekum
Abstract: A critical flaw of existing inverse reinforcement learning (IRL) methods is their inability to significantly outperform the demonstrator. This is because IRL typically seeks a reward function that makes the demonstrator appear near-optimal, rather than inferring the underlying intentions of the demonstrator that may have been poorly executed in practice. In this paper, we introduce a novel reward-learning-from-observation algorithm, Trajectory-ranked Reward EXtrapolation (T-REX), that extrapolates beyond a set of (approximately) ranked demonstrations in order to infer high-quality reward functions from a set of potentially poor demonstrations. When combined with deep reinforcement learning, T-REX outperforms state-of-the-art imitation learning and IRL methods on multiple Atari and MuJoCo benchmark tasks and achieves performance that is often more than twice the performance of the best demonstration. We also demonstrate that T-REX is robust to ranking noise and can accurately extrapolate intention by simply watching a learner noisily improve at a task over time.
Title: Deep Counterfactual Regret Minimization
Author: Noam Brown, Adam Lerer, Sam Gross, Tuomas Sandholm
Abstract: Counterfactual Regret Minimization (CFR) is the leading framework for solving large imperfectinformation games. It converges to an equilibrium by iteratively traversing the game tree. In order to deal with extremely large games, abstraction is typically applied before running CFR. The abstracted game is solved with tabular CFR, and its solution is mapped back to the full game. This process can be problematic because aspects of abstraction are often manual and domain specific, abstraction algorithms may miss important strategic nuances of the game, and there is a chickenand-egg problem because determining a good abstraction requires knowledge of the equilibrium of the game. This paper introduces Deep Counterfactual Regret Minimization, a form of CFR that obviates the need for abstraction by instead using deep neural networks to approximate the behavior of CFR in the full game. We show that Deep CFR is principled and achieves strong performance in large poker games. This is the first non-tabular variant of CFR to be successful in large games.
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Title: Understanding the Origins of Bias in Word Embeddings
Author: Marc-Etienne Brunet, Colleen Alkalay-Houlihan, Ashton Anderson, Richard Zemel
Abstract: Popular word embedding algorithms exhibit stereotypical biases, such as gender bias. The widespread use of these algorithms in machine learning systems can thus amplify stereotypes in important contexts. Although some methods have been developed to mitigate this problem, how word embedding biases arise during training is poorly understood. In this work, we develop a technique to address this question. Given a word embedding, our method reveals how perturbing the training corpus would affect the resulting embedding bias. By tracing the origins of word embedding bias back to the original training documents, one can identify subsets of documents whose removal would most reduce bias. We demonstrate our methodology on Wikipedia and New York Times corpora, and find it to be very accurate.
Title: Low Latency Privacy Preserving Inference
Author: Alon Brutzkus, Ran Gilad-Bachrach, Oren Elisha
Abstract: When applying machine learning to sensitive data, one has to find a balance between accuracy, information security, and computational complexity. Recent studies combined Homomorphic Encryption with neural networks to make inferences while protecting against information leakage. However, these methods are limited by the width and depth of neural networks that can be used (and hence the accuracy) and exhibit high latency even for relatively simple networks. In this study we provide two solutions that address these limitations. In the first solution, we present more than 10× improvement in latency and enable inference on wider networks compared to prior attempts with the same level of security. The improved performance is achieved by novel methods to represent the data during the computation. In the second solution, we apply the method of transfer learning to provide private inference services using deep networks with latency of ∼ 0.16 seconds. We demonstrate the efficacy of our methods on several computer vision tasks.
Title: Why do Larger Models Generalize Better? A Theoretical Perspective via the XOR Problem
Author: Alon Brutzkus, Amir Globerson
Abstract: Empirical evidence suggests that neural networks with ReLU activations generalize better with overparameterization. However, there is currently no theoretical analysis that explains this observation. In this work, we provide theoretical and empirical evidence that, in certain cases, overparameterized convolutional networks generalize better than small networks because of an interplay between weight clustering and feature exploration at initialization. We demonstrate this theoretically for a 3-layer convolutional neural network with max-pooling, in a novel setting which extends the XOR problem. We show that this interplay implies that with overparameterization, gradient descent converges to global minima with better generalization performance compared to global minima of small networks. Empirically, we demonstrate these phenomena for a 3-layer convolutional neural network in the MNIST task.
Title: Adversarial examples from computational constraints
Author: Sebastien Bubeck, Yin Tat Lee, Eric Price, Ilya Razenshteyn
Abstract: Why are classifiers in high dimension vulnerable to “adversarial” perturbations? We show that it is likely not due to information theoretic limitations, but rather it could be due to computational constraints. First we prove that, for a broad set of classification tasks, the mere existence of a robust classifier implies that it can be found by a possibly exponential-time algorithm with relatively few training examples. Then we give two particular classification tasks where learning a robust classifier is computationally intractable. More precisely we construct two binary classifications task in high dimensional space which are (i) information theoretically easy to learn robustly for large perturbations, (ii) efficiently learnable (nonrobustly) by a simple linear separator, (iii) yet are not efficiently robustly learnable, even for small perturbations. Specifically, for the first task hardness holds for any efficient algorithm in the statistical query (SQ) model, while for the second task we rule out any efficient algorithm under a cryptographic assumption. These examples give an exponential separation between classical learning and robust learning in the statistical query model or under a cryptographic assumption. It suggests that adversarial examples may be an unavoidable byproduct of computational limitations of learning algorithms.
Title: Self-similar Epochs: Value in arrangement
Author: Eliav Buchnik, Edith Cohen, Avinatan Hasidim, Yossi Matias
Abstract: Optimization of machine learning models is commonly performed through stochastic gradient updates on randomly ordered training examples. This practice means that each fraction of an epoch comprises an independent random sample of the training data that may not preserve informative structure present in the full data. We hypothesize that the training can be more effective with self-similar arrangements that potentially allow each epoch to provide benefits of multiple ones. We study this for “matrix factorization” – the common task of learning metric embeddings of entities such as queries, videos, or words from example pairwise associations. We construct arrangements that preserve the weighted Jaccard similarities of rows and columns and experimentally observe training acceleration of 3%-37% on synthetic and recommendation datasets. Principled arrangements of training examples emerge as a novel and potentially powerful enhancement to SGD that merits further exploration.
Title: Learning Generative Models across Incomparable Spaces
Author: Charlotte Bunne, David Alvarez-Melis, Andreas Krause, Stefanie Jegelka
Abstract: Generative Adversarial Networks have shown remarkable success in learning a distribution that faithfully recovers a reference distribution in its entirety. However, in some cases, we may want to only learn some aspects (e.g., cluster or manifold structure), while modifying others (e.g., style, orientation or dimension). In this work, we propose an approach to learn generative models across such incomparable spaces, and demonstrate how to steer the learned distribution towards target properties. A key component of our model is the Gromov-Wasserstein distance, a notion of discrepancy that compares distributions relationally rather than absolutely. While this framework subsumes current generative models in identically reproducing distributions, its inherent flexibility allows application to tasks in manifold learning, relational learning and cross-domain learning.
Title: Rates of Convergence for Sparse Variational Gaussian Process Regression
Author: David Burt, Carl Edward Rasmussen, Mark Van Der Wilk
Abstract: Excellent variational approximations to Gaussian process posteriors have been developed which avoid the scaling with dataset size . They reduce the computational cost to , with the number of inducing variables, which summarise the process. While the computational cost seems to be linear in N, the true complexity of the algorithm depends on how M must increase to ensure a certain quality of approximation. We show that with high probability the KL divergence can be made arbitrarily small by growing more slowly than . A particular case is that for regression with normally distributed inputs in D-dimensions with the Squared Exponential kernel, suffices. Our results show that as datasets grow, Gaussian process posteriors can be approximated cheaply, and provide a concrete rule for how to increase in continual learning scenario.
Title: What is the Effect of Importance Weighting in Deep Learning?
Author: Jonathon Byrd, Zachary Lipton
Abstract: Importance-weighted risk minimization is a key ingredient in many machine learning algorithms for causal inference, domain adaptation, class imbalance, and off-policy reinforcement learning. While the effect of importance weighting is wellcharacterized for low-capacity misspecified models, little is known about how it impacts overparameterized, deep neural networks. Inspired by recent theoretical results showing that on (linearly) separable data, deep linear networks optimized by SGD learn weight-agnostic solutions, we ask, for realistic deep networks, for which many practical datasets are separable, what is the effect of importance weighting? We present the surprising finding that while importance weighting impacts deep nets early in training, so long as the nets are able to separate the training data, its effect diminishes over successive epochs. Moreover, while L2 regularization and batch normalization (but not dropout), restore some of the impact of importance weighting, they express the effect via (seemingly) the wrong abstraction: why should practitioners tweak the L2 regularization, and by how much, to produce the correct weighting effect? We experimentally confirm these findings across a range of architectures and datasets.
Title: A Quantitative Analysis of the Effect of Batch Normalization on Gradient Descent
Author: Yongqiang Cai, Qianxiao Li, Zuowei Shen
Abstract: Despite its empirical success and recent theoretical progress, there generally lacks a quantitative analysis of the effect of batch normalization (BN) on the convergence and stability of gradient descent. In this paper, we provide such an analysis on the simple problem of ordinary least squares (OLS), where the precise dynamical properties of gradient descent (GD) is completely known, thus allowing us to isolate and compare the additional effects of BN. More precisely, we show that unlike GD, gradient descent with BN (BNGD) converges for arbitrary learning rates for the weights, and the convergence remains linear under mild conditions. Moreover, we quantify two different sources of acceleration of BNGD over GD – one due to over-parameterization which improves the effective condition number and another due having a large range of learning rates giving rise to fast descent. These phenomena set BNGD apart from GD and could account for much of its robustness properties. These findings are confirmed quantitatively by numerical experiments, which further show that many of the uncovered properties of BNGD in OLS are also observed qualitatively in more complex supervised learning problems.
Title: Accelerated Linear Convergence of Stochastic Momentum Methods in Wasserstein Distances
Author: Bugra Can, Mert Gurbuzbalaban, Lingjiong Zhu
Abstract: Momentum methods such as Polyak’s heavy ball (HB) method, Nesterov’s accelerated gradient (AG) as well as accelerated projected gradient (APG) method have been commonly used in machine learning practice, but their performance is quite sensitive to noise in the gradients. We study these methods under a first-order stochastic oracle model where noisy estimates of the gradients are available. For strongly convex problems, we show that the distribution of the iterates of AG converges with the accelerated linear rate to a ball of radius centered at a unique invariant distribution in the 1-Wasserstein metric where is the condition number as long as the noise variance is smaller than an explicit upper bound we can provide. Our analysis also certifies linear convergence rates as a function of the stepsize, momentum parameter and the noise variance; recovering the accelerated rates in the noiseless case and quantifying the level of noise that can be tolerated to achieve a given performance. To the best of our knowledge, these are the first linear convergence results for stochastic momentum methods under the stochastic oracle model. We also develop finer results for the special case of quadratic objectives, extend our results to the APG method and weakly convex functions showing accelerated rates when the noise magnitude is sufficiently small.
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Title: Active Embedding Search via Noisy Paired Comparisons
Author: Gregory Canal, Andy Massimino, Mark Davenport, Christopher Rozell
Abstract: Suppose that we wish to estimate a user’s preference vector from paired comparisons of the form “does user prefer item or item ?,” where both the user and items are embedded in a low-dimensional Euclidean space with distances that reflect user and item similarities. Such observations arise in numerous settings, including psychometrics and psychology experiments, search tasks, advertising, and recommender systems. In such tasks, queries can be extremely costly and subject to varying levels of response noise; thus, we aim to actively choose pairs that are most informative given the results of previous comparisons. We provide new theoretical insights into the benefits and challenges of greedy information maximization in this setting, and develop two novel strategies that maximize lower bounds on information gain and are simpler to analyze and compute respectively. We use simulated responses from a real-world dataset to validate our strategies through their similar performance to greedy information maximization, and their superior preference estimation over state-of-the-art selection methods as well as random queries.
Title: Dynamic Learning with Frequent New Product Launches: A Sequential Multinomial Logit Bandit Problem
Author: Junyu Cao, Wei Sun
Abstract: Motivated by the phenomenon that companies introduce new products to keep abreast with customers’ rapidly changing tastes, we consider a novel online learning setting where a profit-maximizing seller needs to learn customers’ preferences through offering recommendations, which may contain existing products and new products that are launched in the middle of a selling period. We propose a sequential multinomial logit (SMNL) model to characterize customers’ behavior when product recommendations are presented in tiers. For the offline version with known customers’ preferences, we propose a polynomialtime algorithm and characterize the properties of the optimal tiered product recommendation. For the online problem, we propose a learning algorithm and quantify its regret bound. Moreover, we extend the setting to incorporate a constraint which ensures every new product is learned to a given accuracy. Our results demonstrate the tier structure can be used to mitigate the risks associated with learning new products.
Title: Competing Against Nash Equilibria in Adversarially Changing Zero-Sum Games
Author: Adrian Rivera Cardoso, Jacob Abernethy, He Wang, Huan Xu
Abstract: We study the problem of repeated play in a zerosum game in which the payoff matrix may change, in a possibly adversarial fashion, on each round; we call these Online Matrix Games. Finding the Nash Equilibrium (NE) of a two player zero-sum game is core to many problems in statistics, optimization, and economics, and for a fixed game matrix this can be easily reduced to solving a linear program. But when the payoff matrix evolves over time our goal is to find a sequential algorithm that can compete with, in a certain sense, the NE of the long-term-averaged payoff matrix. We design an algorithm with small NE regret–that is, we ensure that the long-term payoff of both players is close to minimax optimum in hindsight. Our algorithm achieves near-optimal dependence with respect to the number of rounds and depends poly-logarithmically on the number of available actions of the players. Additionally, we show that the naive reduction, where each player simply minimizes its own regret, fails to achieve the stated objective regardless of which algorithm is used. Lastly, we consider the so-called bandit setting, where the feedback is significantly limited, and we provide an algorithm with small NE regret using one-point estimates of each payoff matrix.
Title: Automated Model Selection with Bayesian Quadrature
Author: Henry Chai, Jean-Francois Ton, Michael A. Osborne, Roman Garnett
Abstract: We present a novel technique for tailoring Bayesian quadrature (BQ) to model selection. The state-of-the-art for comparing the evidence of multiple models relies on Monte Carlo methods, which converge slowly and are unreliable for computationally expensive models. Although previous research has shown that BQ offers sample efficiency superior to Monte Carlo in computing the evidence of an individual model, applying BQ directly to model comparison may waste computation producing an overly-accurate estimate for the evidence of a clearly poor model. We propose an automated and efficient algorithm for computing the most-relevant quantity for model selection: the posterior model probability. Our technique maximizes the mutual information between this quantity and observations of the models’ likelihoods, yielding efficient sample acquisition across disparate model spaces when likelihood observations are limited. Our method produces moreaccurate posterior estimates using fewer likelihood evaluations than standard Bayesian quadrature and Monte Carlo estimators, as we demonstrate on synthetic and real-world examples.
Title: Learning Action Representations for Reinforcement Learning
Author: Yash Chandak, Georgios Theocharous, James Kostas, Scott Jordan, Philip Thomas
Abstract: Most model-free reinforcement learning methods leverage state representations (embeddings) for generalization, but either ignore structure in the space of actions or assume the structure is provided a priori. We show how a policy can be decomposed into a component that acts in a lowdimensional space of action representations and a component that transforms these representations into actual actions. These representations improve generalization over large, finite action sets by allowing the agent to infer the outcomes of actions similar to actions already taken. We provide an algorithm to both learn and use action representations and provide conditions for its convergence. The efficacy of the proposed method is demonstrated on large-scale real-world problems.
Title: Dynamic Measurement Scheduling for Event Forecasting using Deep RL
Author: Chun-Hao Chang, Mingjie Mai, Anna Goldenberg
Abstract: Imagine a patient in critical condition. What and when should be measured to forecast detrimental events, especially under the budget constraints? We answer this question by deep reinforcement learning (RL) that jointly minimizes the measurement cost and maximizes predictive gain, by scheduling strategically-timed measurements. We learn our policy to be dynamically dependent on the patient’s health history. To scale our framework to exponentially large action space, we distribute our reward in a sequential setting that makes the learning easier. In our simulation, our policy outperforms heuristic-based scheduling with higher predictive gain and lower cost. In a real-world ICU mortality prediction task (MIMIC3), our policies reduce the total number of measurements by 31% or improve predictive gain by a factor of 3 as compared to physicians, under the off-policy policy evaluation.
Title: On Symmetric Losses for Learning from Corrupted Labels
Author: Nontawat Charoenphakdee, Jongyeong Lee, Masashi Sugiyama
Abstract: This paper aims to provide a better understanding of a symmetric loss. First, we emphasize that using a symmetric loss is advantageous in the balanced error rate (BER) minimization and area under the receiver operating characteristic curve (AUC) maximization from corrupted labels. Second, we prove general theoretical properties of symmetric losses, including a classificationcalibration condition, excess risk bound, conditional risk minimizer, and AUC-consistency condition. Third, since all nonnegative symmetric losses are non-convex, we propose a convex barrier hinge loss that benefits significantly from the symmetric condition, although it is not symmetric everywhere. Finally, we conduct experiments to validate the relevance of the symmetric condition.
Title: Online learning with kernel losses
Author: Niladri Chatterji, Aldo Pacchiano, Peter Bartlett
Abstract: We present a generalization of the adversarial linear bandits framework, where the underlying losses are kernel functions (with an associated reproducing kernel Hilbert space) rather than linear functions. We study a version of the exponential weights algorithm and bound its regret in this setting. Under conditions on the eigen-decay of the kernel we provide a sharp characterization of the regret for this algorithm. When we have polynomial eigen-decay , we find that the regret is bounded by . While under the assumption of exponential eigendecay we get an even tighter bound on the regret . When the eigen-decay is polynomial we also show a non-matching minimax lower bound on the regret of and a lower bound of when the decay in the eigenvalues is exponentially fast. We also study the full information setting when the underlying losses are kernel functions and present an adapted exponential weights algorithm and a conditional gradient descent algorithm.
Title: Neural Network Attributions: A Causal Perspective
Author: Aditya Chattopadhyay, Piyushi Manupriya, Anirban Sarkar, Vineeth N Balasubramanian
Abstract: We propose a new attribution method for neural networks developed using first principles of causality (to the best of our knowledge, the first such). The neural network architecture is viewed as a Structural Causal Model, and a methodology to compute the causal effect of each feature on the output is presented. With reasonable assumptions on the causal structure of the input data, we propose algorithms to efficiently compute the causal effects, as well as scale the approach to data with large dimensionality. We also show how this method can be used for recurrent neural networks. We report experimental results on both simulated and real datasets showcasing the promise and usefulness of the proposed algorithm.
Title: PAC Identification of Many Good Arms in Stochastic Multi-Armed Bandits
Author: Arghya Roy Chaudhuri, Shivaram Kalyanakrishnan
Abstract: We consider the problem of identifying any out of the best arms in an -armed stochastic multi-armed bandit; framed in the PAC setting, this particular problem generalises both the problem of “best subset selection” (Kalyanakrishnan & Stone, 2010) and that of selecting “one out of the best m” arms (Roy Chaudhuri & Kalyanakrishnan, 2017). We present a lower bound on the worstcase sample complexity for general , and a fully sequential PAC algorithm, LUCB-k-m, which is more sample-efficient on easy instances. Also, extending our analysis to infinite-armed bandits, we present a PAC algorithm that is independent of , which identifies an arm from the best fraction of arms using at most an additive poly-log number of samples than compared to the lower bound, thereby improving over Roy Chaudhuri & Kalyanakrishnan (2017) and Aziz et al. (2018). The problem of identifying distinct arms from the best fraction is not always well-defined; for a special class of this problem, we present lower and upper bounds. Finally, through a reduction, we establish a relation between upper bounds for the “one out of the best ” problem for infinite instances and the “one out of the best ” problem for finite instances. We conjecture that it is more efficient to solve “small” finite instances using the latter formulation, rather than going through the former.
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Title: Nearest Neighbor and Kernel Survival Analysis: Nonasymptotic Error Bounds and Strong Consistency Rates
Author: George Chen
Abstract: We establish the first nonasymptotic error bounds for Kaplan-Meier-based nearest neighbor and kernel survival probability estimators where feature vectors reside in metric spaces. Our bounds imply rates of strong consistency for these nonparametric estimators and, up to a log factor, match an existing lower bound for conditional CDF estimation. Our proof strategy also yields nonasymptotic guarantees for nearest neighbor and kernel variants of the Nelson-Aalen cumulative hazards estimator. We experimentally compare these methods on four datasets. We find that for the kernel survival estimator, a good choice of kernel is one learned using random survival forests.
Title: Stein Point Markov Chain Monte Carlo
Author: Wilson Ye Chen, Alessandro Barp, Francois-Xavier Briol, Jackson Gorham, Mark Girolami, Lester Mackey, Chris Oates
Abstract: An important task in machine learning and statistics is the approximation of a probability measure by an empirical measure supported on a discrete point set. Stein Points are a class of algorithms for this task, which proceed by sequentially minimising a Stein discrepancy between the empirical measure and the target and, hence, require the solution of a non-convex optimisation problem to obtain each new point. This paper removes the need to solve this optimisation problem by, instead, selecting each new point based on a Markov chain sample path. This significantly reduces the computational cost of Stein Points and leads to a suite of algorithms that are straightforward to implement. The new algorithms are illustrated on a set of challenging Bayesian inference problems, and rigorous theoretical guarantees of consistency are established.
Title: Particle Flow Bayes’ Rule
Author: Xinshi Chen, Hanjun Dai, Le Song
Abstract: We present a particle flow realization of Bayes’ rule, where an ODE-based neural operator is used to transport particles from a prior to its posterior after a new observation. We prove that such an ODE operator exists. Its neural parameterization can be trained in a meta-learning framework, allowing this operator to reason about the effect of an individual observation on the posterior, and thus generalize across different priors, observations and to sequential Bayesian inference. We demonstrated the generalization ability of our particle flow Bayes operator in several canonical and high dimensional examples.
Title: Proportionally Fair Clustering
Author: Xingyu Chen, Brandon Fain, Liang Lyu, Kamesh Munagala
Abstract: We extend the fair machine learning literature by considering the problem of proportional centroid clustering in a metric context. For clustering points with centers, we define fairness as proportionality to mean that any points are entitled to form their own cluster if there is another center that is closer in distance for all points. We seek clustering solutions to which there are no such justified complaints from any subsets of agents, without assuming any a priori notion of protected subsets. We present and analyze algorithms to efficiently compute, optimize, and audit proportional solutions. We conclude with an empirical examination of the tradeoff between proportional solutions and the -means objective.
Comments: Clustering
Title: Information-Theoretic Considerations in Batch Reinforcement Learning
Author: Jinglin Chen, Nan Jiang
Abstract: Value-function approximation methods that operate in batch mode have foundational importance to reinforcement learning (RL). Finite sample guarantees for these methods often crucially rely on two types of assumptions: (1) mild distribution shift, and (2) representation conditions that are stronger than realizability. However, the necessity (“why do we need them?”) and the naturalness (“when do they hold?”) of such assumptions have largely eluded the literature. In this paper, we revisit these assumptions and provide theoretical results towards answering the above questions, and make steps towards a deeper understanding of value-function approximation.
Title: Generative Adversarial User Model for Reinforcement Learning Based Recommendation System
Author: Xinshi Chen, Shuang Li, Hui Li, Shaohua Jiang, Yuan Qi, Le Song
Abstract: There are great interests as well as many challenges in applying reinforcement learning (RL) to recommendation systems. In this setting, an online user is the environment; neither the reward function nor the environment dynamics are clearly defined, making the application of RL challenging. In this paper, we propose a novel model-based reinforcement learning framework for recommendation systems, where we develop a generative adversarial network to imitate user behavior dynamics and learn her reward function. Using this user model as the simulation environment, we develop a novel Cascading DQN algorithm to obtain a combinatorial recommendation policy which can handle a large number of candidate items efficiently. In our experiments with real data, we show this generative adversarial user model can better explain user behavior than alternatives, and the RL policy based on this model can lead to a better long-term reward for the user and higher click rate for the system.
Title: Understanding and Utilizing Deep Neural Networks Trained with Noisy Labels
Author: Pengfei Chen, Ben Ben Liao, Guangyong Chen, Shengyu Zhang
Abstract: Noisy labels are ubiquitous in real-world datasets, which poses a challenge for robustly training deep neural networks (DNNs) as DNNs usually have the high capacity to memorize the noisy labels. In this paper, we find that the test accuracy can be quantitatively characterized in terms of the noise ratio in datasets. In particular, the test accuracy is a quadratic function of the noise ratio in the case of symmetric noise, which explains the experimental findings previously published. Based on our analysis, we apply cross-validation to randomly split noisy datasets, which identifies most samples that have correct labels. Then we adopt the Co-teaching strategy which takes full advantage of the identified samples to train DNNs robustly against noisy labels. Compared with extensive state-of-the-art methods, our strategy consistently improves the generalization performance of DNNs under both synthetic and real-world training noise.
Title: A Gradual, Semi-Discrete Approach to Generative Network Training via Explicit Wasserstein Minimization
Author: Yucheng Chen, Matus Telgarsky, Chao Zhang, Bolton Bailey, Daniel Hsu, Jian Peng
Abstract: This paper provides a simple procedure to fit generative networks to target distributions, with the goal of a small Wasserstein distance (or other optimal transport cost). The approach is based on two principles: (a) if the source randomness of the network is a continuous distribution (the “semidiscrete” setting), then the Wasserstein distance is realized by a deterministic optimal transport mapping; (b) given an optimal transport mapping between a generator network and a target distribution, the Wasserstein distance may be decreased via a regression between the generated data and the mapped target points. The procedure here therefore alternates these two steps, forming an optimal transport and regressing against it, gradually adjusting the generator network towards the target distribution. Mathematically, this approach is shown to minimize the Wasserstein distance to both the empirical target distribution, and also its underlying population counterpart. Empirically, good performance is demonstrated on the training and testing sets of the MNIST and Thin-8 data. The paper closes with a discussion of the unsuitability of the Wasserstein distance for certain tasks, as has been identified in prior work (Arora et al., 2017; Huang et al., 2017).
Title: Transferability vs. Discriminability: Batch Spectral Penalization for Adversarial Domain Adaptation
Author: Xinyang Chen, Sinan Wang, Mingsheng Long, Jianmin Wang
Abstract: Adversarial domain adaptation has made remarkable advances in learning transferable representations for knowledge transfer across domains. While adversarial learning strengthens the feature transferability which the community focuses on, its impact on the feature discriminability has not been fully explored. In this paper, a series of experiments based on spectral analysis of the feature representations have been conducted, revealing an unexpected deterioration of the discriminability while learning transferable features adversarially. Our key finding is that the eigenvectors with the largest singular values will dominate the feature transferability. As a consequence, the transferability is enhanced at the expense of over penalization of other eigenvectors that embody rich structures crucial for discriminability. Towards this problem, we present Batch Spectral Penalization (BSP), a general approach to penalizing the largest singular values so that other eigenvectors can be relatively strengthened to boost the feature discriminability. Experiments show that the approach significantly improves upon representative adversarial domain adaptation methods to yield state of the art results.
Title: Fast Incremental von Neumann Graph Entropy Computation: Theory, Algorithm, and Applications
Author: Pin-Yu Chen, Lingfei Wu, Sijia Liu, Indika Rajapakse
Abstract: The von Neumann graph entropy (VNGE) facilitates measurement of information divergence and distance between graphs in a graph sequence. It has been successfully applied to various learning tasks driven by network-based data. While effective, VNGE is computationally demanding as it requires the full eigenspectrum of the graph Laplacian matrix. In this paper, we propose a new computational framework, Fast Incremental von Neumann Graph EntRopy (FINGER), which approaches VNGE with a performance guarantee. FINGER reduces the cubic complexity of VNGE to linear complexity in the number of nodes and edges, and thus enables online computation based on incremental graph changes. We also show asymptotic equivalence of FINGER to the exact VNGE, and derive its approximation error bounds. Based on FINGER, we propose efficient algorithms for computing Jensen-Shannon distance between graphs. Our experimental results on different random graph models demonstrate the computational efficiency and the asymptotic equivalence of FINGER. In addition, we apply FINGER to two real-world applications and one synthesized anomaly detection dataset, and corroborate its superior performance over seven baseline graph similarity methods.
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Title: Katalyst: Boosting Convex Katayusha for Non-Convex Problems with a Large Condition Number
Author: Zaiyi Chen, Yi Xu, Haoyuan Hu, Tianbao Yang
Abstract: An important class of non-convex objectives that has wide applications in machine learning consists of a sum of smooth functions and a non-smooth convex function. Tremendous studies have been devoted to conquering these problems by leveraging one of the two types of variance reduction techniques, i.e., SVRG-type that computes a full gradient occasionally and SAGA-type that maintains stochastic gradients at every iteration. An interesting question that has been largely ignored is how to improve the complexity of variance reduction methods for problems with a large condition number that measures the degree to which the objective is close to a convex function. In this paper, we present a simple but non-trivial boosting of a state-of-the-art SVRG-type method for convex problems (namely Katyusha) to enjoy an improved complexity for solving non-convex problems with a large condition number (that is close to a convex function). To the best of our knowledge, its complexity has the best dependence on and the degree of non-convexity, and also matches that of a recent SAGA-type accelerated stochastic algorithm for a constrained non-convex smooth optimization problem. Numerical experiments verify the effectiveness of the proposed algorithm in comparison with its competitors.
Title: Multivariate-Information Adversarial Ensemble for Scalable Joint Distribution Matching
Author: Ziliang Chen, Zhanfu Yang, Xiaoxi Wang, Xiaodan Liang, Xiaopeng Yan, Guanbin Li, Liang Lin
Abstract: A broad range of cross--domain generation researches boil down to matching a joint distribution by deep generative models (DGMs). Hitherto algorithms excel in pairwise domains while as increases, remain struggling to scale themselves to fit a joint distribution. In this paper, we propose a domain-scalable DGM, i.e., MMI-ALI for -domain joint distribution matching. As an -domain ensemble model of ALIs (Dumoulin et al., 2016), MMI-ALI is adversarially trained with maximizing Multivariate Mutual Information (MMI) w.r.t. joint variables of each pair of domains and their shared feature. The negative MMIs are upper bounded by a series of feasible losses that provably lead to matching -domain joint distributions. MMI-ALI linearly scales as increases and thus, strikes a right balance between efficacy and scalability. We evaluate MMI-ALI in diverse challenging -domain scenarios and verify its superiority.
Title: Robust Decision Trees Against Adversarial Examples
Author: Hongge Chen, Huan Zhang, Duane Boning, Cho-Jui Hsieh
Abstract: Although adversarial examples and model robustness have been extensively studied in the context of linear models and neural networks, research on this issue in tree-based models and how to make tree-based models robust against adversarial examples is still limited. In this paper, we show that tree based models are also vulnerable to adversarial examples and develop a novel algorithm to learn robust trees. At its core, our method aims to optimize the performance under the worstcase perturbation of input features, which leads to a max-min saddle point problem. Incorporating this saddle point objective into the decision tree building procedure is non-trivial due to the discrete nature of trees—a naive approach to finding the best split according to this saddle point objective will take exponential time. To make our approach practical and scalable, we propose efficient tree building algorithms by approximating the inner minimizer in this saddle point problem, and present efficient implementations for classical information gain based trees as well as state-of-the-art tree boosting models such as XGBoost. Experimental results on real world datasets demonstrate that the proposed algorithms can substantially improve the robustness of tree-based models against adversarial examples.
Title: RaFM: Rank-Aware Factorization Machines
Author: Xiaoshuang Chen, Yin Zheng, Jiaxing Wang, Wenye Ma, Junzhou Huang
Abstract: Fatorization machines (FM) are a popular model class to learn pairwise interactions by a low-rank approximation. Different from existing FM-based approaches which use a fixed rank for all features, this paper proposes a Rank-Aware FM (RaFM) model which adopts pairwise interactions from embeddings with different ranks. The proposed model achieves a better performance on real-world datasets where different features have significantly varying frequencies of occurrences. Moreover, we prove that the RaFM model can be stored, evaluated, and trained as efficiently as one single FM, and under some reasonable conditions it can be even significantly more efficient than FM. RaFM improves the performance of FMs in both regression tasks and classification tasks while incurring less computational burden, therefore also has attractive potential in industrial applications.
Title: Control Regularization for Reduced Variance Reinforcement Learning
Author: Richard Cheng, Abhinav Verma, Gabor Orosz, Swarat Chaudhuri, Yisong Yue, Joel Burdick
Abstract: Dealing with high variance is a significant challenge in model-free reinforcement learning (RL). Existing methods are unreliable, exhibiting high variance in performance from run to run using different initializations/seeds. Focusing on problems arising in continuous control, we propose a functional regularization approach to augmenting model-free RL. In particular, we regularize the behavior of the deep policy to be similar to a policy prior, i.e., we regularize in function space. We show that functional regularization yields a biasvariance trade-off, and propose an adaptive tuning strategy to optimize this trade off. When the policy prior has control-theoretic stability guarantees, we further show that this regularization approximately preserves those stability guarantees throughout learning. We validate our approach empirically on a range of settings, and demonstrate significantly reduced variance, guaranteed dynamic stability, and more efficient learning than deep RL alone.
Title: Predictor-Corrector Policy Optimization
Author: Ching-An Cheng, Xinyan Yan, Nathan Ratliff, Byron Boots
Abstract: We present a predictor-corrector framework, called PICCOLO, that can transform a first-order model-free reinforcement or imitation learning algorithm into a new hybrid method that leverages predictive models to accelerate policy learning. The new “PICCOLOed” algorithm optimizes a policy by recursively repeating two steps: In the Prediction Step, the learner uses a model to predict the unseen future gradient and then applies the predicted estimate to update the policy; in the Correction Step, the learner runs the updated policy in the environment, receives the true gradient, and then corrects the policy using the gradient error. Unlike previous algorithms, PICCOLO corrects for the mistakes of using imperfect predicted gradients and hence does not suffer from model bias. The development of PICCOLO is made possible by a novel reduction from predictable online learning to adversarial online learning, which provides a systematic way to modify existing firstorder algorithms to achieve the optimal regret with respect to predictable information. We show, in both theory and simulation, that the convergence rate of several first-order model-free algorithms can be improved by PICCOLO.
Title: Variational Inference for sparse network reconstruction from count data
Author: Julien Chiquet, Stephane Robin, Mahendra Mariadassou
Abstract: The problem of network reconstruction from continuous data has been extensively studied and most state of the art methods rely on variants of Gaussian Graphical Models (GGM). GGM are unfortunately badly suited to sparse count data spanning several orders of magnitude. Most inference methods for count data (SparCC, REBACCA, SPIEC-EASI, gCoda, etc) first transform counts to pseudo-Gaussian observations before using GGM. We rely instead on a PoissonLogNormal (PLN) model where counts follow Poisson distributions with parameters sampled from a latent multivariate Gaussian variable, and infer the network in the latent space using a variational inference procedure. This model allows us to (i) control for confounding covariates and differences in sampling efforts and (ii) integrate data sets from different origins. It is also competitive in terms of speed and accuracy with state of the art methods.
Title: Random Walks on Hypergraphs with Edge-Dependent Vertex Weights
Author: Uthsav Chitra, Benjamin Raphael
Abstract: Hypergraphs are used in machine learning to model higher-order relationships in data. While spectral methods for graphs are well-established, spectral theory for hypergraphs remains an active area of research. In this paper, we use random walks to develop a spectral theory for hypergraphs with edge dependent vertex weights: hypergraphs where every vertex has a weight for each incident hyperedge that describes the contribution of to the hyperedge . We derive a random walk-based hypergraph Laplacian, and bound the mixing time of random walks on such hypergraphs. Moreover, we give conditions under which random walks on such hypergraphs are equivalent to random walks on graphs. As a corollary, we show that current machine learning methods that rely on Laplacians derived from random walks on hypergraphs with edge-independent vertex weights do not utilize higher-order relationships in the data. Finally, we demonstrate the advantages of hypergraphs with edge-dependent vertex weights on ranking applications using realworld datasets.
Title: Neural Joint Source-Channel Coding
Author: Kristy Choi, Kedar Tatwawadi, Aditya Grover, Tsachy Weissman, Stefano Ermon
Abstract: For reliable transmission across a noisy communication channel, classical results from information theory show that it is asymptotically optimal to separate out the source and channel coding processes. However, this decomposition can fall short in the finite bit-length regime, as it requires nontrivial tuning of hand-crafted codes and assumes infinite computational power for decoding. In this work, we propose to jointly learn the encoding and decoding processes using a new discrete variational autoencoder model. By adding noise into the latent codes to simulate the channel during training, we learn to both compress and errorcorrect given a fixed bit-length and computational budget. We obtain codes that are not only competitive against several separation schemes, but also learn useful robust representations of the data for downstream tasks such as classification. Finally, inference amortization yields an extremely fast neural decoder, almost an order of magnitude faster compared to standard decoding methods based on iterative belief propagation.
Title: Beyond Backprop: Online Alternating Minimization with Auxiliary Variables
Author: Anna Choromanska, Benjamin Cowen, Sadhana Kumaravel, Ronny Luss, Mattia Rigotti, Irina Rish, Paolo Diachille, Viatcheslav Gurev, Brian Kingsbury, Ravi Tejwani, Djallel Bouneffouf
Abstract: Despite significant recent advances in deep neural networks, training them remains a challenge due to the highly non-convex nature of the objective function. State-of-the-art methods rely on error backpropagation, which suffers from several wellknown issues, such as vanishing and exploding gradients, inability to handle non-differentiable nonlinearities and to parallelize weight-updates across layers, and biological implausibility. These limitations continue to motivate exploration of alternative training algorithms, including several recently proposed auxiliary-variable methods which break the complex nested objective function into local subproblems. However, those techniques are mainly offline (batch), which limits their applicability to extremely large datasets, as well as to online, continual or reinforcement learning. The main contribution of our work is a novel online (stochastic/mini-batch) alternating minimization (AM) approach for training deep neural networks, together with the first theoretical convergence guarantees for AM in stochastic settings and promising empirical results on a variety of architectures and datasets.
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Title: Unifying Orthogonal Monte Carlo Methods
Author: Krzysztof Choromanski, Mark Rowland, Wenyu Chen, Adrian Weller
Abstract: Many machine learning methods making use of Monte Carlo sampling in vector spaces have been shown to be improved by conditioning samples to be mutually orthogonal. Exact orthogonal coupling of samples is computationally intensive, hence approximate methods have been of great interest. In this paper, we present a unifying perspective of many approximate methods by considering Givens transformations, propose new approximate methods based on this framework, and demonstrate the first statistical guarantees for families of approximate methods in kernel approximation. We provide extensive empirical evaluations with guidance for practitioners.
Title: Probability Functional Descent: A Unifying Perspective on GANs, Variational Inference, and Reinforcement Learning
Author: Casey Chu, Jose Blanchet, Peter Glynn
Abstract: The goal of this paper is to provide a unifying view of a wide range of problems of interest in machine learning by framing them as the minimization of functionals defined on the space of probability measures. In particular, we show that generative adversarial networks, variational inference, and actor-critic methods in reinforcement learning can all be seen through the lens of our framework. We then discuss a generic optimization algorithm for our formulation, called probability functional descent (PFD), and show how this algorithm recovers existing methods developed independently in the settings mentioned earlier.
Title: MeanSum: A Neural Model for Unsupervised Multi-Document Abstractive Summarization
Author: Eric Chu, Peter Liu
Abstract: Abstractive summarization has been studied using neural sequence transduction methods with datasets of large, paired document-summary examples. However, such datasets are rare and the models trained from them do not generalize to other domains. Recently, some progress has been made in learning sequence-to-sequence mappings with only unpaired examples. In our work, we consider the setting where there are only documents (product or business reviews) with no summaries provided, and propose an end-to-end, neural model architecture to perform unsupervised abstractive summarization. Our proposed model consists of an auto-encoder where the mean of the representations of the input reviews decodes to a reasonable summary-review while not relying on any review-specific features. We consider variants of the proposed architecture and perform an ablation study to show the importance of specific components. We show through automated metrics and human evaluation that the generated summaries are highly abstractive, fluent, relevant, and representative of the average sentiment of the input reviews. Finally, we collect a reference evaluation dataset and show that our model outperforms a strong extractive baseline.
Title: Weak Detection of Signal in the Spiked Wigner Model
Author: Hye Won Chung, Ji Oon Lee
Abstract: We consider the problem of detecting the presence of the signal in a rank-one signal-plus-noise data matrix. In case the signal-to-noise ratio is under the threshold below which a reliable detection is impossible, we propose a hypothesis test based on the linear spectral statistics of the data matrix. When the noise is Gaussian, the error of the proposed test is optimal as it matches the error of the likelihood ratio test that minimizes the sum of the Type-I and Type-II errors. The test is datadriven and does not depend on the distribution of the signal or the noise. If the density of the noise is known, it can be further improved by an entrywise transformation to lower the error of the test.
Title: New results on information theoretic clustering
Author: Ferdinando Cicalese, Eduardo Laber, Lucas Murtinho
Abstract: We study the problem of optimizing the clustering of a set of vectors when the quality of the clustering is measured by the Entropy or the Gini impurity measure. Our results contribute to the state of the art both in terms of best known approximation guarantees and inapproximability bounds: (i) we give the first polynomial time algorithm for Entropy impurity based clustering with approximation guarantee independent of the number of vectors and (ii) we show that the problem of clustering based on entropy impurity does not admit a PTAS. This also implies an inapproximability result in information theoretic clustering for probability distributions closing a problem left open in [Chaudhury and McGregor, COLT08] and [Ackermann et al., ECCC11]. We also report experiments with a new clustering method that was designed on top of the theoretical tools leading to the above results. These experiments suggest a practical applicability for our method, in particular, when the number of clusters is large.
Comments: Clustering
Title: Sensitivity Analysis of Linear Structural Causal Models
Author: Carlos Cinelli, Daniel Kumor, Bryant Chen, Judea Pearl, Elias Bareinboim
Abstract: Causal inference requires assumptions about the data generating process, many of which are unverifiable from the data. Given that some causal assumptions might be uncertain or disputed, formal methods are needed to quantify how sensitive research conclusions are to violations of those assumptions. Although an extensive literature exists on the topic, most results are limited to specific model structures, while a general-purpose algorithmic framework for sensitivity analysis is still lacking. In this paper, we develop a formal, systematic approach to sensitivity analysis for arbitrary linear Structural Causal Models (SCMs). We start by formalizing sensitivity analysis as a constrained identification problem. We then develop an efficient, graph-based identification algorithm that exploits non-zero constraints on both directed and bidirected edges. This allows researchers to systematically derive sensitivity curves for a target causal quantity with an arbitrary set of path coefficients and error covariances as sensitivity parameters. These results can be used to display the degree to which violations of causal assumptions affect the target quantity of interest, and to judge, on scientific grounds, whether problematic degrees of violations are plausible.
Title: Dimensionality Reduction for Tukey Regression
Author: Kenneth Clarkson, Ruosong Wang, David Woodruff
Abstract: We give the first dimensionality reduction methods for the overconstrained Tukey regression problem. The Tukey loss function has for residual errors smaller than a prescribed threshold , but becomes constant for errors . Our results depend on a new structural result, proven constructively, showing that for any -dimensional subspace , there is a fixed bounded-size subset of coordinates containing, for every , all the large coordinates, with respect to the Tukey loss function, of . Our methods reduce a given Tukey regression problem to a smaller weighted version, whose solution is a provably good approximate solution to the original problem. Our reductions are fast, simple and easy to implement, and we give empirical results demonstrating their practicality, using existing heuristic solvers for the small versions. We also give exponentialtime algorithms giving provably good solutions, and hardness results suggesting that a significant speedup in the worst case is unlikely.
Title: On Medians of (Randomized) Pairwise Means
Author: Pierre Laforgue, Stephan Clemencon, Patrice Bertail
Abstract: Tournament procedures, recently introduced in Lugosi & Mendelson (2016), offer an appealing alternative, from a theoretical perspective at least, to the principle of Empirical Risk Minimization in machine learning. Statistical learning by Medianof-Means (MoM) basically consists in segmenting the training data into blocks of equal size and comparing the statistical performance of every pair of candidate decision rules on each data block: that with highest performance on the majority of the blocks is declared as the winner. In the context of nonparametric regression, functions having won all their duels have been shown to outperform empirical risk minimizers w.r.t. the mean squared error under minimal assumptions, while exhibiting robustness properties. It is the purpose of this paper to extend this approach, in order to address other learning problems in particular, for which the performance criterion takes the form of an expectation over pairs of observations rather than over one single observation, as may be the case in pairwise ranking, clustering or metric learning. Precisely, it is proved here that the bounds achieved by MoM are essentially conserved when the blocks are built by means of independent sampling without replacement schemes instead of a simple segmentation. These results are next extended to situations where the risk is related to a pairwise loss function and its empirical counterpart is of the form of a -statistic. Beyond theoretical results guaranteeing the performance of the learning/estimation methods proposed, some numerical experiments provide empirical evidence of their relevance in practice.
Title: Quantifying Generalization in Reinforcement Learning
Author: Karl Cobbe, Oleg Klimov, Chris Hesse, Taehoon Kim, John Schulman
Abstract: In this paper, we investigate the problem of overfitting in deep reinforcement learning. Among the most common benchmarks in RL, it is customary to use the same environments for both training and testing. This practice offers relatively little insight into an agent’s ability to generalize. We address this issue by using procedurally generated environments to construct distinct training and test sets. Most notably, we introduce a new environment called CoinRun, designed as a benchmark for generalization in RL. Using CoinRun, we find that agents overfit to surprisingly large training sets. We then show that deeper convolutional architectures improve generalization, as do methods traditionally found in supervised learning, including L2 regularization, dropout, data augmentation and batch normalization.
Title: Empirical Analysis of Beam Search Performance Degradation in Neural Sequence Models
Author: Eldan Cohen, Christopher Beck
Abstract: Beam search is the most popular inference algorithm for decoding neural sequence models. Unlike greedy search, beam search allows for non-greedy local decisions that can potentially lead to a sequence with a higher overall probability. However, work on a number of applications has found that the quality of the highest probability hypothesis found by beam search degrades with large beam widths. We perform an empirical study of the behavior of beam search across three sequence synthesis tasks. We find that increasing the beam width leads to sequences that are disproportionately based on early, very low probability tokens that are followed by a sequence of tokens with higher (conditional) probability. We show that, empirically, such sequences are more likely to have a lower evaluation score than lower probability sequences without this pattern. Using the notion of search discrepancies from heuristic search, we hypothesize that large discrepancies are the cause of the performance degradation. We show that this hypothesis generalizes the previous ones in machine translation and image captioning. To validate our hypothesis, we show that constraining beam search to avoid large discrepancies eliminates the performance degradation.
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Title: Learning Linear-Quadratic Regulators Efficiently with only Regret
Author: Alon Cohen, Tomer Koren, Yishay Mansour
Abstract: We present the first computationally-efficient algorithm with regret for learning in Linear Quadratic Control systems with unknown dynamics. By that, we resolve an open question of Abbasi-Yadkori and Szepesvari (2011) and Dean, ´ Mania, Matni, Recht, and Tu (2018).
Title: Certified Adversarial Robustness via Randomized Smoothing
Author: Jeremy Cohen, Elan Rosenfeld, Zico Kolter
Abstract: We show how to turn any classifier that classifies well under Gaussian noise into a new classifier that is certifiably robust to adversarial perturbations under the norm. While this “randomized smoothing” technique has been proposed before in the literature, we are the first to provide a tight analysis, which establishes a close connection between robustness and Gaussian noise. We use the technique to train an ImageNet classifier with e.g. a certified top-1 accuracy of 49% under adversarial perturbations with norm less than 0.5 (=127/255). Smoothing is the only approach to certifiably robust classification which has been shown feasible on full-resolution ImageNet. On smaller-scale datasets where competing approaches to certified robustness are viable, smoothing delivers higher certified accuracies. The empirical success of the approach suggests that provable methods based on randomization at prediction time are a promising direction for future research into adversarially robust classification. Code and models are available at http://github.com/locuslab/smoothing.
Title: Gauge Equivariant Convolutional Networks and the Icosahedral CNN
Author: Taco Cohen, Maurice Weiler, Berkay Kicanaoglu, Max Welling
Abstract: The principle of equivariance to symmetry transformations enables a theoretically grounded approach to neural network architecture design. Equivariant networks have shown excellent performance and data efficiency on vision and medical imaging problems that exhibit symmetries. Here we show how this principle can be extended beyond global symmetries to local gauge transformations. This enables the development of a very general class of convolutional neural networks on manifolds that depend only on the intrinsic geometry, and which includes many popular methods from equivariant and geometric deep learning.
We implement gauge equivariant CNNs for signals defined on the surface of the icosahedron, which provides a reasonable approximation of the sphere. By choosing to work with this very regular manifold, we are able to implement the gauge equivariant convolution using a single conv2d call, making it a highly scalable and practical alternative to Spherical CNNs. Using this method, we demonstrate substantial improvements over previous methods on the task of segmenting omnidirectional images and global climate patterns.
Title: CURIOUS: Intrinsically Motivated Modular Multi-Goal Reinforcement Learning
Author: Cédric Colas, Pierre Fournier, Mohamed Chetouani, Olivier Sigaud, Pierre-Yves Oudeyer
Abstract: In open-ended environments, autonomous learning agents must set their own goals and build their own curriculum through an intrinsically motivated exploration. They may consider a large diversity of goals, aiming to discover what is controllable in their environments, and what is not. Because some goals might prove easy and some impossible, agents must actively select which goal to practice at any moment, to maximize their overall mastery on the set of learnable goals. This paper proposes CURIOUS, an algorithm that leverages 1) a modular Universal Value Function Approximator with hindsight learning to achieve a diversity of goals of different kinds within a unique policy and 2) an automated curriculum learning mechanism that biases the attention of the agent towards goals maximizing the absolute learning progress. Agents focus sequentially on goals of increasing complexity, and focus back on goals that are being forgotten. Experiments conducted in a new modular-goal robotic environment show the resulting developmental self-organization of a learning curriculum, and demonstrate properties of robustness to distracting goals, forgetting and changes in body properties.
Title: A fully differentiable beam search decoder
Author: Ronan Collobert, Awni Hannun, Gabriel Synnaeve
Abstract: We introduce a new beam search decoder that is fully differentiable, making it possible to optimize at training time through the inference procedure. Our decoder allows us to combine models which operate at different granularities (e.g. acoustic and language models). It can be used when target sequences are not aligned to input sequences by considering all possible alignments between the two. We demonstrate our approach scales by applying it to speech recognition, jointly training acoustic and word-level language models. The system is end-to-end, with gradients flowing through the whole architecture from the word-level transcriptions. Recent research efforts have shown that deep neural networks with attention-based mechanisms can successfully train an acoustic model from the final transcription, while implicitly learning a language model. Instead, we show that it is possible to discriminatively train an acoustic model jointly with an explicit and possibly pretrained language model.
Title: Scalable Metropolis-Hastings for Exact Bayesian Inference with Large Datasets
Author: Rob Cornish, Paul Vanetti, Alexandre Bouchard-Cote, George Deligiannidis, Arnaud Doucet
Abstract: Bayesian inference via standard Markov Chain Monte Carlo (MCMC) methods is too computationally intensive to handle large datasets, since the cost per step usually scales like in the number of data points . We propose the Scalable Metropolis–Hastings (SMH) kernel that exploits Gaussian concentration of the posterior to require processing on average only or even data points per step. This scheme is based on a combination of factorized acceptance probabilities, procedures for fast simulation of Bernoulli processes, and control variate ideas. Contrary to many MCMC subsampling schemes such as fixed step-size Stochastic Gradient Langevin Dynamics, our approach is exact insofar as the invariant distribution is the true posterior and not an approximation to it. We characterise the performance of our algorithm theoretically, and give realistic and verifiable conditions under which it is geometrically ergodic. This theory is borne out by empirical results that demonstrate overall performance benefits over standard Metropolis–Hastings and various subsampling algorithms.
Title: Adjustment Criteria for Generalizing Experimental Findings
Author: Juan Correa, Jin Tian, Elias Bareinboim
Abstract: Generalizing causal effects from a controlled experiment to settings beyond the particular study population is arguably one of the central tasks found in empirical circles. While a proper design and careful execution of the experiment would support, under mild conditions, the validity of inferences about the population in which the experiment was conducted, two challenges make the extrapolation step to different populations somewhat involved, namely, transportability and sampling selection bias. The former is concerned with disparities in the distributions and causal mechanisms between the domain (i.e., settings, population, environment) where the experiment is conducted and where the inferences are intended; the latter with distortions in the sample’s proportions due to preferential selection of units into the study. In this paper, we investigate the assumptions and machinery necessary for using covariate adjustment to correct for the biases generated by both of these problems, and generalize experimental data to infer causal effects in a new domain. We derive complete graphical conditions to determine if a set of covariates is admissible for adjustment in this new setting. Building on the graphical characterization, we develop an efficient algorithm that enumerates all possible admissible sets with polytime delay guarantee; this can be useful for when some variables are preferred over the others due to different costs or amenability to measurement.
Title: Online Learning with Sleeping Experts and Feedback Graphs
Author: Corinna Cortes, Giulia Desalvo, Claudio Gentile, Mehryar Mohri, Scott Yang
Abstract: We consider the scenario of online learning with sleeping experts, where not all experts are available at each round, and analyze the general framework of learning with feedback graphs, where the loss observations associated with each expert are characterized by a graph. A critical assumption in this framework is that the loss observations and the set of sleeping experts at each round are independent. We first extend the classical sleeping experts algorithm of Kleinberg et al. (2008) to the feedback graphs scenario, and prove matching upper and lower bounds for the sleeping regret of the resulting algorithm under the independence assumption. Our main contribution is then to relax this assumption, present a more general notion of sleeping regret, and derive a general algorithm with strong theoretical guarantees. We apply this new framework to the important scenario of online learning with abstention, where a learner can elect to abstain from making a prediction at the price of a certain cost. We empirically validate our algorithm against multiple online abstention algorithms on several real-world datasets, showing substantial performance improvements.
Title: Active Learning with Disagreement Graphs
Author: Corinna Cortes, Giulia Desalvo, Mehryar Mohri, Ningshan Zhang, Claudio Gentile
Abstract: We present two novel enhancements of an online importance-weighted active learning algorithm IWAL, using the properties of disagreements among hypotheses. The first enhancement, IWALD, prunes the hypothesis set with a more aggressive strategy based on the disagreement graph. We show that IWAL-D improves the generalization performance and the label complexity of the original IWAL, and quantify the improvement in terms of a disagreement graph coefficient. The second enhancement, IZOOM, further improves IWAL-D by adaptively zooming into the current version space and thus reducing the best-in-class error. We show that IZOOM admits favorable theoretical guarantees with the changing hypothesis set. We report experimental results on multiple datasets and demonstrate that the proposed algorithms achieve better test performances than IWAL given the same amount of labeling budget.
Title: Shape Constraints for Set Functions
Author: Andrew Cotter, Maya Gupta, Heinrich Jiang, Erez Louidor, James Muller, Tamann Narayan, Serena Wang, Tao Zhu
Abstract: Set functions predict a label from a permutationinvariant variable-size collection of feature vectors. We propose making set functions more understandable and regularized by capturing domain knowledge through shape constraints. We show how prior work in monotonic constraints can be adapted to set functions, and then propose two new shape constraints designed to generalize the conditioning role of weights in a weighted mean. We show how one can train standard functions and set functions that satisfy these shape constraints with a deep lattice network. We propose a nonlinear estimation strategy we call the semantic feature engine that uses set functions with the proposed shape constraints to estimate labels for compound sparse categorical features. Experiments on real-world data show the achieved accuracy is similar to deep sets or deep neural networks, but provides guarantees on the model behavior, which makes it easier to explain and debug.
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Title: Training Well-Generalizing Classifiers for Fairness Metrics and Other Data-Dependent Constraints
Author: Andrew Cotter, Maya Gupta, Heinrich Jiang, Nathan Srebro, Karthik Sridharan, Serena Wang, Blake Woodworth, Seungil You
Abstract: Classifiers can be trained with data-dependent constraints to satisfy fairness goals, reduce churn, achieve a targeted false positive rate, or other policy goals. We study the generalization performance for such constrained optimization problems, in terms of how well the constraints are satisfied at evaluation time, given that they are satisfied at training time. To improve generalization, we frame the problem as a two-player game where one player optimizes the model parameters on a training dataset, and the other player enforces the constraints on an independent validation dataset. We build on recent work in two-player constrained optimization to show that if one uses this twodataset approach, then constraint generalization can be significantly improved. As we illustrate experimentally, this approach works not only in theory, but also in practice.
Title: Monge blunts Bayes: Hardness Results for Adversarial Training
Author: Zac Cranko, Aditya Menon, Richard Nock, Cheng Soon Ong, Zhan Shi, Christian Walder
Abstract: The last few years have seen a staggering number of empirical studies of the robustness of neural networks in a model of adversarial perturbations of their inputs. Most rely on an adversary which carries out local modifications within prescribed balls. None however has so far questioned the broader picture: how to frame a resource-bounded adversary so that it can be severely detrimental to learning, a non-trivial problem which entails at a minimum the choice of loss and classifiers.
We suggest a formal answer for losses that satisfy the minimal statistical requirement of being proper. We pin down a simple sufficient property for any given class of adversaries to be detrimental to learning, involving a central measure of “harmfulness” which generalizes the well-known class of integral probability metrics. A key feature of our result is that it holds for all proper losses, and for a popular subset of these, the optimisation of this central measure appears to be independent of the loss. When classifiers are Lipschitz – a now popular approach in adversarial training –, this optimisation resorts to optimal transport to make a low-budget compression of class marginals. Toy experiments reveal a finding recently separately observed: training against a sufficiently budgeted adversary of this kind improves generalization.
Title: Boosted Density Estimation Remastered
Author: Zac Cranko, Richard Nock
Abstract: There has recently been a steady increase in the number iterative approaches to density estimation. However, an accompanying burst of formal convergence guarantees has not followed; all results pay the price of heavy assumptions which are often unrealistic or hard to check. The Generative Adversarial Network (GAN) literature — seemingly orthogonal to the aforementioned pursuit — has had the side effect of a renewed interest in variational divergence minimisation (notably -GAN). We show how to combine this latter approach and the classical boosting theory in supervised learning to get the first density estimation algorithm that provably achieves geometric convergence under very weak assumptions. We do so by a trick allowing to combine classifiers as the sufficient statistics of an exponential family. Our analysis includes an improved variational characterisation of -GAN.
Title: Submodular Cost Submodular Cover with an Approximate Oracle
Author: Victoria Crawford, Alan Kuhnle, My Thai
Abstract: In this work, we study the Submodular Cost Submodular Cover problem, which is to minimize the submodular cost required to ensure that the submodular benefit function exceeds a given threshold. Existing approximation ratios for the greedy algorithm assume a value oracle to the benefit function. However, access to a value oracle is not a realistic assumption for many applications of this problem, where the benefit function is difficult to compute. We present two incomparable approximation ratios for this problem with an approximate value oracle and demonstrate that the ratios take on empirically relevant values through a case study with the Influence Threshold problem in online social networks.
Title: Flexibly Fair Representation Learning by Disentanglement
Author: Elliot Creager, David Madras, Joern-Henrik Jacobsen, Marissa Weis, Kevin Swersky, Toniann Pitassi, Richard Zemel
Abstract: We consider the problem of learning representations that achieve group and subgroup fairness with respect to multiple sensitive attributes. Taking inspiration from the disentangled representation learning literature, we propose an algorithm for learning compact representations of datasets that are useful for reconstruction and prediction, but are also flexibly fair, meaning they can be easily modified at test time to achieve subgroup demographic parity with respect to multiple sensitive attributes and their conjunctions. We show empirically that the resulting encoder— which does not require the sensitive attributes for inference—enables the adaptation of a single representation to a variety of fair classification tasks with new target labels and subgroup definitions.
Title: Anytime Online-to-Batch, Optimism and Acceleration
Author: Ashok Cutkosky
Abstract: A standard way to obtain convergence guarantees in stochastic convex optimization is to run an online learning algorithm and then output the average of its iterates: the actual iterates of the online learning algorithm do not come with individual guarantees. We close this gap by introducing a black box modification to any online learning algorithm whose iterates converge to the optimum in stochastic scenarios. We then consider the case of smooth losses, and show that combining our approach with optimistic online learning algorithms immediately yields a fast convergence rate of on -smooth problems with variance in the gradients. Finally, we provide a reduction that converts any adaptive online algorithm into one that obtains the optimal accelerated rate of , while still maintaining convergence in the nonsmooth setting. Importantly, our algorithms adapt to and automatically: they do not need to know either to obtain these rates.
Title: Matrix-Free Preconditioning in Online Learning
Author: Ashok Cutkosky, Tamas Sarlos
Abstract: We provide an online convex optimization algorithm with regret that interpolates between the regret of an algorithm using an optimal preconditioning matrix and one using a diagonal preconditioning matrix. Our regret bound is never worse than that obtained by diagonal preconditioning, and in certain setting even surpasses that of algorithms with full-matrix preconditioning. Importantly, our algorithm runs in the same time and space complexity as online gradient descent. Along the way we incorporate new techniques that mildly streamline and improve logarithmic factors in prior regret analyses. We conclude by benchmarking our algorithm on synthetic data and deep learning tasks.
Title: Minimal Achievable Sufficient Statistic Learning
Author: Milan Cvitkovic, Günther Koliander
Abstract: We introduce Minimal Achievable Sufficient Statistic (MASS) Learning, a machine learning training objective for which the minima are minimal sufficient statistics with respect to a class of functions being optimized over (e.g., deep networks). In deriving MASS Learning, we also introduce Conserved Differential Information (CDI), an information-theoretic quantity that — unlike standard mutual information — can be usefully applied to deterministically-dependent continuous random variables like the input and output of a deep network. In a series of experiments, we show that deep networks trained with MASS Learning achieve competitive performance on supervised learning, regularization, and uncertainty quantification benchmarks.
Title: Open Vocabulary Learning on Source Code with a Graph-Structured Cache
Author: Milan Cvitkovic, Badal Singh, Animashree Anandkumar
Abstract: Machine learning models that take computer program source code as input typically use Natural Language Processing (NLP) techniques. However, a major challenge is that code is written using an open, rapidly changing vocabulary due to, e.g., the coinage of new variable and method names. Reasoning over such a vocabulary is not something for which most NLP methods are designed. We introduce a Graph–Structured Cache to address this problem; this cache contains a node for each new word the model encounters with edges connecting each word to its occurrences in the code. We find that combining this graph–structured cache strategy with recent Graph–Neural–Network–based models for supervised learning on code improves the models’ performance on a code completion task and a variable naming task — with over 100% relative improvement on the latter — at the cost of a moderate increase in computation time.
Title: The Value Function Polytope in Reinforcement Learning
Author: Robert Dadashi, Adrien Ali Taiga, Nicolas Le Roux, Dale Schuurmans, Marc G. Bellemare
Abstract: We establish geometric and topological properties of the space of value functions in finite stateaction Markov decision processes. Our main contribution is the characterization of the nature of its shape: a general polytope (Aigner et al., 2010). To demonstrate this result, we exhibit several properties of the structural relationship between policies and value functions including the line theorem, which shows that the value functions of policies constrained on all but one state describe a line segment. Finally, we use this novel perspective to introduce visualizations to enhance the understanding of the dynamics of reinforcement learning algorithms.