NeurIPS 2018 Papers

Generative Adversarial Networks (GANs) are one of the most practical methods for learning data distributions. A popular GAN formulation is based on the use of Wasserstein distance as a metric between probability distributions. Unfortunately, minimizing the Wasserstein distance between the data distribution and the generative model distribution is a computationally challenging problem as its objective is non-convex, non-smooth, and even hard to compute. In this work, we show that obtaining gradient information of the smoothed Wasserstein GAN formulation, which is based on regularized Optimal Transport (OT), is computationally effortless and hence one can apply first order optimization methods to minimize this objective. Consequently, we establish theoretical convergence guarantee to stationarity for a proposed class of GAN optimization algorithms. Unlike the original non-smooth formulation, our algorithm only requires solving the discriminator to approximate optimality. We apply our method to learning MNIST digits as well as CIFAR-10 images. Our experiments show that our method is computationally efficient and generates images comparable to the state of the art algorithms given the same architecture and computational power.

We study the interplay between sequential decision making and avoiding discrimination against protected groups, when examples arrive online and do not follow distributional assumptions. We consider the most basic extension of classical online learning: Given a class of predictors that are individually non-discriminatory with respect to a particular metric, how can we combine them to perform as well as the best predictor, while preserving non-discrimination? Surprisingly we show that this task is unachievable for the prevalent notion of "equalized odds" that requires equal false negative rates and equal false positive rates across groups. On the positive side, for another notion of non-discrimination, "equalized error rates", we show that running separate instances of the classical multiplicative weights algorithm for each group achieves this guarantee. Interestingly, even for this notion, we show that algorithms with stronger performance guarantees than multiplicative weights cannot preserve non-discrimination.

We propose a principled method for gradient-based regularization of the critic of GAN-like models trained by adversarially optimizing the kernel of a Maximum Mean Discrepancy (MMD). We show that controlling the gradient of the critic is vital to having a sensible loss function, and devise a method to enforce exact, analytical gradient constraints at no additional cost compared to existing approximate techniques based on additive regularizers. The new loss function is provably continuous, and experiments show that it stabilizes and accelerates training, giving image generation models that outperform state-of-the art methods on $160 \times 160$ CelebA and $64 \times 64$ unconditional ImageNet.

The widespread online misinformation could cause public panic and serious economic damages. The misinformation containment problem aims at limiting the spread of misinformation in online social networks by launching competing campaigns. Motivated by realistic scenarios, we present the first analysis of the misinformation containment problem for the case when an arbitrary number of cascades are allowed. This paper makes four contributions. First, we provide a formal model for multi-cascade diffusion and introduce an important concept called as cascade priority. Second, we show that the misinformation containment problem cannot be approximated within a factor of $\Omega(2^{\log^{1-\epsilon}n^4})$ in polynomial time unless $NP \subseteq DTIME(n^{\polylog{n}})$. Third, we introduce several types of cascade priority that are frequently seen in real social networks. Finally, we design novel algorithms for solving the misinformation containment problem. The effectiveness of the proposed algorithm is supported by encouraging experimental results.

Stochastic gradient methods are the workhorse (algorithms) of large-scale optimization problems in machine learning, signal processing, and other computational sciences and engineering. This paper studies Markov chain gradient descent, a variant of stochastic gradient descent where the random samples are taken on the trajectory of a Markov chain. Existing results of this method assume convex objectives and a reversible Markov chain and thus have their limitations. We establish new non-ergodic convergence under wider step sizes, for nonconvex problems, and for non-reversible finite-state Markov chains. Nonconvexity makes our method applicable to broader problem classes. Non-reversible finite-state Markov chains, on the other hand, can mix substatially faster. To obtain these results, we introduce a new technique that varies the mixing levels of the Markov chains. The reported numerical results validate our contributions.

The problem of estimating an unknown discrete distribution from its samples is a fundamental tenet of statistical learning. Over the past decade, it attracted significant research effort and has been solved for a variety of divergence measures. Surprisingly, an equally important problem, estimating an unknown Markov chain from its samples, is still far from understood. We consider two problems related to the min-max risk (expected loss) of estimating an unknown k-state Markov chain from its n sequential samples: predicting the conditional distribution of the next sample with respect to the KL-divergence, and estimating the transition matrix with respect to a natural loss induced by KL or a more general f-divergence measure.

In many sequential decision making tasks, it is challenging to design reward functions that help an RL agent efficiently learn behavior that is considered good by the agent designer. A number of different formulations of the reward-design problem, or close variants thereof, have been proposed in the literature. In this paper we build on the Optimal Rewards Framework of Singh et al. that defines the optimal intrinsic reward function as one that when used by an RL agent achieves behavior that optimizes the task-specifying or extrinsic reward function. Previous work in this framework has shown how good intrinsic reward functions can be learned for lookahead search based planning agents. Whether it is possible to learn intrinsic reward functions for learning agents remains an open problem. In this paper we derive a novel algorithm for learning intrinsic rewards for policy-gradient based learning agents. We compare the performance of an augmented agent that uses our algorithm to provide additive intrinsic rewards to an A2C-based policy learner (for Atari games) and a PPO-based policy learner (for Mujoco domains) with a baseline agent that uses the same policy learners but with only extrinsic rewards. Our results show improved performance on most but not all of the domains.

Leverage score sampling provides an appealing way to perform approximate com- putations for large matrices. Indeed, it allows to derive faithful approximations with a complexity adapted to the problem at hand. Yet, performing leverage scores sampling is a challenge in its own right requiring further approximations. In this paper, we study the problem of leverage score sampling for positive definite ma- trices defined by a kernel. Our contribution is twofold. First we provide a novel algorithm for leverage score sampling and second, we exploit the proposed method in statistical learning by deriving a novel solver for kernel ridge regression. Our main technical contribution is showing that the proposed algorithms are currently the most efficient and accurate for these problems.

Converting an n-dimensional vector to a probability distribution over n objects is a commonly used component in many machine learning tasks like multiclass classification, multilabel classification, attention mechanisms etc. For this, several probability mapping functions have been proposed and employed in literature such as softmax, sum-normalization, spherical softmax, and sparsemax, but there is very little understanding in terms how they relate with each other. Further, none of the above formulations offer an explicit control over the degree of sparsity. To address this, we develop a unified framework that encompasses all these formulations as special cases. This framework ensures simple closed-form solutions and existence of sub-gradients suitable for learning via backpropagation. Within this framework, we propose two novel sparse formulations, sparsegen-lin and sparsehourglass, that seek to provide a control over the degree of desired sparsity. We further develop novel convex loss functions that help induce the behavior of aforementioned formulations in the multilabel classification setting, showing improved performance. We also demonstrate empirically that the proposed formulations, when used to compute attention weights, achieve better or comparable performance on standard seq2seq tasks like neural machine translation and abstractive summarization.

In pattern recognition, a random label Y is to be predicted based upon observing a random vector X valued in $\mathbb{R}^d$ with d>1 by means of a classification rule with minimum probability of error. In a wide variety of applications, ranging from finance/insurance to environmental sciences through teletraffic data analysis for instance, extreme (i.e. very large) observations X are of crucial importance, while contributing in a negligible manner to the (empirical) error however, simply because of their rarity. As a consequence, empirical risk minimizers generally perform very poorly in extreme regions. It is the purpose of this paper to develop a general framework for classification in the extremes. Precisely, under non-parametric heavy-tail assumptions for the class distributions, we prove that a natural and asymptotic notion of risk, accounting for predictive performance in extreme regions of the input space, can be defined and show that minimizers of an empirical version of a non-asymptotic approximant of this dedicated risk, based on a fraction of the largest observations, lead to classification rules with good generalization capacity, by means of maximal deviation inequalities in low probability regions. Beyond theoretical results, numerical experiments are presented in order to illustrate the relevance of the approach developed.

Inverse reinforcement learning (IRL) attempts to infer human rewards or preferences from observed behavior. Since human planning systematically deviates from rationality, several approaches have been tried to account for specific human shortcomings. However, the general problem of inferring the reward function of an agent of unknown rationality has received little attention. Unlike the well-known ambiguity problems in IRL, this one is practically relevant but cannot be resolved by observing the agent's policy in enough environments. This paper shows (1) that a No Free Lunch result implies it is impossible to uniquely decompose a policy into a planning algorithm and reward function, and (2) that even with a reasonable simplicity prior/Occam's razor on the set of decompositions, we cannot distinguish between the true decomposition and others that lead to high regret. To address this, we need simple `normative' assumptions, which cannot be deduced exclusively from observations.

Inferring directional couplings from the spike data of networks is desired in various scientific fields such as neuroscience. Here, we apply a recently proposed objective procedure to the spike data obtained from the Hodgkin-Huxley type models and in vitro neuronal networks cultured in a circular structure. As a result, we succeed in reconstructing synaptic connections accurately from the evoked activity as well as the spontaneous one. To obtain the results, we invent an analytic formula approximately implementing a method of screening relevant couplings. This significantly reduces the computational cost of the screening method employed in the proposed objective procedure, making it possible to treat large-size systems as in this study.

Generalization has been one of the major challenges for learning dynamics models in model-based reinforcement learning. However, previous work on action-conditioned dynamics prediction focuses on learning the pixel-level motion and thus does not generalize well to novel environments with different object layouts. In this paper, we present a novel object-oriented framework, called object-oriented dynamics predictor (OODP), which decomposes the environment into objects and predicts the dynamics of objects conditioned on both actions and object-to-object relations. It is an end-to-end neural network and can be trained in an unsupervised manner. To enable the generalization ability of dynamics learning, we design a novel CNN-based relation mechanism that is class-specific (rather than object-specific) and exploits the locality principle. Empirical results show that OODP significantly outperforms previous methods in terms of generalization over novel environments with various object layouts. OODP is able to learn from very few environments and accurately predict dynamics in a large number of unseen environments. In addition, OODP learns semantically and visually interpretable dynamics models.

Neyshabur and Srebro proposed SIMPLE-LSH, which is the state-of-the-art hashing based algorithm for maximum inner product search (MIPS). We found that the performance of SIMPLE-LSH, in both theory and practice, suffers from long tails in the 2-norm distribution of real datasets. We propose NORM-RANGING LSH, which addresses the excessive normalization problem caused by long tails by partitioning a dataset into sub-datasets and building a hash index for each sub-dataset independently. We prove that NORM-RANGING LSH achieves lower query time complexity than SIMPLE-LSH under mild conditions. We also show that the idea of dataset partitioning can improve another hashing based MIPS algorithm. Experiments show that NORM-RANGING LSH probes much less items than SIMPLE-LSH at the same recall, thus significantly benefiting MIPS based applications.

Bayesian learning is built on an assumption that the model space contains a true reflection of the data generating mechanism. This assumption is problematic, particularly in complex data environments. Here we present a Bayesian nonparametric approach to learning that makes use of statistical models, but does not assume that the model is true. Our approach has provably better properties than using a parametric model and admits a Monte Carlo sampling scheme that can afford massive scalability on modern computer architectures. The model-based aspect of learning is particularly attractive for regularizing nonparametric inference when the sample size is small, and also for correcting approximate approaches such as variational Bayes (VB). We demonstrate the approach on a number of examples including VB classifiers and Bayesian random forests.

We study minimax convergence rates of nonparametric density estimation under a large class of loss functions called ``adversarial losses'', which, besides classical L^p losses, includes maximum mean discrepancy (MMD), Wasserstein distance, and total variation distance. These losses are closely related to the losses encoded by discriminator networks in generative adversarial networks (GANs). In a general framework, we study how the choice of loss and the assumed smoothness of the underlying density together determine the minimax rate. We also discuss implications for training GANs based on deep ReLU networks, and more general connections to learning implicit generative models in a minimax statistical sense.

We propose Lomax delegate racing (LDR) to explicitly model the mechanism of survival under competing risks and to interpret how the covariates accelerate or decelerate the time to event. LDR explains non-monotonic covariate effects by racing a potentially infinite number of sub-risks, and consequently relaxes the ubiquitous proportional-hazards assumption which may be too restrictive. Moreover, LDR is naturally able to model not only censoring, but also missing event times or event types. For inference, we develop a Gibbs sampler under data augmentation for moderately sized data, along with a stochastic gradient descent maximum a posteriori inference algorithm for big data applications. Illustrative experiments are provided on both synthetic and real datasets, and comparison with various benchmark algorithms for survival analysis with competing risks demonstrates distinguished performance of LDR.

Nonlocal neural networks have been proposed and shown to be effective in several computer vision tasks, where the nonlocal operations can directly capture long-range dependencies in the feature space. In this paper, we study the nature of diffusion and damping effect of nonlocal networks by doing spectrum analysis on the weight matrices of the well-trained networks, and then propose a new formulation of the nonlocal block. The new block not only learns the nonlocal interactions but also has stable dynamics, thus allowing deeper nonlocal structures. Moreover, we interpret our formulation from the general nonlocal modeling perspective, where we make connections between the proposed nonlocal network and other nonlocal models, such as nonlocal diffusion process and Markov jump process.

In this paper we consider parallelization for applications whose objective can be expressed as maximizing a non-monotone submodular function under a cardinality constraint. Our main result is an algorithm whose approximation is arbitrarily close to 1/2e in O(log^2 n) adaptive rounds, where n is the size of the ground set. This is an exponential speedup in parallel running time over any previously studied algorithm for constrained non-monotone submodular maximization. Beyond its provable guarantees, the algorithm performs well in practice. Specifically, experiments on traffic monitoring and personalized data summarization applications show that the algorithm finds solutions whose values are competitive with state-of-the-art algorithms while running in exponentially fewer parallel iterations.