NeurIPS 2019 Papers

Segmentation algorithms are prone to make topological errors on fine-scale struc- tures, e.g., broken connections. We propose a novel method that learns to segment with correct topology. In particular, we design a continuous-valued loss function that enforces a segmentation to have the same topology as the ground truth, i.e.,having the same Betti number. The proposed topology-preserving loss function is differentiable and can be incorporated into end-to-end training of a deep neural network. Our method achieves much better performance on the Betti number error, which directly accounts for the topological correctness. It also performs superior on other topology-relevant metrics, e.g., the Adjusted Rand Index and the Variation of Information, without sacrificing per-pixel accuracy. We illustrate the effectiveness of the proposed method on a broad spectrum of natural and biomedical datasets.

We consider the problem of computing the best-fitting ReLU with respect to square-loss on a training set when the examples have been drawn according to a spherical Gaussian distribution (the labels can be arbitrary). Let $\opt < 1$ be the population loss of the best-fitting ReLU. We prove: \begin{itemize} \item Finding a ReLU with square-loss $\opt + \epsilon$ is as hard as the problem of learning sparse parities with noise, widely thought to be computationally intractable. This is the first hardness result for learning a ReLU with respect to Gaussian marginals, and our results imply --{\em unconditionally}-- that gradient descent cannot converge to the global minimum in polynomial time. \item There exists an efficient approximation algorithm for finding the best-fitting ReLU that achieves error $O(\opt^{2/3})$. The algorithm uses a novel reduction to noisy halfspace learning with respect to $0/1$ loss. \end{itemize} Prior work due to Soltanolkotabi \cite{soltanolkotabi2017learning} showed that gradient descent {\em can} find the best-fitting ReLU with respect to Gaussian marginals, if the training set is {\em exactly} labeled by a ReLU.

A good generative model for time-series data should preserve temporal dynamics, in the sense that new sequences respect the original relationships between variables across time. Existing methods that bring generative adversarial networks (GANs) into the sequential setting do not adequately attend to the temporal correlations unique to time-series data. At the same time, supervised models for sequence prediction - which allow finer control over network dynamics - are inherently deterministic. We propose a novel framework for generating realistic time-series data that combines the flexibility of the unsupervised paradigm with the control afforded by supervised training. Through a learned embedding space jointly optimized with both supervised and adversarial objectives, we encourage the network to adhere to the dynamics of the training data during sampling. Empirically, we evaluate the ability of our method to generate realistic samples using a variety of real and synthetic time-series datasets. Qualitatively and quantitatively, we find that the proposed framework consistently and significantly outperforms state-of-the-art benchmarks with respect to measures of similarity and predictive ability.

Regularization is typically understood as improving generalization by altering the landscape of local extrema to which the model eventually converges. Deep neural networks (DNNs), however, challenge this view: We show that removing regularization after an initial transient period has little effect on generalization, even if the final loss landscape is the same as if there had been no regularization. In some cases, generalization even improves after interrupting regularization. Conversely, if regularization is applied only after the initial transient, it has no effect on the final solution, whose generalization gap is as bad as if regularization never happened. This suggests that what matters for training deep networks is not just whether or how, but when to regularize. The phenomena we observe are manifest in different datasets (CIFAR-10, CIFAR-100, SVHN, ImageNet), different architectures (ResNet-18, All-CNN), different regularization methods (weight decay, data augmentation, mixup), different learning rate schedules (exponential, piece-wise constant). They collectively suggest that there is a "critical period'' for regularizing deep networks that is decisive of the final performance. More analysis should, therefore, focus on the transient rather than asymptotic behavior of learning.

We study the sample complexity of learning one-hidden-layer convolutional neural networks (CNNs) with non-overlapping filters. We propose a novel algorithm called approximate gradient descent for training CNNs, and show that, with high probability, the proposed algorithm with random initialization grants a linear convergence to the ground-truth parameters up to statistical precision. Compared with existing work, our result applies to general non-trivial, monotonic and Lipschitz continuous activation functions including ReLU, Leaky ReLU, Sigmod and Softplus etc. Moreover, our sample complexity beats existing results in the dependency of the number of hidden nodes and filter size. In fact, our result matches the information-theoretic lower bound for learning one-hidden-layer CNNs with linear activation functions, suggesting that our sample complexity is tight. Our theoretical analysis is backed up by numerical experiments.

State-of-the-art efficient model-based Reinforcement Learning (RL) algorithms typically act by iteratively solving empirical models, i.e., by performing full-planning on Markov Decision Processes (MDPs) built by the gathered experience. In this paper, we focus on model-based RL in the finite-state finite-horizon MDP setting and establish that exploring with greedy policies -- act by 1-step planning -- can achieve tight minimax performance in terms of regret, O(\sqrt{HSAT}). Thus, full-planning in model-based RL can be avoided altogether without any performance degradation, and, by doing so, the computational complexity decreases by a factor of S. The results are based on a novel analysis of real-time dynamic programming, then extended to model-based RL. Specifically, we generalize existing algorithms that perform full-planning to such that act by 1-step planning. For these generalizations, we prove regret bounds with the same rate as their full-planning counterparts.

We revisit the classic randomized sketch of a tensor product of $q$ vectors $x_i\in\mathbb{R}^n$. The $i$-th coordinate $(Sx)_i$ of the sketch is equal to $\prod_{j = 1}^q \langle u^{i, j}, x^j \rangle / \sqrt{m}$, where $u^{i,j}$ are independent random sign vectors. Kar and Karnick (JMLR, 2012) show that if the sketching dimension $m = \Omega(\epsilon^{-2} C_{\Omega}^2 \log (1/\delta))$, where $C_{\Omega}$ is a certain property of the point set $\Omega$ one wants to sketch, then with probability $1-\delta$, $\|Sx\|_2 = (1\pm \epsilon)\|x\|_2$ for all $x\in\Omega$. However, in their analysis $C_{\Omega}^2$ can be as large as $\Theta(n^{2q})$, even for a set $\Omega$ of $O(1)$ vectors $x$. We give a new analysis of this sketch, providing nearly optimal bounds. Namely, we show an upper bound of $m = \Theta \left (\epsilon^{-2} \log(n/\delta) + \epsilon^{-1} \log^q(n/\delta) \right ),$ which by composing with CountSketch, can be improved to $\Theta(\epsilon^{-2}\log(1/(\delta \epsilon)) + \epsilon^{-1} \log^q (1/(\delta \epsilon))$. For the important case of $q = 2$ and $\delta = 1/\poly(n)$, this shows that $m = \Theta(\epsilon^{-2} \log(n) + \epsilon^{-1} \log^2(n))$, demonstrating that the $\epsilon^{-2}$ and $\log^2(n)$ terms do not multiply each other. We also show a nearly matching lower bound of $m = \Omega(\eps^{-2} \log(1/(\delta)) + \eps^{-1} \log^q(1/(\delta)))$. In a number of applications, one has $|\Omega| = \poly(n)$ and in this case our bounds are optimal up to a constant factor. This is the first high probability sketch for tensor products that has optimal sketch size and can be implemented in $m \cdot \sum_{i=1}^q \textrm{nnz}(x_i)$ time, where $\textrm{nnz}(x_i)$ is the number of non-zero entries of $x_i$. Lastly, we empirically compare our sketch to other sketches for tensor products, and give a novel application to compressing neural networks.

We study the convergence of Stochastic Gradient Descent (SGD) for strongly convex objective functions. We prove for all $t$ a lower bound on the expected convergence rate after the $t$-th SGD iteration; the lower bound is over all possible sequences of diminishing step sizes. It implies that recently proposed sequences of step sizes at ICML 2018 and ICML 2019 are {\em universally} close to optimal in that the expected convergence rate after {\em each} iteration is within a factor $32$ of our lower bound. This factor is independent of dimension $d$. We offer a framework for comparing with lower bounds in state-of-the-art literature and when applied to SGD for strongly convex objective functions our lower bound is a significant factor $775\cdot d$ larger compared to existing work.

Strong theoretical guarantees of robustness can be given for ensembles of classifiers generated by input randomization. Specifically, an $\ell_2$ bounded adversary cannot alter the ensemble prediction generated by an additive isotropic Gaussian noise, where the radius for the adversary depends on both the variance of the distribution as well as the ensemble margin at the point of interest. We build on and considerably expand this work across broad classes of distributions. In particular, we offer adversarial robustness guarantees and associated algorithms for the discrete case where the adversary is $\ell_0$ bounded. Moreover, we exemplify how the guarantees can be tightened with specific assumptions about the function class of the classifier such as a decision tree. We empirically illustrate these results with and without functional restrictions across image and molecule datasets.

We consider the thresholding bandit problem, whose goal is to find arms of mean rewards above a given threshold $\theta$, with a fixed budget of $T$ trials. We introduce LSA, a new, simple and anytime algorithm that aims to minimize the aggregate regret (or the expected number of mis-classified arms). We prove that our algorithm is instance-wise asymptotically optimal. We also provide comprehensive empirical results to demonstrate the algorithm's superior performance over existing algorithms under a variety of different scenarios.

We consider a finite-horizon multi-armed bandit (MAB) problem in a Bayesian setting, for which we propose an information relaxation sampling framework. With this framework, we define an intuitive family of control policies that include Thompson sampling (TS) and the Bayesian optimal policy as endpoints. Analogous to TS, which, at each decision epoch pulls an arm that is best with respect to the randomly sampled parameters, our algorithms sample entire future reward realizations and take the corresponding best action. However, this is done in the presence of “penalties” that seek to compensate for the availability of future information.

We consider a dynamic assortment selection problem where the goal is to offer a sequence of assortments that maximizes the expected cumulative revenue, or alternatively, minimize the expected regret. The feedback here is the item that the user picks from the assortment. The distinguishing feature in this work is that this feedback has a multinomial logistic distribution. The utility of each item is a dynamic function of contextual information of both the item and the user. We propose two Thompson sampling algorithms for this multinomial logit contextual bandit. Our first algorithm maintains a posterior distribution of the true parameter and establishes $\tilde{O}(d\sqrt{T})$ Bayesian regret over $T$ rounds with $d$ dimensional context vector. The worst-case computational complexity of this algorithm could be high when the prior distribution is not a conjugate. The second algorithm approximates the posterior by a Gaussian distribution, and uses a new optimistic sampling procedure to address the issues that arise in worst-case regret analysis. This algorithm achieves $\tilde{O}(d^{3/2}\sqrt{T})$ worst-case (frequentist) regret bound. The numerical experiments show that the practical performance of both methods is in line with the theoretical guarantees.

We study the effects of approximate inference on the performance of Thompson sampling in the $k$-armed bandit problems. Thompson sampling is a successful algorithm for online decision-making but requires posterior inference, which often must be approximated in practice. We show that even small constant inference error (in $\alpha$-divergence) can lead to poor performance (linear regret) due to under-exploration (for $\alpha<1$) or over-exploration (for $\alpha>0$) by the approximation. While for $\alpha > 0$ this is unavoidable, for $\alpha \leq 0$ the regret can be improved by adding a small amount of forced exploration even when the inference error is a large constant.

When we are faced with challenging image classification tasks, we often explain our reasoning by dissecting the image, and pointing out prototypical aspects of one class or another. The mounting evidence for each of the classes helps us make our final decision. In this work, we introduce a deep network architecture -- prototypical part network (ProtoPNet), that reasons in a similar way: the network dissects the image by finding prototypical parts, and combines evidence from the prototypes to make a final classification. The model thus reasons in a way that is qualitatively similar to the way ornithologists, physicians, and others would explain to people on how to solve challenging image classification tasks. The network uses only image-level labels for training without any annotations for parts of images. We demonstrate our method on the CUB-200-2011 dataset and the Stanford Cars dataset. Our experiments show that ProtoPNet can achieve comparable accuracy with its analogous non-interpretable counterpart, and when several ProtoPNets are combined into a larger network, it can achieve an accuracy that is on par with some of the best-performing deep models. Moreover, ProtoPNet provides a level of interpretability that is absent in other interpretable deep models.

We study a generalized setup for learning from demonstration to build an agent that can manipulate novel objects in unseen scenarios by looking at only a single video of human demonstration from a third-person perspective. To accomplish this goal, our agent should not only learn to understand the intent of the demonstrated third-person video in its context but also perform the intended task in its environment configuration. Our central insight is to enforce this structure explicitly during learning by decoupling what to achieve (intended task) from how to perform it (controller). We propose a hierarchical setup where a high-level module learns to generate a series of first-person sub-goals conditioned on the third-person video demonstration, and a low-level controller predicts the actions to achieve those sub-goals. Our agent acts from raw image observations without any access to the full state information. We show results on a real robotic platform using Baxter for the manipulation tasks of pouring and placing objects in a box. Project video is available at https://pathak22.github.io/hierarchical-imitation/

This paper discusses one of the most fundamental issues about point processes that what is the best sampling method for point processes. We propose \textit{thinning} as a downsampling method for accelerating the learning of point processes. We find that the thinning operation preserves the structure of intensity, and is able to estimate parameters with less time and without much loss of accuracy. Theoretical results including intensity, parameter and gradient estimation on a thinned history are presented for point processes with decouplable intensities. A stochastic optimization algorithm based on the thinned gradient is proposed. Experimental results on synthetic and real-world datasets validate the effectiveness of thinning in the tasks of parameter and gradient estimation, as well as stochastic optimization.

We present two new algorithms, ASYNCADA and HEDGEHOG, for asynchronous sparse online and stochastic optimization. ASYNCADA is, to our knowledge, the first asynchronous stochastic optimization algorithm with finite-time data-dependent convergence guarantees for generic convex constraints. In addition, ASYNCADA: (a) allows for proximal (i.e., composite-objective) updates and adaptive step-sizes; (b) enjoys any-time convergence guarantees without requiring an exact global clock; and (c) when the data is sufficiently sparse, its convergence rate for (non-)smooth, (non-)strongly-convex, and even a limited class of non-convex objectives matches the corresponding serial rate, implying a theoretical “linear speed-up”. The second algorithm, HEDGEHOG, is an asynchronous parallel version of the Exponentiated Gradient (EG) algorithm for optimization over the probability simplex (a.k.a. Hedge in online learning), and, to our knowledge, the first asynchronous algorithm enjoying linear speed-ups under sparsity with non-SGD-style updates. Unlike previous work, ASYNCADA and HEDGEHOG and their convergence and speed-up analyses are not limited to individual coordinate-wise (i.e., “box-shaped”) constraints or smooth and strongly-convex objectives. Underlying both results is a generic analysis framework that is of independent interest, and further applicable to distributed and delayed feedback optimization

Forecasting high-dimensional time series plays a crucial role in many applications such as demand forecasting and financial predictions. Modern datasets can have millions of correlated time-series that evolve together, i.e they are extremely high dimensional (one dimension for each individual time-series). There is a need for exploiting global patterns and coupling them with local calibration for better prediction. However, most recent deep learning approaches in the literature are one-dimensional, i.e, even though they are trained on the whole dataset, during prediction, the future forecast for a single dimension mainly depends on past values from the same dimension. In this paper, we seek to correct this deficiency and propose DeepGLO, a deep forecasting model which thinks globally and acts locally. In particular, DeepGLO is a hybrid model that combines a global matrix factorization model regularized by a temporal convolution network, along with another temporal network that can capture local properties of each time-series and associated covariates. Our model can be trained effectively on high-dimensional but diverse time series, where different time series can have vastly different scales, without a priori normalization or rescaling. Empirical results demonstrate that DeepGLO can outperform state-of-the-art approaches; for example, we see more than 25% improvement in WAPE over other methods on a public dataset that contains more than 100K-dimensional time series.

This paper investigates the theory of robustness against adversarial attacks. It focuses on the family of randomization techniques that consist in injecting noise in the network at inference time. These techniques have proven effective in many contexts, but lack theoretical arguments. We close this gap by presenting a theo- retical analysis of these approaches, hence explaining why they perform well in practice. More precisely, we make two new contributions. The first one relates the randomization rate to robustness to adversarial attacks. This result applies for the general family of exponential distributions, and thus extends and unifies the previous approaches. The second contribution consists in devising a new upper bound on the adversarial risk gap of randomized neural networks. We support our theoretical claims with a set of experiments.