NeurIPS 2017 Papers

Density ratio estimation is a vital tool in both machine learning and statistical community. However, due to the unbounded nature of density ratio, the estimation proceudre can be vulnerable to corrupted data points, which often pushes the estimated ratio toward infinity. In this paper, we present a robust estimator which automatically identifies and trims outliers. The proposed estimator has a convex formulation, and the global optimum can be obtained via subgradient descent. We analyze the parameter estimation error of this estimator under high-dimensional settings. Experiments are conducted to verify the effectiveness of the estimator.

A Triangle Generative Adversarial Network ($\Delta$-GAN) is developed for semi-supervised cross-domain joint distribution matching, where the training data consists of samples from each domain, and supervision of domain correspondence is provided by only a few paired samples. $\Delta$-GAN consists of four neural networks, two generators and two discriminators. The generators are designed to learn the two-way conditional distributions between the two domains, while the discriminators implicitly define a ternary discriminative function, which is trained to distinguish real data pairs and two kinds of fake data pairs. The generators and discriminators are trained together using adversarial learning. Under mild assumptions, in theory the joint distributions characterized by the two generators concentrate to the data distribution. In experiments, three different kinds of domain pairs are considered, image-label, image-image and image-attribute pairs. Experiments on semi-supervised image classification, image-to-image translation and attribute-based image generation demonstrate the superiority of the proposed approach.

In this paper, we introduce a robust algorithm, \textsl{TranSync}, for the 1D translation synchronization problem, in which the aim is to recover the global coordinates of a set of nodes from noisy measurements of relative coordinates along an observation graph. The basic idea of TranSync is to apply truncated least squares, where the solution at each step is used to gradually prune out noisy measurements. We analyze TranSync under both deterministic and randomized noisy models, demonstrating its robustness and stability. Experimental results on synthetic and real datasets show that TranSync is superior to state-of-the-art convex formulations in terms of both efficiency and accuracy.

Self-localization during navigation with noisy sensors in an ambiguous world is computationally challenging, yet animals and humans excel at it. In robotics, {\em Simultaneous Location and Mapping} (SLAM) algorithms solve this problem through joint sequential probabilistic inference of their own coordinates and those of external spatial landmarks. We generate the first neural solution to the SLAM problem by training recurrent LSTM networks to perform a set of hard 2D navigation tasks that require generalization to completely novel trajectories and environments. Our goal is to make sense of how the diverse phenomenology in the brain's spatial navigation circuits is related to their function. We show that the hidden unit representations exhibit several key properties of hippocampal place cells, including stable tuning curves that remap between environments. Our result is also a proof of concept for end-to-end-learning of a SLAM algorithm using recurrent networks, and a demonstration of why this approach may have some advantages for robotic SLAM.

Currently, deep neural networks are deployed on low-power portable devices by first training a full-precision model using powerful hardware, and then deriving a corresponding low-precision model for efficient inference on such systems. However, training models directly with coarsely quantized weights is a key step towards learning on embedded platforms that have limited computing resources, memory capacity, and power consumption. Numerous recent publications have studied methods for training quantized networks, but these studies have mostly been empirical. In this work, we investigate training methods for quantized neural networks from a theoretical viewpoint. We first explore accuracy guarantees for training methods under convexity assumptions. We then look at the behavior of these algorithms for non-convex problems, and show that training algorithms that exploit high-precision representations have an important greedy search phase that purely quantized training methods lack, which explains the difficulty of training using low-precision arithmetic.

Deep learning methods achieve state-of-the-art performance in many application scenarios. Yet, these methods require a significant amount of hyperparameters tuning in order to achieve the best results. In particular, tuning the learning rates in the stochastic optimization process is still one of the main bottlenecks. In this paper, we propose a new stochastic gradient descent procedure for deep networks that does not require any learning rate setting. Contrary to previous methods, we do not adapt the learning rates nor we make use of the assumed curvature of the objective function. Instead, we reduce the optimization process to a game of betting on a coin and propose a learning rate free optimal algorithm for this scenario. Theoretical convergence is proven for convex and quasi-convex functions and empirical evidence shows the advantage of our algorithm over popular stochastic gradient algorithms.

Background: Deep learning models are typically trained using stochastic gradient descent or one of its variants. These methods update the weights using their gradient, estimated from a small fraction of the training data. It has been observed that when using large batch sizes there is a persistent degradation in generalization performance - known as the "generalization gap" phenomenon. Identifying the origin of this gap and closing it had remained an open problem. Contributions: We examine the initial high learning rate training phase. We find that the weight distance from its initialization grows logarithmically with the number of weight updates. We therefore propose a "random walk on a random landscape" statistical model which is known to exhibit similar "ultra-slow" diffusion behavior. Following this hypothesis we conducted experiments to show empirically that the "generalization gap" stems from the relatively small number of updates rather than the batch size, and can be completely eliminated by adapting the training regime used. We further investigate different techniques to train models in the large-batch regime and present a novel algorithm named "Ghost Batch Normalization" which enables significant decrease in the generalization gap without increasing the number of updates. To validate our findings we conduct several additional experiments on MNIST, CIFAR-10, CIFAR-100 and ImageNet. Finally, we reassess common practices and beliefs concerning training of deep models and suggest they may not be optimal to achieve good generalization.

Recently, the Probabilistic Sentential Decision Diagram (PSDD) has been proposed as a framework for systematically inducing and learning distributions over structured objects, including combinatorial objects such as permutations and rankings, paths and matchings on a graph, etc. In this paper, we study the scalability of such models in the context of representing and learning distributions over routes on a map. In particular, we introduce the notion of a hierarchical route distribution and show how they can be leveraged to construct tractable PSDDs over route distributions, allowing them to scale to larger maps. We illustrate the utility of our model empirically, in a route prediction task, showing how accuracy can be increased significantly compared to Markov models.

The remarkable successes of deep learning in speech recognition and computer vision have motivated efforts to adapt similar techniques to other problem domains, including reinforcement learning (RL). Consequently, RL methods have produced rich motor behaviors on simulated robot tasks, with their success largely attributed to the use of multi-layer neural networks. This work is among the first to carefully study what might be responsible for these recent advancements. Our main result calls this emerging narrative into question by showing that much simpler architectures -- based on linear and RBF parameterizations -- achieve comparable performance to state of the art results. We not only study different policy representations with regard to performance measures at hand, but also towards robustness to external perturbations. We again find that the learned neural network policies --- under the standard training scenarios --- are no more robust than linear (or RBF) policies; in fact, all three are remarkably brittle. Finally, we then directly modify the training scenarios in order to favor more robust policies, and we again do not find a compelling case to favor multi-layer architectures. Overall, this study suggests that multi-layer architectures should not be the default choice, unless a side-by-side comparison to simpler architectures shows otherwise. More generally, we hope that these results lead to more interest in carefully studying the architectural choices, and associated trade-offs, for training generalizable and robust policies.

We introduce a novel scheme to train binary convolutional neural networks (CNNs) -- CNNs with weights and activations constrained to {-1,+1} at run-time. It has been known that using binary weights and activations drastically reduce memory size and accesses, and can replace arithmetic operations with more efficient bitwise operations, leading to much faster test-time inference and lower power consumption. However, previous works on binarizing CNNs usually result in severe prediction accuracy degradation. In this paper, we address this issue with two major innovations: (1) approximating full-precision weights with the linear combination of multiple binary weight bases; (2) employing multiple binary activations to alleviate information loss. The implementation of the resulting binary CNN, denoted as ABC-Net, is shown to achieve much closer performance to its full-precision counterpart, and even reach the comparable prediction accuracy on ImageNet and forest trail datasets, given adequate binary weight bases and activations.

Collecting large training datasets, annotated with high-quality labels, is costly and time-consuming. This paper proposes a novel framework for training deep convolutional neural networks from noisy labeled datasets that can be obtained cheaply. The problem is formulated using an undirected graphical model that represents the relationship between noisy and clean labels, trained in a semi-supervised setting. In our formulation, the inference over latent clean labels is tractable and is regularized during training using auxiliary sources of information. The proposed model is applied to the image labeling problem and is shown to be effective in labeling unseen images as well as reducing label noise in training on CIFAR-10 and MS COCO datasets.

Many image-to-image translation problems are ambiguous, as a single input image may correspond to multiple possible outputs. In this work, we aim to model a distribution of possible outputs in a conditional generative modeling setting. The ambiguity of the mapping is distilled in a low-dimensional latent vector, which can be randomly sampled at test time. A generator learns to map the given input, combined with this latent code, to the output. We explicitly encourage the connection between output and the latent code to be invertible. This helps prevent a many-to-one mapping from the latent code to the output during training, also known as the problem of mode collapse, and produces more diverse results. We explore several variants of this approach by employing different training objectives, network architectures, and methods of injecting the latent code. Our proposed method encourages bijective consistency between the latent encoding and output modes. We present a systematic comparison of our method and other variants on both perceptual realism and diversity.

In large part, rodents “see” the world through their whiskers, a powerful tactile sense enabled by a series of brain areas that form the whisker-trigeminal system. Raw sensory data arrives in the form of mechanical input to the exquisitely sensitive, actively-controllable whisker array, and is processed through a sequence of neural circuits, eventually arriving in cortical regions that communicate with decision making and memory areas. Although a long history of experimental studies has characterized many aspects of these processing stages, the computational operations of the whisker-trigeminal system remain largely unknown. In the present work, we take a goal-driven deep neural network (DNN) approach to modeling these computations. First, we construct a biophysically-realistic model of the rat whisker array. We then generate a large dataset of whisker sweeps across a wide variety of 3D objects in highly-varying poses, angles, and speeds. Next, we train DNNs from several distinct architectural families to solve a shape recognition task in this dataset. Each architectural family represents a structurally-distinct hypothesis for processing in the whisker-trigeminal system, corresponding to different ways in which spatial and temporal information can be integrated. We find that most networks perform poorly on the challenging shape recognition task, but that specific architectures from several families can achieve reasonable performance levels. Finally, we show that Representational Dissimilarity Matrices (RDMs), a tool for comparing population codes between neural systems, can separate these higher performing networks with data of a type that could plausibly be collected in a neurophysiological or imaging experiment. Our results are a proof-of-concept that DNN models of the whisker-trigeminal system are potentially within reach.

The paper addresses the classical network tomography problem of inferring local traffic given origin-destination observations. Focussing on large complex public transportation systems, we build a scalable model that exploits input-output information to estimate the unobserved link/station loads and the users path preferences. Based on the reconstruction of the users' travel time distribution, the model is flexible enough to capture possible different path-choice strategies and correlations between users travelling on similar paths at similar times. The corresponding likelihood function is intractable for medium or large-scale networks and we propose two distinct strategies, namely the exact maximum-likelihood inference of an approximate but tractable model and the variational inference of the original intractable model. As an application of our approach, we consider the emblematic case of the London Underground network, where a tap-in/tap-out system tracks the start/exit time and location of all journeys in a day. A set of synthetic simulations and real data provided by Transport For London are used to validate and test the model on the predictions of observable and unobservable quantities.

In this work, we present an additive model for space-time data that splits the data into a temporally correlated component and a spatially correlated component. We model the spatially correlated portion using a time-varying Gaussian graphical model. Under assumptions on the smoothness of changes in covariance matrices, we derive strong single sample convergence results, confirming our ability to estimate meaningful graphical structures as they evolve over time. We apply our methodology to the discovery of time-varying spatial structures in human brain fMRI signals.

The sparse matrix estimation problem consists of estimating the distribution of an $n\times n$ matrix $Y$, from a sparsely observed single instance of this matrix where the entries of $Y$ are independent random variables. This captures a wide array of problems; special instances include matrix completion in the context of recommendation systems, graphon estimation, and community detection in (mixed membership) stochastic block models. Inspired by classical collaborative filtering for recommendation systems, we propose a novel iterative, collaborative filtering-style algorithm for matrix estimation in this generic setting. We show that the mean squared error (MSE) of our estimator converges to $0$ at the rate of $O(d^2 (pn)^{-2/5})$ as long as $\omega(d^5 n)$ random entries from a total of $n^2$ entries of $Y$ are observed (uniformly sampled), $\E[Y]$ has rank $d$, and the entries of $Y$ have bounded support. The maximum squared error across all entries converges to $0$ with high probability as long as we observe a little more, $\Omega(d^5 n \ln^5(n))$ entries. Our results are the best known sample complexity results in this generality.

Sequential decision making problems, such as structured prediction, robotic control, and game playing, require a combination of planning policies and generalisation of those plans. In this paper, we present Expert Iteration (ExIt), a novel reinforcement learning algorithm which decomposes the problem into separate planning and generalisation tasks. Planning new policies is performed by tree search, while a deep neural network generalises those plans. Subsequently, tree search is improved by using the neural network policy to guide search, increasing the strength of new plans. In contrast, standard deep Reinforcement Learning algorithms rely on a neural network not only to generalise plans, but to discover them too. We show that ExIt outperforms REINFORCE for training a neural network to play the board game Hex, and our final tree search agent, trained tabula rasa, defeats MoHex1.0, the most recent Olympiad Champion player to be publicly released.

Categorical models are a natural fit for many problems. When learning the distribution of categories from samples, high-dimensionality may dilute the data. Minimax optimality is too pessimistic to remedy this issue. A serendipitously discovered estimator, absolute discounting, corrects empirical frequencies by subtracting a constant from observed categories, which it then redistributes among the unobserved. It outperforms classical estimators empirically, and has been used extensively in natural language modeling. In this paper, we rigorously explain the prowess of this estimator using less pessimistic notions. We show that (1) absolute discounting recovers classical minimax KL-risk rates, (2) it is \emph{adaptive} to an effective dimension rather than the true dimension, (3) it is strongly related to the Good-Turing estimator and inherits its \emph{competitive} properties. We use power-law distributions as the cornerstone of these results. We validate the theory via synthetic data and an application to the Global Terrorism Database.

We examine a class of embeddings based on structured random matrices with orthogonal rows which can be applied in many machine learning applications including dimensionality reduction and kernel approximation. For both the Johnson-Lindenstrauss transform and the angular kernel, we show that we can select matrices yielding guaranteed improved performance in accuracy and/or speed compared to earlier methods. We introduce matrices with complex entries which give significant further accuracy improvement. We provide geometric and Markov chain-based perspectives to help understand the benefits, and empirical results which suggest that the approach is helpful in a wider range of applications.