NeurIPS 2017 Papers

Adversarial training has proved to be competitive against supervised learning methods on computer vision tasks. However, studies have mainly been confined to generative tasks such as image synthesis. In this paper, we apply adversarial training techniques to the discriminative task of learning a steganographic algorithm. Steganography is a collection of techniques for concealing the existence of information by embedding it within a non-secret medium, such as cover texts or images. We show that adversarial training can produce robust steganographic techniques: our unsupervised training scheme produces a steganographic algorithm that competes with state-of-the-art steganographic techniques. We also show that supervised training of our adversarial model produces a robust steganalyzer, which performs the discriminative task of deciding if an image contains secret information. We define a game between three parties, Alice, Bob and Eve, in order to simultaneously train both a steganographic algorithm and a steganalyzer. Alice and Bob attempt to communicate a secret message contained within an image, while Eve eavesdrops on their conversation and attempts to determine if secret information is embedded within the image. We represent Alice, Bob and Eve by neural networks, and validate our scheme on two independent image datasets, showing our novel method of studying steganographic problems is surprisingly competitive against established steganographic techniques.

Recently, a new class of machine learning algorithms has emerged, where models and discriminators are generated in a competitive setting. The most prominent example is Generative Adversarial Networks (GANs). In this paper we examine how these algorithms relate to the Turing test, and derive what - from a Turing perspective - can be considered their defining features. Based on these features, we outline directions for generalizing GANs - resulting in the family of algorithms referred to as Turing Learning. One such direction is to allow the discriminators to interact with the processes from which the data samples are obtained, making them "interrogators", as in the Turing test. We validate this idea using two case studies. In the first case study, a computer infers the behavior of an agent while controlling its environment. In the second case study, a robot infers its own sensor configuration while controlling its movements. The results confirm that by allowing discriminators to interrogate, the accuracy of models is improved.

Estimation in generalized linear models (GLM) is complicated by the presence of constraints. One can handle constraints by maximizing a penalized log-likelihood. Penalties such as the lasso are effective in high dimensions but often lead to severe shrinkage. This paper explores instead penalizing the squared distance to constraint sets. Distance penalties are more flexible than algebraic and regularization penalties, and avoid the drawback of shrinkage. To optimize distance penalized objectives, we make use of the majorization-minimization principle. Resulting algorithms constructed within this framework are amenable to acceleration and come with global convergence guarantees. Applications to shape constraints, sparse regression, and rank-restricted matrix regression on synthetic and real data showcase the strong empirical performance of distance penalization, even under non-convex constraints.

We study the generalization properties of ridge regression with random features in the statistical learning framework. We show for the first time that $O(1/\sqrt{n})$ learning bounds can be achieved with only $O(\sqrt{n}\log n)$ random features rather than $O({n})$ as suggested by previous results. Further, we prove faster learning rates and show that they might require more random features, unless they are sampled according to a possibly problem dependent distribution. Our results shed light on the statistical computational trade-offs in large scale kernelized learning, showing the potential effectiveness of random features in reducing the computational complexity while keeping optimal generalization properties.

A large body of recent work focuses on methods for extracting low-dimensional latent structure from multi-neuron spike train data. Most such methods employ either linear latent dynamics or linear mappings from latent space to log spike rates. Here we propose a doubly nonlinear latent variable model that can identify low-dimensional structure underlying apparently high-dimensional spike train data. We introduce the Poisson Gaussian-Process Latent Variable Model (P-GPLVM), which consists of Poisson spiking observations and two underlying Gaussian processes—one governing a temporal latent variable and another governing a set of nonlinear tuning curves. The use of nonlinear tuning curves enables discovery of low-dimensional latent structure even when spike responses exhibit high linear dimensionality (e.g., as found in hippocampal place cell codes). To learn the model from data, we introduce the decoupled Laplace approximation, a fast approximate inference method that allows us to efficiently optimize the latent path while marginalizing over tuning curves. We show that this method outperforms previous Laplace-approximation-based inference methods in both the speed of convergence and accuracy. We apply the model to spike trains recorded from hippocampal place cells and show that it compares favorably to a variety of previous methods for latent structure discovery, including variational auto-encoder (VAE) based methods that parametrize the nonlinear mapping from latent space to spike rates with a deep neural network.

Kernel methods have recently attracted resurgent interest, showing performance competitive with deep neural networks in tasks such as speech recognition. The random Fourier features map is a technique commonly used to scale up kernel machines, but employing the randomized feature map means that $O(\epsilon^{-2})$ samples are required to achieve an approximation error of at most $\epsilon$. We investigate some alternative schemes for constructing feature maps that are deterministic, rather than random, by approximating the kernel in the frequency domain using Gaussian quadrature. We show that deterministic feature maps can be constructed, for any $\gamma > 0$, to achieve error $\epsilon$ with $O(e^{e^\gamma} + \epsilon^{-1/\gamma})$ samples as $\epsilon$ goes to 0. Our method works particularly well with sparse ANOVA kernels, which are inspired by the convolutional layer of CNNs. We validate our methods on datasets in different domains, such as MNIST and TIMIT, showing that deterministic features are faster to generate and achieve accuracy comparable to the state-of-the-art kernel methods based on random Fourier features.

Computing partition function is the most important statistical inference task arising in applications of Graphical Models (GM). Since it is computationally intractable, approximate methods have been used in practice, where mean-field (MF) and belief propagation (BP) are arguably the most popular and successful approaches of a variational type. In this paper, we propose two new variational schemes, coined Gauged-MF (G-MF) and Gauged-BP (G-BP), improving MF and BP, respectively. Both provide lower bounds for the partition function by utilizing the so-called gauge transformation which modifies factors of GM while keeping the partition function invariant. Moreover, we prove that both G-MF and G-BP are exact for GMs with a single loop of a special structure, even though the bare MF and BP perform badly in this case. Our extensive experiments indeed confirm that the proposed algorithms outperform and generalize MF and BP.

Optical Character Recognition (OCR) aims to recognize text in natural images. Inspired by a recently proposed model for general image classification, Recurrent Convolution Neural Network (RCNN), we propose a new architecture named Gated RCNN (GRCNN) for solving this problem. Its critical component, Gated Recurrent Convolution Layer (GRCL), is constructed by adding a gate to the Recurrent Convolution Layer (RCL), the critical component of RCNN. The gate controls the context modulation in RCL and balances the feed-forward information and the recurrent information. In addition, an efficient Bidirectional Long Short-Term Memory (BLSTM) is built for sequence modeling. The GRCNN is combined with BLSTM to recognize text in natural images. The entire GRCNN-BLSTM model can be trained end-to-end. Experiments show that the proposed model outperforms existing methods on several benchmark datasets including the IIIT-5K, Street View Text (SVT) and ICDAR.

A fundamental goal in network neuroscience is to understand how activity in one brain region drives activity elsewhere, a process referred to as effective connectivity. Here we propose to model this causal interaction using integro-differential equations and causal kernels that allow for a rich analysis of effective connectivity. The approach combines the tractability and flexibility of autoregressive modeling with the biophysical interpretability of dynamic causal modeling. The causal kernels are learned nonparametrically using Gaussian process regression, yielding an efficient framework for causal inference. We construct a novel class of causal covariance functions that enforce the desired properties of the causal kernels, an approach which we call GP CaKe. By construction, the model and its hyperparameters have biophysical meaning and are therefore easily interpretable. We demonstrate the efficacy of GP CaKe on a number of simulations and give an example of a realistic application on magnetoencephalography (MEG) data.

Generative Adversarial Networks (GANs) excel at creating realistic images with complex models for which maximum likelihood is infeasible. However, the convergence of GAN training has still not been proved. We propose a two time-scale update rule (TTUR) for training GANs with stochastic gradient descent on arbitrary GAN loss functions. TTUR has an individual learning rate for both the discriminator and the generator. Using the theory of stochastic approximation, we prove that the TTUR converges under mild assumptions to a stationary local Nash equilibrium. The convergence carries over to the popular Adam optimization, for which we prove that it follows the dynamics of a heavy ball with friction and thus prefers flat minima in the objective landscape. For the evaluation of the performance of GANs at image generation, we introduce the `Fréchet Inception Distance'' (FID) which captures the similarity of generated images to real ones better than the Inception Score. In experiments, TTUR improves learning for DCGANs and Improved Wasserstein GANs (WGAN-GP) outperforming conventional GAN training on CelebA, CIFAR-10, SVHN, LSUN Bedrooms, and the One Billion Word Benchmark.

Learning cooperative policies for multi-agent systems is often challenged by partial observability and a lack of coordination. In some settings, the structure of a problem allows a distributed solution with limited communication. Here, we consider a scenario where no communication is available, and instead we learn local policies for all agents that collectively mimic the solution to a centralized multi-agent static optimization problem. Our main contribution is an information theoretic framework based on rate distortion theory which facilitates analysis of how well the resulting fully decentralized policies are able to reconstruct the optimal solution. Moreover, this framework provides a natural extension that addresses which nodes an agent should communicate with to improve the performance of its individual policy.

Discovering statistical structure from links is a fundamental problem in the analysis of social networks. Choosing a misspecified model, or equivalently, an incorrect inference algorithm will result in an invalid analysis or even falsely uncover patterns that are in fact artifacts of the model. This work focuses on unifying two of the most widely used link-formation models: the stochastic block model (SBM) and the small world (or latent space) model (SWM). Integrating techniques from kernel learning, spectral graph theory, and nonlinear dimensionality reduction, we develop the first statistically sound polynomial-time algorithm to discover latent patterns in sparse graphs for both models. When the network comes from an SBM, the algorithm outputs a block structure. When it is from an SWM, the algorithm outputs estimates of each node's latent position.

The adoption of automated, data-driven decision making in an ever expanding range of applications has raised concerns about its potential unfairness towards certain social groups. In this context, a number of recent studies have focused on defining, detecting, and removing unfairness from data-driven decision systems. However, the existing notions of fairness, based on parity (equality) in treatment or outcomes for different social groups, tend to be quite stringent, limiting the overall decision making accuracy. In this paper, we draw inspiration from the fair-division and envy-freeness literature in economics and game theory and propose preference-based notions of fairness -- given the choice between various sets of decision treatments or outcomes, any group of users would collectively prefer its treatment or outcomes, regardless of the (dis)parity as compared to the other groups. Then, we introduce tractable proxies to design margin-based classifiers that satisfy these preference-based notions of fairness. Finally, we experiment with a variety of synthetic and real-world datasets and show that preference-based fairness allows for greater decision accuracy than parity-based fairness.

The iterations of many first-order algorithms, when applied to minimizing common regularized regression functions, often resemble neural network layers with pre-specified weights. This observation has prompted the development of learning-based approaches that purport to replace these iterations with enhanced surrogates forged as DNN models from available training data. For example, important NP-hard sparse estimation problems have recently benefitted from this genre of upgrade, with simple feedforward or recurrent networks ousting proximal gradient-based iterations. Analogously, this paper demonstrates that more powerful Bayesian algorithms for promoting sparsity, which rely on complex multi-loop majorization-minimization techniques, mirror the structure of more sophisticated long short-term memory (LSTM) networks, or alternative gated feedback networks previously designed for sequence prediction. As part of this development, we examine the parallels between latent variable trajectories operating across multiple time-scales during optimization, and the activations within deep network structures designed to adaptively model such characteristic sequences. The resulting insights lead to a novel sparse estimation system that, when granted training data, can estimate optimal solutions efficiently in regimes where other algorithms fail, including practical direction-of-arrival (DOA) and 3D geometry recovery problems. The underlying principles we expose are also suggestive of a learning process for a richer class of multi-loop algorithms in other domains.

Recent work has shown that state-of-the-art classifiers are quite brittle, in the sense that a small adversarial change of an originally with high confidence correctly classified input leads to a wrong classification again with high confidence. This raises concerns that such classifiers are vulnerable to attacks and calls into question their usage in safety-critical systems. We show in this paper for the first time formal guarantees on the robustness of a classifier by giving instance-specific \emph{lower bounds} on the norm of the input manipulation required to change the classifier decision. Based on this analysis we propose the Cross-Lipschitz regularization functional. We show that using this form of regularization in kernel methods resp. neural networks improves the robustness of the classifier without any loss in prediction performance.

Deep neural networks are commonly developed and trained in 32-bit floating point format. Significant gains in performance and energy efficiency could be realized by training and inference in numerical formats optimized for deep learning. Despite advances in limited precision inference in recent years, training of neural networks in low bit-width remains a challenging problem. Here we present the Flexpoint data format, aiming at a complete replacement of 32-bit floating point format training and inference, designed to support modern deep network topologies without modifications. Flexpoint tensors have a shared exponent that is dynamically adjusted to minimize overflows and maximize available dynamic range. We validate Flexpoint by training AlexNet, a deep residual network and a generative adversarial network, using a simulator implemented with the \emph{neon} deep learning framework. We demonstrate that 16-bit Flexpoint closely matches 32-bit floating point in training all three models, without any need for tuning of model hyperparameters. Our results suggest Flexpoint as a promising numerical format for future hardware for training and inference.

Mechanistic models of single-neuron dynamics have been extensively studied in computational neuroscience. However, identifying which models can quantitatively reproduce empirically measured data has been challenging. We propose to overcome this limitation by using likelihood-free inference approaches (also known as Approximate Bayesian Computation, ABC) to perform full Bayesian inference on single-neuron models. Our approach builds on recent advances in ABC by learning a neural network which maps features of the observed data to the posterior distribution over parameters. We learn a Bayesian mixture-density network approximating the posterior over multiple rounds of adaptively chosen simulations. Furthermore, we propose an efficient approach for handling missing features and parameter settings for which the simulator fails, as well as a strategy for automatically learning relevant features using recurrent neural networks. On synthetic data, our approach efficiently estimates posterior distributions and recovers ground-truth parameters. On in-vitro recordings of membrane voltages, we recover multivariate posteriors over biophysical parameters, which yield model-predicted voltage traces that accurately match empirical data. Our approach will enable neuroscientists to perform Bayesian inference on complex neuron models without having to design model-specific algorithms, closing the gap between mechanistic and statistical approaches to single-neuron modelling.

Several important applications, such as streaming PCA and semidefinite programming, involve a large-scale positive-semidefinite (psd) matrix that is presented as a sequence of linear updates. Because of storage limitations, it may only be possible to retain a sketch of the psd matrix. This paper develops a new algorithm for fixed-rank psd approximation from a sketch. The approach combines the Nyström approximation with a novel mechanism for rank truncation. Theoretical analysis establishes that the proposed method can achieve any prescribed relative error in the Schatten 1-norm and that it exploits the spectral decay of the input matrix. Computer experiments show that the proposed method dominates alternative techniques for fixed-rank psd matrix approximation across a wide range of examples.

In this paper, we develop an algorithm that approximates the residual error of Tucker decomposition, one of the most popular tensor decomposition methods, with a provable guarantee. Given an order-$K$ tensor $X\in\mathbb{R}^{N_1\times\cdots\times N_K}$, our algorithm randomly samples a constant number $s$ of indices for each mode and creates a ``mini'' tensor $\tilde{X}\in\mathbb{R}^{s\times\cdots\times s}$, whose elements are given by the intersection of the sampled indices on $X$. Then, we show that the residual error of the Tucker decomposition of $\tilde{X}$ is sufficiently close to that of $X$ with high probability. This result implies that we can figure out how much we can fit a low-rank tensor to $X$ \emph{in constant time}, regardless of the size of $X$. This is useful for guessing the favorable rank of Tucker decomposition. Finally, we demonstrate how the sampling method works quickly and accurately using multiple real datasets.