A new form of variational autoencoder (VAE) is developed, in which the joint distribution of data and codes is considered in two (symmetric) forms: (i) from observed data fed through the encoder to yield codes, and (ii) from latent codes drawn from a simple prior and propagated through the decoder to manifest data. Lower bounds are learned for marginal log-likelihood fits observed data and latent codes. When learning with the variational bound, one seeks to minimize the symmetric Kullback-Leibler divergence of joint density functions from (i) and (ii), while simultaneously seeking to maximize the two marginal log-likelihoods. To facilitate learning, a new form of adversarial training is developed. An extensive set of experiments is performed, in which we demonstrate state-of-the-art data reconstruction and generation on several image benchmarks datasets.

Learning latent representations from long text sequences is an important first step in many natural language processing applications. Recurrent Neural Networks (RNNs) have become a cornerstone for this challenging task.

This paper explores image caption generation using conditional variational auto-encoders (CVAEs). Standard CVAEs with a fixed Gaussian prior yield descriptions with too little variability. Instead, we propose two models that explicitly structure the latent space around K components corresponding to different types of image content, and combine components to create priors for images that contain multiple types of content simultaneously (e.g., several kinds of objects). Our first model uses a Gaussian Mixture model (GMM) prior, while the second one defines a novel Additive Gaussian (AG) prior that linearly combines component means. We show that both models produce captions that are more diverse and more accurate than a strong LSTM baseline or a "vanilla" CVAE with a fixed Gaussian prior, with AG-CVAE showing particular promise.

Selective classification techniques (also known as reject option) have not yet been considered in the context of deep neural networks (DNNs). These techniques can potentially significantly improve DNNs prediction performance by trading-off coverage. In this paper we propose a method to construct a selective classifier given a trained neural network. Our method allows a user to set a desired risk level. At test time, the classifier rejects instances as needed, to grant the desired risk (with high probability). Empirical results over CIFAR and ImageNet convincingly demonstrate the viability of our method, which opens up possibilities to operate DNNs in mission-critical applications. For example, using our method an unprecedented 2% error in top-5 ImageNet classification can be guaranteed with probability 99.9%, with almost 60% test coverage.

In machine learning and compressed sensing, it is of central importance to understand when a tractable algorithm recovers the support of a sparse signal from its compressed measurements. In this paper, we present a principled analysis on the support recovery performance for a family of hard thresholding algorithms. To this end, we appeal to the partial hard thresholding (PHT) operator proposed recently by Jain et al. [IEEE Trans.

Thompson sampling has emerged as an effective heuristic for a broad range of online decision problems. In its basic form, the algorithm requires computing and sampling from a posterior distribution over models, which is tractable only for simple special cases. This paper develops ensemble sampling, which aims to approximate Thompson sampling while maintaining tractability even in the face of complex models such as neural networks. Ensemble sampling dramatically expands on the range of applications for which Thompson sampling is viable. We establish a theoretical basis that supports the approach and present computational results that offer further insight.

Universal style transfer aims to transfer arbitrary visual styles to content images. Existing feed-forward based methods, while enjoying the inference efficiency, are mainly limited by inability of generalizing to unseen styles or compromised visual quality. In this paper, we present a simple yet effective method that tackles these limitations without training on any pre-defined styles. The key ingredient of our method is a pair of feature transforms, whitening and coloring, that are embedded to an image reconstruction network. The whitening and coloring transforms reflect direct matching of feature covariance of the content image to a given style image, which shares similar spirits with the optimization of Gram matrix based cost in neural style transfer. We demonstrate the effectiveness of our algorithm by generating high-quality stylized images with comparisons to a number of recent methods. We also analyze our method by visualizing the whitened features and synthesizing textures by simple feature coloring.

Computing optimal transport distances such as the earth mover's distance is a fundamental problem in machine learning, statistics, and computer vision. Despite the recent introduction of several algorithms with good empirical performance, it is unknown whether general optimal transport distances can be approximated in near-linear time. This paper demonstrates that this ambitious goal is in fact achieved by Cuturi's Sinkhorn Distances. This result relies on a new analysis of Sinkhorn iterations, which also directly suggests a new greedy coordinate descent algorithm Greenkhorn with the same theoretical guarantees. Numerical simulations illustrate that Greenkhorn significantly outperforms the classical Sinkhorn algorithm in practice.

We show that the standard stochastic gradient decent (SGD) algorithm is guaranteed to learn, in polynomial time, a function that is competitive with the best function in the conjugate kernel space of the network, as defined in Daniely, Frostig and Singer. The result holds for log-depth networks from a rich family of architectures. To the best of our knowledge, it is the first polynomial-time guarantee for the standard neural network learning algorithm for networks of depth more that two. As corollaries, it follows that for neural networks of any depth between 2 and log(n), SGD is guaranteed to learn, in polynomial time, constant degree polynomials with polynomially bounded coefficients. Likewise, it follows that SGD on large enough networks can learn any continuous function (not in polynomial time), complementing classical expressivity results.

We propose a novel method to {\it directly} learn a stochastic transition operator whose repeated application provides generated samples. Traditional undirected graphical models approach this problem indirectly by learning a Markov chain model whose stationary distribution obeys detailed balance with respect to a parameterized energy function. The energy function is then modified so the model and data distributions match, with no guarantee on the number of steps required for the Markov chain to converge. Moreover, the detailed balance condition is highly restrictive: energy based models corresponding to neural networks must have symmetric weights, unlike biological neural circuits. In contrast, we develop a method for directly learning arbitrarily parameterized transition operators capable of expressing non-equilibrium stationary distributions that violate detailed balance, thereby enabling us to learn more biologically plausible asymmetric neural networks and more general non-energy based dynamical systems. The proposed training objective, which we derive via principled variational methods, encourages the transition operator to walk back (prefer to revert its steps) in multi-step trajectories that start at data-points, as quickly as possible back to the original data points. We present a series of experimental results illustrating the soundness of the proposed approach, Variational Walkback (VW), on the MNIST, CIFAR-10, SVHN and CelebA datasets, demonstrating superior samples compared to earlier attempts to learn a transition operator. We also show that although each rapid training trajectory is limited to a finite but variable number of steps, our transition operator continues to generate good samples well past the length of such trajectories, thereby demonstrating the match of its non-equilibrium stationary distribution to the data distribution.