We propose a vector-valued regression problem whose solution is equivalent to the reproducing kernel Hilbert space (RKHS) embedding of the Bayesian posterior distribution. This equivalence provides a new understanding of kernel Bayesian inference. Moreover, the optimization problem induces a new regularization for the posterior embedding estimator, which is faster and has comparable performance to the squared regularization in kernel Bayes' rule. This regularization coincides with a former thresholding approach used in kernel POMDPs whose consistency remains to be established. Our theoretical work solves this open problem and provides consistency analysis in regression settings. Based on our optimizational formulation, we propose a flexible Bayesian posterior regularization framework which for the first time enables us to put regularization at the distribution level. We apply this method to nonparametric state-space filtering tasks with extremely nonlinear dynamics and show performance gains over all other baselines.

We propose two stochastic gradient MCMC methods for sampling from Bayesian posterior distributions defined on Riemann manifolds with a known geodesic flow, e.g.

Deep generative models (DGMs) have shown promise in image generation. However, most of the existing methods learn a model by simply optimizing a divergence between the marginal distributions of the model and the data, and often fail to capture rich structures, such as attributes of objects and their relationships, in an image. Human knowledge is a crucial element to the success of DGMs to infer these structures, especially in unsupervised learning. In this paper, we propose amortized structural regularization (ASR), which adopts posterior regularization (PR) to embed human knowledge into DGMs via a set of structural constraints. We derive a lower bound of the regularized log-likelihood in PR and adopt the amortized inference technique to jointly optimize the generative model and an auxiliary recognition model for inference efficiently. Empirical results show that ASR outperforms the DGM baselines in terms of inference performance and sample quality.

We propose Generative Well-intentioned Networks (GWINs), a novel framework for increasing the accuracy of certainty-based, closed-world classifiers. A conditional generative network recovers the distribution of observations that the classifier labels correctly with high certainty. We introduce a reject option to the classifier during inference, allowing the classifier to reject an observation instance rather than predict an uncertain label. These rejected observations are translated by the generative network to high-certainty representations, which are then relabeled by the classifier. This architecture allows for any certainty-based classifier or rejection function and is not limited to multilayer perceptrons. The capability of this framework is assessed using benchmark classification datasets and shows that GWINs significantly improve the accuracy of uncertain observations.

We study the problem of conditional generative modeling based on designated semantics or structures. Existing models that build conditional generators either require massive labeled instances as supervision or are unable to accurately control the semantics of generated samples. We propose structured generative adversarial networks (SGANs) for semi-supervised conditional generative modeling. SGAN assumes the data x is generated conditioned on two independent latent variables: y that encodes the designated semantics, and z that contains other factors of variation. To ensure disentangled semantics in y and z, SGAN builds two collaborative games in the hidden space to minimize the reconstruction error of y and z, respectively. Training SGAN also involves solving two adversarial games that have their equilibrium concentrating at the true joint data distributions p(x, z) and p(x, y), avoiding distributing the probability mass diffusely over data space that MLE-based methods may suffer. We assess SGAN by evaluating its trained networks, and its performance on downstream tasks. We show that SGAN delivers a highly controllable generator, and disentangled representations; it also establishes start-of-the-art results across multiple datasets when applied for semi-supervised image classification (1.27%, 5.73%, 17.26% error rates on MNIST, SVHN and CIFAR-10 using 50, 1000 and 4000 labels, respectively). Benefiting from the separate modeling of y and z, SGAN can generate images with high visual quality and strictly following the designated semantic, and can be extended to a wide spectrum of applications, such as style transfer.

Generative Adversarial Nets (GANs) have shown promise in image generation and semi-supervised learning (SSL). However, existing GANs in SSL have two problems: (1) the generator and the discriminator (i.e. the classifier) may not be optimal at the same time; and (2) the generator cannot control the semantics of the generated samples. The problems essentially arise from the two-player formulation, where a single discriminator shares incompatible roles of identifying fake samples and predicting labels and it only estimates the data without considering the labels. To address the problems, we present triple generative adversarial net (Triple-GAN), which consists of three players--a generator, a discriminator and a classifier. The generator and the classifier characterize the conditional distributions between images and labels, and the discriminator solely focuses on identifying fake image-label pairs. We design compatible utilities to ensure that the distributions characterized by the classifier and the generator both converge to the data distribution. Our results on various datasets demonstrate that Triple-GAN as a unified model can simultaneously (1) achieve the state-of-the-art classification results among deep generative models, and (2) disentangle the classes and styles of the input and transfer smoothly in the data space via interpolation in the latent space class-conditionally.

Neural Information Processing Systems http://nips.cc/

We propose Graphical Generative Adversarial Networks (Graphical-GAN) to model structured data.

Although the recent progress is substantial, deep learning methods can be vulnerable to the maliciously generated adversarial examples. In this paper, we present a novel training procedure and a thresholding test strategy, towards robust detection of adversarial examples. In training, we propose to minimize the reverse crossentropy (RCE), which encourages a deep network to learn latent representations that better distinguish adversarial examples from normal ones. In testing, we propose to use a thresholding strategy as the detector to filter out adversarial examples for reliable predictions. Our method is simple to implement using standard algorithms, with little extra training cost compared to the common cross-entropy minimization. We apply our method to defend various attacking methods on the widely used MNIST and CIFAR-10 datasets, and achieve significant improvements on robust predictions under all the threat models in the adversarial setting.

We propose Graphical Generative Adversarial Networks (Graphical-GAN) to model structured data.