We propose a unified game-theoretical framework to perform classification and conditional image generation given limited supervision. It is formulated as a three-player minimax game consisting of a generator, a classifier and a discriminator, and therefore is referred to as Triple Generative Adversarial Network (Triple-GAN). The generator and the classifier characterize the conditional distributions between images and labels to perform conditional generation and classification, respectively. The discriminator solely focuses on identifying fake image-label pairs. Theoretically, the three-player formulation guarantees consistency. Namely, under a nonparametric assumption, the unique equilibrium of the game is that the distributions characterized by the generator and the classifier converge to the data distribution. As a byproduct of the three-player formulation, Triple-GAN is flexible to incorporate different semi-supervised classifiers and GAN architectures. We evaluate Triple-GAN in two challenging settings, namely, semi-supervised learning and the extremely low data regime. In both settings, Triple-GAN can achieve excellent classification results and generate meaningful samples in a specific class simultaneously. In particular, using a commonly adopted 13-layer CNN classifier, Triple-GAN outperforms extensive semi-supervised learning methods substantially on several benchmarks no matter data augmentation is applied or not.

This paper presents new estimates of the score function and its gradient with respect to the model parameters in a general energy-based latent variable model (EBLVM). The score function and its gradient can be expressed as combinations of expectation and covariance terms over the (generally intractable) posterior of the latent variables. New estimates are obtained by introducing a variational posterior to approximate the true posterior in these terms. The variational posterior is trained to minimize a certain divergence (e.g., the KL divergence) between itself and the true posterior. Theoretically, the divergence characterizes upper bounds of the bias of the estimates. In principle, our estimates can be applied to a wide range of objectives, including kernelized Stein discrepancy (KSD), score matching (SM)-based methods and exact Fisher divergence with a minimal model assumption. In particular, these estimates applied to SM-based methods outperform existing methods in learning EBLVMs on several image datasets.

The (partial) ranking loss is a commonly used evaluation measure for multi-label classification, which is usually optimized with convex surrogates for computational efficiency. Prior theoretical efforts on multi-label ranking mainly focus on (Fisher) consistency analyses. However, there is a gap between existing theory and practice --- some inconsistent pairwise losses can lead to promising performance, while some consistent univariate losses usually have no clear superiority in practice. To take a step towards filling up this gap, this paper presents a systematic study from two complementary perspectives of consistency and generalization error bounds of learning algorithms. We theoretically find two key factors of the distribution (or dataset) that affect the learning guarantees of algorithms: the instance-wise class imbalance and the label size $c$. Specifically, in an extremely imbalanced case, the algorithm with the consistent univariate loss has an error bound of $O(c)$, while the one with the inconsistent pairwise loss depends on $O(\sqrt{c})$ as shown in prior work. This may shed light on the superior performance of pairwise methods in practice, where real datasets are usually highly imbalanced. Moreover, we present an inconsistent reweighted univariate loss-based algorithm that enjoys an error bound of $O(\sqrt{c})$ for promising performance as well as the computational efficiency of univariate losses. Finally, experimental results confirm our theoretical findings.

Generative adversarial networks (GANs) are effective in generating realistic images but the training is often unstable. There are existing efforts that model the training dynamics of GANs in the parameter space but the analysis cannot directly motivate practically effective stabilizing methods. To this end, we present a conceptually novel perspective from control theory to directly model the dynamics of GANs in the frequency domain and provide simple yet effective methods to stabilize GAN’s training. We first analyze the training dynamic of a prototypical Dirac GAN and adopt the widely-used closed-loop control (CLC) to improve its stability. We then extend CLC to stabilize the training dynamic of normal GANs, which can be implemented as an L2 regularizer on the output of the discriminator. Empirical results show that our method can effectively stabilize the training and obtain state-of-the-art performance on data generation tasks.

Though deep neural networks have achieved significant progress on various tasks, often enhanced by model ensemble, existing high-performance models can be vulnerable to adversarial attacks. Many efforts have been devoted to enhancing the robustness of individual networks and then constructing a straightforward ensemble, e.g., by directly averaging the outputs, which ignores the interaction among networks. This paper presents a new method that explores the interaction among individual networks to improve robustness for ensemble models. Technically, we define a new notion of ensemble diversity in the adversarial setting as the diversity among non-maximal predictions of individual members, and present an adaptive diversity promoting (ADP) regularizer to encourage the diversity, which leads to globally better robustness for the ensemble by making adversarial examples difficult to transfer among individual members. Our method is computationally efficient and compatible with the defense methods acting on individual networks. Empirical results on various datasets verify that our method can improve adversarial robustness while maintaining state-of-the-art accuracy on normal examples.