Leveraging Contaminated Datasets to Learn Clean-Data Distribution with Purified Generative Adversarial Networks

Generative adversarial networks (GANs) are known for their strong abilities on capturing the underlying distribution of training instances. Since the seminal work of GAN, many variants of GAN have been proposed. However, existing GANs are almost established on the assumption that the training dataset is clean. But in many real-world applications, this may not hold, that is, the training dataset may be contaminated by a proportion of undesired instances. When training on such datasets, existing GANs will learn a mixture distribution of desired and contaminated instances, rather than the desired distribution of desired data only (target distribution). To learn the target distribution from contaminated datasets, two purified generative adversarial networks (PuriGAN) are developed, in which the discriminators are augmented with the capability to distinguish between target and contaminated instances by leveraging an extra dataset solely composed of contamination instances. We prove that under some mild conditions, the proposed PuriGANs are guaranteed to converge to the distribution of desired instances. Experimental results on several datasets demonstrate that the proposed PuriGANs are able to generate much better images from the desired distribution than comparable baselines when trained on contaminated datasets. In addition, we also demonstrate the usefulness of PuriGAN on downstream applications by applying it to the tasks of semi-supervised anomaly detection on contaminated datasets and PU-learning. Experimental results show that PuriGAN is able to deliver the best performance over comparable baselines on both tasks.

Anomaly Detection by Leveraging Incomplete Anomalous Knowledge with Anomaly-Aware Bidirectional GANs

The goal of anomaly detection is to identify anomalous samples from normal ones. In this paper, a small number of anomalies are assumed to be available at the training stage, but they are assumed to be collected only from several anomaly types, leaving the majority of anomaly types not represented in the collected anomaly dataset at all. To effectively leverage this kind of incomplete anomalous knowledge represented by the collected anomalies, we propose to learn a probability distribution that can not only model the normal samples, but also guarantee to assign low density values for the collected anomalies. To this end, an anomaly-aware generative adversarial network (GAN) is developed, which, in addition to modeling the normal samples as most GANs do, is able to explicitly avoid assigning probabilities for collected anomalous samples. Moreover, to facilitate the computation of anomaly detection criteria like reconstruction error, the proposed anomaly-aware GAN is designed to be bidirectional, attaching an encoder for the generator. Extensive experimental results demonstrate that our proposed method is able to effectively make use of the incomplete anomalous information, leading to significant performance gains compared to existing methods.

Global Convergence and Stability of Stochastic Gradient Descent

In machine learning, stochastic gradient descent (SGD) is widely deployed to train models using highly non-convex objectives with equally complex noise models. Unfortunately, SGD theory often makes restrictive assumptions that fail to capture the non-convexity of real problems, and almost entirely ignore the complex noise models that exist in practice. In this work, we make substantial progress on this shortcoming. First, we establish that SGD's iterates will either globally converge to a stationary point or diverge under nearly arbitrary nonconvexity and noise models. Under a slightly more restrictive assumption on the joint behavior of the non-convexity and noise model that generalizes current assumptions in the literature, we show that the objective function cannot diverge, even if the iterates diverge. As a consequence of our results, SGD can be applied to a greater range of stochastic optimization problems with confidence about its global convergence behavior and stability.