2021/01/22 by Todd Huster, Jérémy E. Cohen, Huster, Todd +13 · 2 citations
Computer Science · Physics and Astronomy · #Explainable Artificial Intelligence (XAI) #FOS: Computer and information sciences #Generative Adversarial Networks and Image Synthesis #Machine Learning (cs.LG) #Machine Learning in Healthcare #Model Reduction and Neural Networks
paper · pdf · doi:10.48550/arxiv.2101.09113
openalex publication_date 2021/01/22 · openalex created_date 2021/06/22 · openalex updated_date 2026/07/28
Generative adversarial networks (GANs) are often billed as "universal distribution learners", but precisely what distributions they can represent and learn is still an open question. Heavy-tailed distributions are prevalent in many different domains such as financial risk-assessment, physics, and epidemiology. We observe that existing GAN architectures do a poor job of matching the asymptotic behavior of heavy-tailed distributions, a problem that we show stems from their construction. Additionally, when faced with the infinite moments and large distances between outlier points that are characteristic of heavy-tailed distributions, common loss functions produce unstable or near-zero gradients. We address these problems with the Pareto GAN. A Pareto GAN leverages extreme value theory and the functional properties of neural networks to learn a distribution that matches the asymptotic behavior of the marginal distributions of the features. We identify issues with standard loss functions and propose the use of alternative metric spaces that enable stable and efficient learning. Finally, we evaluate our proposed approach on a variety of heavy-tailed datasets.