Pareto GAN: Extending the Representational Power of GANs to Heavy-Tailed Distributions
This work addresses a limitation in generative modeling for domains with heavy-tailed data, offering a novel method that could improve applications in risk assessment and physics, though it is incremental in extending GAN capabilities.
The authors tackled the problem of GANs failing to represent heavy-tailed distributions, which are common in fields like finance and epidemiology, by introducing Pareto GAN, which leverages extreme value theory and alternative loss functions to match asymptotic behavior and achieve stable learning, as demonstrated on various datasets.
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.