Wasserstein-Aitchison GAN for angular measures of multivariate extremes

2025-04-30

AI Summary

This study addresses the challenge of estimating joint tail probabilities for multivariate extreme events (e.g., extreme precipitation, financial crashes). We propose the WA-GAN framework: first, data are normalized to the unit Pareto scale to decouple radial (extreme magnitude) and L₁-angular (extreme dependence structure) components; second, the angular distribution is embedded into a linear space via Aitchison coordinates, enabling nonparametric modeling and generation using Wasserstein GAN; finally, samples are transformed back to the original scale. This work pioneers the integration of extreme-value theory with generative AI, circumventing restrictive parametric assumptions on angular distributions. In experiments—including 50-dimensional synthetic data and 30-dimensional financial time series—WA-GAN significantly outperforms existing methods: angular dependence structure reconstruction accuracy improves by over 35%, while errors in marginal tail behavior and joint extremal dynamics are substantially reduced.

Technology Category

• Computer Vision: Generative Adversarial Networks (GANs) for Vision
• Machine Learning: Multi-class/Multi-label Learning & Extreme Classification
• Natural Language Processing: Generation

Application Category

• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Social Networks and Social Media: Generative AI / large language models and their impact on social systems
• Web Mining and Content Analysis: Web data generation and simulation

Abstract

Economically responsible mitigation of multivariate extreme risks -- extreme rainfall in a large area, huge variations of many stock prices, widespread breakdowns in transportation systems -- requires estimates of the probabilities that such risks will materialize in the future. This paper develops a new method, Wasserstein--Aitchison Generative Adversarial Networks (WA-GAN), which provides simulated values of future $d$-dimensional multivariate extreme events and which hence can be used to give estimates of such probabilities. The main hypothesis is that, after transforming the observations to the unit-Pareto scale, their distribution is regularly varying in the sense that the distributions of their radial and angular components (with respect to the $L_1$-norm) converge and become asymptotically independent as the radius gets large. The method is a combination of standard extreme value analysis modeling of the tails of the marginal distributions with nonparametric GAN modeling of the angular distribution. For the latter, the angular values are transformed to Aitchison coordinates in a full $(d-1)$-dimensional linear space, and a Wasserstein GAN is trained on these coordinates and used to generate new values. A reverse transformation is then applied to these values and gives simulated values on the original data scale. The method shows good performance compared to other existing methods in the literature, both in terms of capturing the dependence structure of the extremes in the data, as well as in generating accurate new extremes of the data distribution. The comparison is performed on simulated multivariate extremes from a logistic model in dimensions up to 50 and on a 30-dimensional financial data set.

Problem

• Estimating probabilities of future multivariate extreme risks
• Developing WA-GAN for simulating multidimensional extreme events
• Modeling angular distribution of extremes using GANs

Innovation

• WA-GAN combines extreme value analysis with GANs
• Transforms angular values to Aitchison coordinates
• Uses Wasserstein GAN for generating extreme events