# Simulation of Multivariate Extremes: a Wasserstein-Aitchison GAN approach

arXiv: https://arxiv.org/abs/2504.21438 · HTML: https://mlsanity.com/paper/2504.21438/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 63 references that are in the map.
- First posted on arXiv 30 Apr 2025.

## Builds on (most cited first, 18 of 18)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [ExGAN: Adversarial Generation of Extreme Samples](https://mlsanity.com/paper/2009.08454/) (2020)
- [Some Theoretical Insights into Wasserstein GANs](https://mlsanity.com/paper/2006.02682/) (2020)
- [Pareto GAN: Extending the Representational Power of GANs to Heavy-Tailed Distributions](https://mlsanity.com/paper/2101.09113/) (2021)
- [Decompositions of Dependence for High-Dimensional Extremes](https://mlsanity.com/paper/1612.07190/) (2016)
- [Flexible Tails for Normalizing Flows](https://mlsanity.com/paper/2406.16971/) (2024)
- [k-means clustering of extremes](https://mlsanity.com/paper/1904.02970/) (2019)
- [A VAE Approach to Sample Multivariate Extremes](https://mlsanity.com/paper/2306.10987/) (2023)
- [Concentration bounds for the empirical angular measure with statistical learning applications](https://mlsanity.com/paper/2104.03966/) (2021)
- [Modeling Extremes with d-max-decreasing Neural Networks](https://mlsanity.com/paper/2102.09042/) (2021)
- [GPDFlow: Generative Multivariate Threshold Exceedance Modeling via Normalizing Flows](https://mlsanity.com/paper/2503.11822/) (2025)
- [Multivariate peaks over thresholds models](https://mlsanity.com/paper/1603.06619/) (2016)
- [Generative Machine Learning for Multivariate Angular Simulation](https://mlsanity.com/paper/2504.21505/) (2025)
- [Statistical Inference on a Changing Extremal Dependence Structure](https://mlsanity.com/paper/2201.06389/) (2022)

## Built on by (most cited first, 1 of 1)

- [An Extreme Value Perspective on Learning Stress Laws](https://mlsanity.com/paper/2607.10700/) (2026)

## Abstract (arXiv)

Economically responsible mitigation of multivariate extreme risks-such as extreme rainfall over large areas, large simultaneous variations in many stock prices, or widespread breakdowns in transportation systems-requires assessing the resilience of the systems under plausible stress scenarios. This paper uses Extreme Value Theory (EVT) to develop a new approach to simulating such multivariate extreme events. Specifically, we assume that after transformation to a standard scale the distribution of the random phenomenon of interest is multivariate regular varying and use this to provide a sampling procedure for extremes on the original scale. Our procedure combines a Wasserstein-Aitchison Generative Adversarial Network (WA-GAN) to simulate the tail dependence structure on the standard scale with joint modeling of the univariate marginal tails on the original scale. The WA-GAN procedure relies on the angular measure-encoding the distribution on the unit simplex of the angles of extreme observations-after transformation to Aitchison coordinates, which allows the Wasserstein-GAN algorithm to be run in a linear space. Our method is applied both to simulated data under various tail dependence scenarios and to a financial data set from the Kenneth French Data Library. The proposed algorithm demonstrates strong performance compared to existing alternatives in the literature, both in capturing tail dependence structures and in generating accurate new extreme observations.