# A VAE Approach to Sample Multivariate Extremes

arXiv: https://arxiv.org/abs/2306.10987 · HTML: https://mlsanity.com/paper/2306.10987/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 58 references that are in the map.
- First posted on arXiv 19 Jun 2023.

## Builds on (most cited first, 17 of 17)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Generating Diverse High-Fidelity Images with VQ-VAE-2](https://mlsanity.com/paper/1906.00446/) (2019)
- [Generating Images with Sparse Representations](https://mlsanity.com/paper/2103.03841/) (2021)
- [Understanding Deep Neural Networks with Rectified Linear Units](https://mlsanity.com/paper/1611.01491/) (2016)
- [Learning Discourse-level Diversity for Neural Dialog Models using Conditional Variational Autoencoders](https://mlsanity.com/paper/1703.10960/) (2017)
- [Pluralistic Image Completion](https://mlsanity.com/paper/1903.04227/) (2019)
- [Implicit Reparameterization Gradients](https://mlsanity.com/paper/1805.08498/) (2018)
- [The Extreme Value Machine](https://mlsanity.com/paper/1506.06112/) (2015)
- [ExGAN: Adversarial Generation of Extreme Samples](https://mlsanity.com/paper/2009.08454/) (2020)
- [Pareto GAN: Extending the Representational Power of GANs to Heavy-Tailed Distributions](https://mlsanity.com/paper/2101.09113/) (2021)
- [Neural Networks for Extreme Quantile Regression with an Application to Forecasting of Flood Risk](https://mlsanity.com/paper/2208.07590/) (2022)
- [Analog ensemble data assimilation and a method for constructing analogs with variational autoencoders](https://mlsanity.com/paper/2006.01101/) (2020)
- [Marginal Tail-Adaptive Normalizing Flows](https://mlsanity.com/paper/2206.10311/) (2022)
- [Principal Component Analysis for Multivariate Extremes](https://mlsanity.com/paper/1906.11043/) (2019)
- [Extremes on river networks](https://mlsanity.com/paper/1501.02663/) (2015)
- [Concentration bounds for the empirical angular measure with statistical learning applications](https://mlsanity.com/paper/2104.03966/) (2021)

## Built on by (most cited first, 10 of 10)

- [Deep Learning of Multivariate Extremes via a Geometric Representation](https://mlsanity.com/paper/2406.19936/) (2024)
- [Generative Machine Learning for Multivariate Angular Simulation](https://mlsanity.com/paper/2504.21505/) (2025)
- [Generalizing Score-based generative models for Heavy-tailed Distributions](https://mlsanity.com/paper/2603.00772/) (2026)
- [Simulation of Multivariate Extremes: a Wasserstein-Aitchison GAN approach](https://mlsanity.com/paper/2504.21438/) (2025)
- [Extrapolation in Statistical Learning with Extreme Value Theory](https://mlsanity.com/paper/2605.01909/) (2026)
- [Phase-Type Variational Autoencoders for Heavy-Tailed Data](https://mlsanity.com/paper/2603.01800/) (2026)
- [Markov Chain Decoders Overcome the Heavy-Tail Limitations of Lipschitz Generative Models](https://mlsanity.com/paper/2605.18931/) (2026)
- [An Extreme Value Perspective on Learning Stress Laws](https://mlsanity.com/paper/2607.10700/) (2026)
- [TailBooster: A Dual-Layer Generative Framework for Extreme Value Augmentation with Operational Validity Enforcement](https://mlsanity.com/paper/2608.11951/) (2026)
- [Radial Tail Repair: Post-Training Correction for Diffusion and Flow Models](https://mlsanity.com/paper/2610.16851/) (2026)

## Abstract (arXiv)

Generating accurate extremes from an observational data set is crucial when seeking to estimate risks associated with the occurrence of future extremes which could be larger than those already observed. Applications range from the occurrence of natural disasters to financial crashes. Generative approaches from the machine learning community do not apply to extreme samples without careful adaptation. Besides, asymptotic results from extreme value theory (EVT) give a theoretical framework to model multivariate extreme events, especially through the notion of multivariate regular variation. Bridging these two fields, this paper details a variational autoencoder (VAE) approach for sampling multivariate heavy-tailed distributions, i.e., distributions likely to have extremes of particularly large intensities. We illustrate the relevance of our approach on a synthetic data set and on a real data set of discharge measurements along the Danube river network. The latter shows the potential of our approach for flood risks' assessment. In addition to outperforming the standard VAE for the tested data sets, we also provide a comparison with a competing EVT-based generative approach. On the tested cases, our approach improves the learning of the dependency structure between extremes.