# Deep Learning of Multivariate Extremes via a Geometric Representation

arXiv: https://arxiv.org/abs/2406.19936 · HTML: https://mlsanity.com/paper/2406.19936/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 57 references that are in the map.
- First posted on arXiv 28 Jun 2024.

## Builds on (most cited first, 10 of 10)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Conditional Density Estimation with Neural Networks: Best Practices and Benchmarks](https://mlsanity.com/paper/1903.00954/) (2019)
- [Neural Networks for Extreme Quantile Regression with an Application to Forecasting of Flood Risk](https://mlsanity.com/paper/2208.07590/) (2022)
- [Regression modelling of spatiotemporal extreme U.S. wildfires via partially-interpretable neural networks](https://mlsanity.com/paper/2208.07581/) (2022)
- [A VAE Approach to Sample Multivariate Extremes](https://mlsanity.com/paper/2306.10987/) (2023)
- [Modeling of spatial extremes in environmental data science: Time to move away from max-stable processes](https://mlsanity.com/paper/2401.17430/) (2024)
- [Modelling multivariate extremes through angular-radial decomposition of the density function](https://mlsanity.com/paper/2310.12711/) (2023)
- [Extreme quantile regression with deep learning](https://mlsanity.com/paper/2404.09154/) (2024)
- [Flexible and efficient emulation of spatial extremes processes via variational autoencoders](https://mlsanity.com/paper/2307.08079/) (2023)
- [Statistical inference for radial generalized Pareto distributions and return sets in geometric extremes](https://mlsanity.com/paper/2310.06130/) (2023)

## Built on by (most cited first, 5 of 5)

- [Generative Machine Learning for Multivariate Angular Simulation](https://mlsanity.com/paper/2504.21505/) (2025)
- [Deep learning joint extremes of metocean variables using the SPAR model](https://mlsanity.com/paper/2412.15808/) (2024)
- [Extrapolation in Statistical Learning with Extreme Value Theory](https://mlsanity.com/paper/2605.01909/) (2026)
- [Neural Bayes estimation and selection for complex bivariate extremal dependence models](https://mlsanity.com/paper/2503.23156/) (2025)
- [Q-Edge: Symmetry-Reduced Quantum Simulation of Structured Extreme Dependence](https://mlsanity.com/paper/2609.03706/) (2026)

## Abstract (arXiv)

The study of geometric extremes, where extremal dependence properties are inferred from the deterministic limiting shapes of scaled sample clouds, provides an exciting approach to modelling the extremes of multivariate data. These shapes, termed limit sets, link together several popular extremal dependence modelling frameworks. Although the geometric approach is becoming an increasingly popular modelling tool, current inference techniques are limited to a low dimensional setting (d < 5), and generally require rigid modelling assumptions. In this work, we propose a range of novel theoretical results to aid with the implementation of the geometric extremes framework and introduce the first approach to modelling limit sets using deep learning. By leveraging neural networks, we construct asymptotically-justified yet flexible semi-parametric models for extremal dependence of high-dimensional data. We showcase the efficacy of our deep approach by modelling the complex extremal dependencies between meteorological and oceanographic variables in the North Sea off the coast of the UK.