# Sparse Structures for Multivariate Extremes

arXiv: https://arxiv.org/abs/2004.12182 · HTML: https://mlsanity.com/paper/2004.12182/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Apr 2020.

## Built on by (most cited first, 12 of 12)

- [Regression modelling of spatiotemporal extreme U.S. wildfires via partially-interpretable neural networks](https://mlsanity.com/paper/2208.07581/) (2022)
- [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)
- [Extreme Conformal Prediction: Reliable Intervals for High-Impact Events](https://mlsanity.com/paper/2505.08578/) (2025)
- [Spectral learning of multivariate extremes](https://mlsanity.com/paper/2111.07799/) (2021)
- [Regular Variation in Hilbert Spaces and Principal Component Analysis for Functional Extremes](https://mlsanity.com/paper/2308.01023/) (2023)
- [Generative Machine Learning for Multivariate Angular Simulation](https://mlsanity.com/paper/2504.21505/) (2025)
- [Kernel PCA for multivariate extremes](https://mlsanity.com/paper/2211.13172/) (2022)
- [High-dimensional variable clustering based on maxima of a weakly dependent random process](https://mlsanity.com/paper/2302.00934/) (2023)
- [Extremal graphical modeling with latent variables via convex optimization](https://mlsanity.com/paper/2403.09604/) (2024)
- [Extrapolation in Statistical Learning with Extreme Value Theory](https://mlsanity.com/paper/2605.01909/) (2026)
- [Modelling and simulating spatial extremes by combining extreme value theory with generative adversarial networks](https://mlsanity.com/paper/2111.00267/) (2021)

## Abstract (arXiv)

Extreme value statistics provides accurate estimates for the small occurrence probabilities of rare events. While theory and statistical tools for univariate extremes are well-developed, methods for high-dimensional and complex data sets are still scarce. Appropriate notions of sparsity and connections to other fields such as machine learning, graphical models and high-dimensional statistics have only recently been established. This article reviews the new domain of research concerned with the detection and modeling of sparse patterns in rare events. We first describe the different forms of extremal dependence that can arise between the largest observations of a multivariate random vector. We then discuss the current research topics including clustering, principal component analysis and graphical modeling for extremes. Identification of groups of variables which can be concomitantly extreme is also addressed. The methods are illustrated with an application to flood risk assessment.