# Parametric and nonparametric symmetries in graphical models for extremes

arXiv: https://arxiv.org/abs/2306.00703 · HTML: https://mlsanity.com/paper/2306.00703/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jun 2023.

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

- [Extremal graphical modeling with latent variables via convex optimization](https://mlsanity.com/paper/2403.09604/) (2024)

## Abstract (arXiv)

Colored graphical models provide a parsimonious approach to modeling high-dimensional data by exploiting symmetries in the model parameters. In this work, we introduce the notion of coloring for extremal graphical models on multivariate Pareto distributions, a natural class of limiting distributions for threshold exceedances. Thanks to a stability property of the multivariate Pareto distributions, colored extremal tree models can be defined fully nonparametrically. For more general graphs, the parametric family of H"usler--Reiss distributions allows for two alternative approaches to colored graphical models. We study both model classes and introduce statistical methodology for parameter estimation. It turns out that for H"usler--Reiss tree models the different definitions of colored graphical models coincide. In addition, we show a general parametric description of extremal conditional independence statements for H"usler--Reiss distributions. Finally, we demonstrate that our methodology outperforms existing approaches on a real data set.