Structure learning for extremal tree models

Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2022 · Volume 84 · Issue 5

Abstract

Extremal graphical models are sparse statistical models for multivariate extreme events. The underlying graph encodes conditional independencies and enables a visual interpretation of the complex extremal dependence structure. For the important case of tree models, we develop a data-driven methodology for learning the graphical structure. We show that sample versions of the extremal correlation and a new summary statistic, which we call the extremal variogram, can be used as weights for a minimum spanning tree to consistently recover the true underlying tree. Remarkably, this implies that extremal tree models can be learned in a completely non-parametric fashion by using simple summary statistics and without the need to assume discrete distributions, existence of densities or parametric models for bivariate distributions.

Keywords

domain of attraction, extreme value theory, graphical models, minimum spanning tree, multivariate Pareto distribution

Enable JavaScript for citation tools and additional paper interactions.