Structure learning for extremal tree models

TL;DR

This paper introduces a non-parametric, data-driven method for learning extremal tree models using extremal correlation and variogram statistics to recover the underlying structure from multivariate extreme event data.

Contribution

It develops a novel, non-parametric approach to infer extremal tree structures directly from data without assuming specific distributional forms.

Findings

Consistent recovery of true tree structure using extremal correlation and variogram-based weights.

Method applicable without parametric assumptions or density requirements.

Enables visual interpretation of complex extremal dependence in multivariate extremes.

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.