Structure learning for extremal tree models

Sebastian Engelke and Stanislav Volgushev

Journal of the Royal Statistical Society Series B, 2022, vol. 84, issue 5, 2055-2087

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.

Date: 2022
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