Structure Learning for Extremal Tree Models

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