Colloque des sciences mathématiques du Québec

18 février 2022 de 15 h 30 à 16 h 30 (heure de Montréal/HNE) Réunion Zoom

Structure learning for Extremal graphical models

Colloque par Stanislav Volgushev (University of Toronto)

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 provide 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 marginal or bivariate distributions.  Extensions to more general graphs are also discussed.