Sparsity in High-Dimensional Extremes: Stanislav Volgushev
From Belle Taylor on July 3rd, 2021
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Name: Stanislav Volgushev
Talk Title: Tree structure learning for 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, this talk will discuss 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 under very general assumptions. 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.
This talk is an invited talk at EVA 2021.