Learning Clusters and Graphs of Multivariate Extremes

Abstract

Which variables become extreme together, and how are they connected in the dependence structure? This talk presents a framework for clustering and structure learning in Hüsler–Reiss extremal graphical models. A normalised Laplacian of pairwise tail-dependence coefficients identifies groups of variables, which are asymptotically independent with each other, followed by connected graph estimation within each group. A magnitude–profile representation provides three simple covariance estimators, while spectral constraints enforce graph connectivity. Simulation studies and applications to river discharge and global equity markets show that our methods outperforms the existing extremal graphical learning methods in terms of accuracy and computational speed.