A clustering algorithm for Hüsler-Reiss graphical models

par Marine Demangeot (Université Paul Valéry)

mardi 7 avr. 2026, 11:15 → 12:15 Europe/Paris

Salle K. Johnson (1R3, 1er étage)

Extreme events, although rare, can have substantial environmental, societal, and economic consequences. Their modeling is typically addressed within the framework of extreme value theory, where statistical inference is challenging due to the scarcity of observations, especially in high dimensions. This motivates the search for parsimonious and interpretable structures. Graphical models provide a natural framework by exploiting conditional independence, leading to sparse representations that facilitate interpretation and estimation. In the Hüsler–Reiss setting, this structure can be captured through an extremal precision matrix, whose zero pattern encodes the underlying graphical dependencies. In this work, we propose a methodology for Hüsler–Reiss graphical models that leverages structural sparsity through clustering. Building on a clustering algorithm proposed by Touw et al. [1], we introduce a convex fusion penalty on the extremal precision matrix during maximum likelihood estimation, encouraging variables with similar tail dependence patterns to cluster together.  This approach promotes block structures, which in turn can induce conditional independence. We study the theoretical properties of the method and prove consistency of the estimator under a block-structured assumption. Simulation studies illustrate the performance of the method.

[1] Touw, D. J. W., Alfons, A., Groenen, P. J. F., & Wilms, I. (2026). Clusterpath Gaussian Graphical Modeling. arXiv preprint arXiv:2407.00644

Joint work with Alexandre Capel, Nicolas Meyer and Gwladys Toulemonde (Université de Montpellier, IMAG)