Extreme Partial Least Squares

par Stéphane GIRARD

lundi 12 janv. 2026, 13:30 → 15:00 Europe/Paris

Fokko du Cloux (La Doua)

The talk deals with dimension-reduction techniques for modelling conditional extreme values. Specifically, we investigate the idea that extreme values of a response variable can be explained by nonlinear functions derived from linear projections of an input random vector. In this context, the estimation of projection directions is examined and the Extreme Partial Least Squares (EPLS) method is introduced as an adaptation of the original Partial Least Squares (PLS) method tailored to the extreme-value framework. Further, an interpretation of EPLS directions as maximum likelihood estimators is proposed, utilizing the von Mises--Fisher distribution applied to hyperballs. The dimension reduction process is enhanced through the Bayesian paradigm, enabling the incorporation of prior information into the projection direction estimation. The maximum a posteriori estimator is derived in two specific cases, elucidating it as a regularization or shrinkage of the EPLS estimator. We also establish its asymptotic behavior as the sample size approaches infinity. A simulation data study is conducted in order to assess the practical utility of our proposed method. This clearly demonstrates its effectiveness even in moderate data problems within high-dimensional settings. Furthermore, we provide an illustrative example of the method's applicability using French farm income data, highlighting its efficacy in real-world scenarios.

This is joint work with J. Arbel, M. Bousebata (Inria), H. Lorenzo (Univ. Aix-Marseille) and C. Pakzad (Univ. Paris-Nanterre).