Concentration of measure and generalized product of random vectors with an application to Hanson-Wright-like inequalities

Abstract

Starting from concentration of measure hypotheses on m random vectors Z_1,, Z_m, this article provides an expression of the concentration of functionals (Z_1,, Z_m) where the variations of on each variable depend on the product of the norms (or semi-norms) of the other variables (as if were a product). We illustrate the importance of this result through various generalizations of the Hanson-Wright concentration inequality as well as through a study of the random matrix XDX^T and its resolvent Q = (I_p - 1nXDX^T)^-1, where X and D are random, which have fundamental interest in statistical machine learning applications.

Tasks

Reproductions