Regularized linear regression in Hilbert space

schedule le mardi 13 février 2018 de 10h45 à 11h45

Organisé par : Castillo, Fischer, Giulini, Gribkova, Levrard, Roquain, Sangnier

Intervenant : Gilles Blanchard (Universität Potsdam)
Lieu : UPMC, salle 15-16.201

Sujet : Regularized linear regression in Hilbert space

Résumé :
Motivated by reproducing kernel methods, I will present a statistical analysis of the convergence of linear regression from (bounded) covariates in Hilbert space, extending and completing previously known results. The nice theoretical setting provided by (basic) deviation inequalities in Hilbert space as well as operator perturbation tools allows us to analyze a large panel of kernel-based algorithms, applications to inverse regression, as well as some very recent extensions for parallelizing such algorithms where computational efficiency becomes an important bottleneck (typically in a "big data" context).

This field was pioneered by the works of De Vito, Caponnetto, Rosasco, Smale and Zhou (between others), and I will present some contributions obtain in collaboration with N. Krämer, N. Mücke, P. Mathé and O. Zadorozhnyi.