Perspectives computationnelles et statistiques pour la régression en grande dimension
Salmon, Joseph · HAL (Le Centre pour la Communication Scientifique Directe) · 2017
This dissertation essentially covers the work done by the author as a `Maître de Conférences'' at the Laboratoire de Traitement et Communication de l'Information (LTCI), at Télécom ParisTech, since December 2012.During this period, the author strengthened his contributions to high-dimensional statistics and in particular sparse regression methods.In particular, the main focus of the dissertation is on computational aspects and to speed-up algorithms for Lasso-type problems, on means to better take into account the unknown noise and on corrections against the bias non-smooth convex regression methods suffer from.This report is not meant to present comprehensive description of the results developed by the author, but rather a synthetic view of his main contributions.The interested reader may consult the referenced articles for additional details and more precise treatment of the topics presented here.