(Non) convex losses and regularizations, some contributions in Statistics. (Pertes et régularisations (non) convexes, quelques contributions en Statistique)

Yohann de Castro

Abstract: This dissertation essentially covers the work done by the author as ‘‘Maître de Conférences'' at the Laboratoire de Mathématiques d'Orsay (LMO), that is to say since the end of his Ph.D. thesis in December 2011 at the Institut de Mathématiques de Toulouse (IMT). During this period, the author strengthened his contributions to high-dimensional statistics and investigated new fields of research that may be summarized under the following labels ‘‘Super Resolution'' (and more generally the extremal moment problem) and ‘‘latent space models'' (and in particular the hidden Markov models). 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 cited articles for further details and the precise mathematical treatment of the topics presented here.