Thèse soutenue

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Auteur / Autrice : Benjamin Guedj
Direction : Gérard BiauÉric Moulines
Type : Thèse de doctorat
Discipline(s) : Mathématiques statistique
Date : Soutenance en 2013
Etablissement(s) : Paris 6

Résumé

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This thesis is devoted to the study of both theoretical and practicalproperties of various aggregation techniques. We first extend thePAC-Bayesian theory to the high dimensional paradigm in the additiveand logistic regression settings. We prove that our estimators arenearly minimax optimal, and we provide an MCMC implementation, backedup by numerical simulations. Next, we introduce an original nonlinearaggregation strategy. Its theoretical merits are presented, and webenchmark the method---called COBRA---on alengthy series of numerical experiments. Finally, a Bayesian approachto model admixture in population genetics is presented, along with itsMCMC implementation. All approaches introduced in this thesis arefreely available on the author's website.