Aggregation of estimators and classifiers : theory and methods

Abstract : This thesis is devoted to the study of both theoretical and practical properties of various aggregation techniques. We first extend the PAC-Bayesian theory to the high dimensional paradigm in the additive and logistic regression settings. We prove that our estimators are nearly minimax optimal, and we provide an MCMC implementation, backed up by numerical simulations. Next, we introduce an original nonlinear aggregation strategy. Its theoretical merits are presented, and we benchmark the method---called COBRA---on a lengthy series of numerical experiments. Finally, a Bayesian approach to model admixture in population genetics is presented, along with its MCMC implementation. All approaches introduced in this thesis are freely available on the author's website.
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Submitted on : Thursday, December 26, 2013 - 10:26:41 AM
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  • HAL Id : tel-00922353, version 1

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Benjamin Guedj. Aggregation of estimators and classifiers : theory and methods. Statistics Theory [stat.TH]. Université Pierre et Marie Curie - Paris VI, 2013. English. ⟨tel-00922353⟩

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