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Theses

Inégalités d’oracle et mélanges

Lucie Montuelle 1, 2
2 SELECT - Model selection in statistical learning
LMO - Laboratoire de Mathématiques d'Orsay, Inria Saclay - Ile de France
Abstract : This manuscript focuses on two functional estimation problems. A non asymptotic guarantee of the proposed estimator’s performances is provided for each problem through an oracle inequality. In the conditional density estimation setting, mixtures of Gaussian regressions with exponential weights depending on the covariate are used. Model selection principle through penalized maximum likelihood estimation is applied and a condition on the penalty is derived. If the chosen penalty is proportional to the model dimension, then the condition is satisfied. This procedure is accompanied by an algorithm mixing EM and Newton algorithm, tested on synthetic and real data sets. In the regression with sub-Gaussian noise framework, aggregating linear estimators using exponential weights allows to obtain an oracle inequality in deviation, thanks to PAC-bayesian technics. The main advantage of the proposed estimator is to be easily calculable. Furthermore, taking the infinity norm of the regression function into account allows to establish a continuum between sharp and weak oracle inequalities.
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  • HAL Id : tel-01109103, version 1

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Lucie Montuelle. Inégalités d’oracle et mélanges. Statistiques [math.ST]. Université Paris-Sud, 2014. Français. ⟨tel-01109103⟩

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