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Quelques questions de sélection de variables autour de l'estimateur LASSO

Abstract : In this thesis, we consider the linear regression model in the high dimensional setup. In particular, estimation methods which exploit the sparsity of the model are studied even when the dimension is larger than the sample size. The ℓ1 penalized least square estimator, also known as the LASSO, is a popular method in such a framework which succeeds in providing sparse estimators. The contributions of the thesis concern extensions of the LASSO which take into account either additional information on the entries, or a semi-supervised data acquisition mode. More precisely, the questions considered in this work are : i) the estimation of the regression parameter when correlation or other structures may exist between the variables (presence of correlations, order structure on the variables or grouping of variables) ; ii) the construction of estimators adapted to the transductive setting. These extensions are derived from a modification of the penalty term in the definition of the LASSO. The performance of the methods is theoretically explored from a non-asymptotic point of view; we prove that the estimators satisfy Sparsity Oracle Inequalities. Moreover variable selection consistency is also established. Furthermore, the practical performance of these procedures is illustrated through numerical experiments on simulated datasets.
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Contributor : Mohamed Hebiri <>
Submitted on : Sunday, August 2, 2009 - 6:32:51 PM
Last modification on : Wednesday, December 9, 2020 - 3:10:17 PM
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  • HAL Id : tel-00408737, version 1


Mohamed Hebiri. Quelques questions de sélection de variables autour de l'estimateur LASSO. Mathématiques [math]. Université Paris-Diderot - Paris VII, 2009. Français. ⟨tel-00408737⟩



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