Alquier, Pierre (2006) Inférence Adaptative, Inductive et Transductive, pour l'Estimation de la Regression et de la Densité. PhD thesis Mathématiques Appliquées, ENSAE.
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Alternative Locations: http://www.crest.fr/pageperso/alquier/papiers/these.pdf
Abstract
The aim of this thesis is the study of statistical properties of learning algorithm in the case of regression and density estimation.
It is divided into three parts.
In the first part, the idea is to generalize Olivier Catoni's
PAC-Bayesian theorems about classification to the case of regression estimation with a general loss function.
In the second part, we focus more particularly on the least square regression and propose a new iterative algorithm for feature selection. This method can be applied to the case of orthonormal function basis, leading to optimal rates of convergences, as well as to kernel type functions, leading to some variants of the well-known
SVM method.
In the third part, we generalize the method proposed in the second part to the density estimation setting with quadratic loss.
| Item Type: | PhD Thesis (PhD) |
|---|---|
| Thesis Supervisor: | Catoni, Olivier |
| Date: | December 2006 |
| Board of examiners: | Baraud, Yannick and Catoni, Olivier and Goloubev, Yuri and Hoffmann, Marc and Kourkova, Irina and Massart, Pascal and Picard, Dominique |
| Ecole Doctorale: | ED 386 SCIENCES MATHEMATIQUES DE PARIS CENTRE |
| Discipline: | Mathématiques Appliquées |
| Collection (Fonds): | ENSAE ?? unspec ?? |
| Institution: | ENSAE |
| Subjects: | 1. Mathematics and Applications |
| Uncontrolled Keywords: | statistical learning theory – modelselection – least square regression estimation – confidence regions – concentration inequalities – pac-bayesian bounds – non-parametricestimation – adaptative estimation – empirical complexity measure – compression schemes – support vector machines – oracle inequalities – randomized estimator – Gibbs distribution – density estimation – wavelets – bound on the risk., théorie de l'apprentissage statistique – sélection de modèles – régression aux moindres carrés – régions de confiance – inégalités de concentration – bornes pac-bayésiennes – estimation non-paramétrique – estimation adaptative – mesures empiriques de la complexité – schémas de compression – machines à vecteur support – inégalités oracles – estimateurs randomisés – distribution de Gibbs – estimation de la densité – ondelettes – borne sur le risque. |
| ID Code: | 2070 |
| Deposited By: | Pierre Alquier |
| Deposited On: | 09 January 2007 |
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