Transductive and Inductive Adaptative Inference for Regression and Density Estimation

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.
Document type :
Theses
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https://pastel.archives-ouvertes.fr/tel-00119593
Contributor : Pierre Alquier <>
Submitted on : Monday, December 11, 2006 - 4:00:27 PM
Last modification on : Wednesday, May 15, 2019 - 3:47:35 AM
Long-term archiving on : Tuesday, April 6, 2010 - 8:49:30 PM

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  • HAL Id : tel-00119593, version 1

Citation

Pierre Alquier. Transductive and Inductive Adaptative Inference for Regression and Density Estimation. Mathematics [math]. ENSAE ParisTech, 2006. English. ⟨tel-00119593⟩

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