Concentration Inequalities and Model Selection: Ecole d'Eté de Probabilités de Saint-Flour XXXIII - 2003 / Edition 1

Concentration Inequalities and Model Selection: Ecole d'Eté de Probabilités de Saint-Flour XXXIII - 2003 / Edition 1

by Pascal Massart
     
 

ISBN-10: 3540484973

ISBN-13: 9783540484974

Pub. Date: 05/04/2007

Publisher: Springer Berlin Heidelberg

Since the impressive works of Talagrand, concentration inequalities have been recognized as fundamental tools in several domains such as geometry of Banach spaces or random combinatorics. They also turn out to be essential tools to develop a non-asymptotic theory in statistics, exactly as the central limit theorem and large deviations are known to play a central

Overview

Since the impressive works of Talagrand, concentration inequalities have been recognized as fundamental tools in several domains such as geometry of Banach spaces or random combinatorics. They also turn out to be essential tools to develop a non-asymptotic theory in statistics, exactly as the central limit theorem and large deviations are known to play a central part in the asymptotic theory. An overview of a non-asymptotic theory for model selection is given here and some selected applications to variable selection, change points detection and statistical learning are discussed. This volume reflects the content of the course given by P. Massart in St. Flour in 2003. It is mostly self-contained and accessible to graduate students.

Product Details

ISBN-13:
9783540484974
Publisher:
Springer Berlin Heidelberg
Publication date:
05/04/2007
Series:
Lecture Notes in Mathematics / Ecole d'Ete de Probabilites de Saint-Flour Series, #1896
Edition description:
2007
Pages:
343
Product dimensions:
6.00(w) x 9.20(h) x 0.80(d)

Table of Contents

Exponential and Information Inequalities.- Gaussian Processes.- Gaussian Model Selection.- Concentration Inequalities.- Maximal Inequalities.- Density Estimation via Model Selection.- Statistical Learning.

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