Statistical Learning Theory and Stochastic Optimization

Ecole d'Eté de Probabilités de Saint-Flour XXXI - 2001

Olivier Catoni - Collection Lectures Notes in Mathematics

272 pages, parution le 13/10/2004

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Résumé

Lecture Notes in Mathematics

This series reports on new developments in mathematical research and teaching - quickly, informally and at a high level.The type of material considered for publication includes

Research monographs
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Statistical learning theory is aimed at analyzing complex data with necessarily approximate models. This book is intended for an audience with a graduate background in probability theory and statistics. It will be useful to any reader wondering why it may be a good idea, to use as is often done in practice a notoriously "wrong" (i.e. over-simplified) model to predict, estimate or classify. This point of view takes its roots in three fields: information theory, statistical mechanics, and PAC-Bayesian theorems. Results on the large deviations of trajectories of Markov chains with rare transitions are also included. They are meant to provide a better understanding of stochastic optimization algorithms of common use in computing estimators. The author focuses on non-asymptotic bounds of the statistical risk, allowing one to choose adoptively between rich and structured families of models and corresponding estimators. Two mathematical objects pervade the book: entropy and Gibbs measures. The goal is to show how to turn them into versatile and efficient technical tools, that will stimulate further studies and results.

Sommaire

Universal lossless data compression
Links between data compression and statistical estimation
Non cumulated mean risk
Gibbs estimators
Randomized estimators and empirical complexity
Deviation inequalities
Markov chains with exponential transitions

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Olivier Catoni
Collection	Lectures Notes in Mathematics
Parution	13/10/2004
Nb. de pages	272
Format	15,5 x 23,5
Couverture	Broché
Poids	442g
Intérieur	Noir et Blanc
EAN13	9783540225720