ENGLISH

Statistical Learning Theory and Stochastic Optimization: Ecole d’Eté de Probabilités de Saint-Flour XXXI - 2001

By Jean Picard (eds.) , Olivier Catoni (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
2004
ISBN
3540225722, 9783540225720
DOI
10.1007/b99352
LCC
QA273 .L28 no. 1851
Open Library ID
OL3315365M
Language
english
Format
PDF
Filesize
2 MB (2449017 bytes)
Series
Lecture Notes in Mathematics 1851
Edition
1
Pages
284\273
Library
Springer
Time added
2009-08-06 07:02:15
Circuits; Probability Theory and Stochastic ProcesStatistical Theory and Methods; Optimization; Arti

Description

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 adaptively 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.

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