Statistical Learning Theory and Stochastic Optimization : Ecole d'Ete de Probabilites de Saint-Flour XXXI - 2001

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.