Statistical learning theory and stochastic optimization
Subtitle: Ecole d'eté de probabilités de Saint-Flour XXXI, 2001
By: Olivier Catoni ; editor, Jean Picard.
Contributors: Catoni, Olivier.; Picard, Jean, 1959-
Series: Lecture notes in mathematics,; 1851; Lecture notes in mathematics (Springer-Verlag) ;; 1851.
Publisher: Springer
Published: 2004
Place of publication: Berlin; New York
Language: eng
Number of pages: 272
Subjects: Probabilities -- Congresses; Mathematical statistics -- Congresses; Statistics -- Congresses
Genres: Congresses.
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.
Notes: Includes bibliographical references and index.
"... lectures were given at the 31st Probability Summer School in Saint-Flour (July 8-25, 2001) ... "--Pref.