Overview
- Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes in Mathematics (LNM, volume 1851)
Part of the book sub series: École d'Été de Probabilités de Saint-Flour (LNMECOLE)
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Table of contents (11 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
Reviews
From the reviews:
"This book is based on a course of lectures given by the author on a circle of ideas lying at the interface of information theory, statistical learning theory and statistical interference. … The book is perhaps the first ever compendium of this circle of ideas and will be a valuable resource for researchers in information theory, statistical learning theory and statistical inference." (Vivek S. Borkar, Mathematical Reviews, Issue 2006 d)
Bibliographic Information
Book Title: Statistical Learning Theory and Stochastic Optimization
Book Subtitle: Ecole d'Eté de Probabilités de Saint-Flour XXXI - 2001
Authors: Olivier Catoni
Editors: Jean Picard
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/b99352
Publisher: Springer Berlin, Heidelberg
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eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag GmbH Germany, part of Springer Nature 2004
Softcover ISBN: 978-3-540-22572-0Published: 25 August 2004
eBook ISBN: 978-3-540-44507-4Published: 30 August 2004
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: VIII, 284
Topics: Probability Theory and Stochastic Processes, Statistical Theory and Methods, Optimization, Artificial Intelligence, Information and Communication, Circuits, Numerical Analysis