Lecture Notes in Mathematics

Statistical Learning Theory and Stochastic Optimization

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

Authors: Catoni, Olivier

Editors: Picard, Jean (Ed.)

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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)


Table of contents (11 chapters)

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-3-540-44507-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.95
price for USA
  • ISBN 978-3-540-22572-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Statistical Learning Theory and Stochastic Optimization
Book Subtitle
Ecole d'Eté de Probabilités de Saint-Flour XXXI - 2001
Authors
Editors
  • Jean Picard
Series Title
Lecture Notes in Mathematics
Series Volume
1851
Copyright
2004
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-44507-4
DOI
10.1007/b99352
Softcover ISBN
978-3-540-22572-0
Series ISSN
0075-8434
Edition Number
1
Number of Pages
VIII, 284
Topics