Statistical Learning Theory and Stochastic Optimization

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

  • Authors
  • Olivier Catoni
  • Editors
  • Jean Picard

Part of the Lecture Notes in Mathematics book series (LNM, volume 1851)

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Olivier Catoni
    Pages 1-4
  3. Olivier Catoni
    Pages 5-54
  4. Olivier Catoni
    Pages 71-95
  5. Olivier Catoni
    Pages 97-154
  6. Olivier Catoni
    Pages 199-222
  7. Olivier Catoni
    Pages 223-260
  8. Olivier Catoni
    Pages 261-265
  9. Olivier Catoni
    Pages 267-269
  10. Back Matter
    Pages 277-280

About this book

Introduction

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.

Keywords

Estimator Measure Probability theory algorithms complexity information theory learning learning theory optimization

Bibliographic information

  • DOI https://doi.org/10.1007/b99352
  • Copyright Information Springer-Verlag Berlin Heidelberg 2004
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-22572-0
  • Online ISBN 978-3-540-44507-4
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book
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