Statistical Learning Theory and Stochastic Optimization : Ecole d'Eté de Probabilités de Saint-Flour XXXI - 2001 / by Olivier Catoni ; edited by Jean Picard.

Format:

Book

Author/Creator:

Catoni, Olivier., author.

Contributor:

Picard, Jean, editor.

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 1851.

Lecture Notes in Mathematics, 0075-8434 ; 1851

Language:

English

Subjects (All):

Distribution (Probability theory).

Mathematical statistics.

Mathematical optimization.

Artificial intelligence.

Mathematics.

Numerical analysis.

Probability Theory and Stochastic Processes.

Statistical Theory and Methods.

Optimization.

Artificial Intelligence.

Information and Communication, Circuits.

Numerical Analysis.

Local Subjects:

Probability Theory and Stochastic Processes.

Statistical Theory and Methods.

Optimization.

Artificial Intelligence.

Information and Communication, Circuits.

Numerical Analysis.

Physical Description:

1 online resource (VIII, 284 pages).

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2004.

System Details:

text file PDF

Summary:

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'' (id est 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.

Contents:

Universal Lossless Data Compression

Links Between Data Compression and Statistical Estimation

Non Cumulated Mean Risk

Gibbs Estimators

Randomized Estimators and Empirical Complexity

Deviation Inequalities

Markov Chains with Exponential Transitions

References

Index.

Other Format:

Printed edition:

ISBN:

9783540445074

Access Restriction:

Restricted for use by site license.