Statistical Learning Theory and Stochastic Optimization: Ecole dEt de Probabilits de Saint-Flour XXXI- 2001 (Lecture Notes in Mathematics, Vol. 1851) (Lecture Notes in Mathematics, 1851)

Catoni, Olivier

ISBN 10: 3540225722 / ISBN 13: 9783540225720

Editore: Springer, 2004

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Dati bibliografici

• Titolo: Statistical Learning Theory and Stochastic Optimization: Ecole dEt de Probabilits de Saint-Flour XXXI- 2001 (Lecture Notes in Mathematics, Vol. 1851) (Lecture Notes in Mathematics, 1851)
• Editore: Springer
• Data di pubblicazione: 2004
• Lingua: Inglese
• ISBN 10: 3540225722
• ISBN 13: 9783540225720
• Rilegatura: Brossura
• Condizione: New

Descrizione articolo

Riassunto

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.