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＜E-Book＞
Statistical Learning Theory and Stochastic Optimization : Ecole d'Eté de Probabilités de Saint-Flour XXXI - 2001 / by Olivier Catoni ; edited by Jean Picard
(École d'Été de Probabilités de Saint-Flour ; 1851)

Edition	1st ed. 2004.
Publisher	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
Year	2004
Size	VIII, 284 p : online resource
Authors	*Catoni, Olivier author Picard, Jean editor SpringerLink (Online service)
Subjects	LCSH:Probabilities LCSH:Statistics  LCSH:Mathematical optimization LCSH:Artificial intelligence LCSH:Computer science—Mathematics LCSH:Numerical analysis FREE:Probability Theory FREE:Statistical Theory and Methods FREE:Optimization FREE:Artificial Intelligence FREE:Mathematical Applications in Computer Science FREE:Numerical Analysis
Notes	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 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 HTTP:URL=https://doi.org/10.1007/b99352

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