Statistical learning theory and stochastic optimization : École d'eté de probabilités de Saint-Flour XXXI - 2001
著者
書誌事項
Statistical learning theory and stochastic optimization : École d'eté de probabilités de Saint-Flour XXXI - 2001
（Lecture notes in mathematics, 1851）
Springer, c2004
- タイトル別名
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Statistical learning theory and stochastic optimization, St. Flour 2001
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注記
"The lectures of this volume are the second part of the St. Flour XXXI-2001 volume that has appeared as LNM 1837"--T.p. verso
"Three series of lectures were given at the 31st Probability Summer School in Saint-Flour (July 8-25, 2001)"--Pref
Includes bibliographical references (p. [261]-265) and index
内容説明・目次
内容説明
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.
目次
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.
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