Statistical Learning Theory and Stochastic Optimization : Ecole d' Ete de Probabilites de Saint-Flour XXXI - 2001 (Lecture Notes in Mathematics Vol.1851) （2004. VIII, 273 p. 23,5 cm）

Catoni, Olivier/ Ed. by Jean Picard

SPRINGER, BERLIN（2004発売）

SPRINGER, BERLIN（2004発売）

• 製本 Hardcover:ハードカバー版／ページ数 273 p.
• 言語 ENG
• 商品コード 9783540225720

Full Description

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.