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

• Record Nr.: UNINA9910144617903321
• Autore: Catoni Olivier
• Pubbl/distr/stampa: Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2004
• ISBN: 3-540-44507-2
• Edizione: [1st ed. 2004.]
• Descrizione fisica: 1 online resource (VIII, 284 p.)
• Collana: École d'Été de Probabilités de Saint-Flour ; ; 1851
• Disciplina: 519.5
• Soggetti: Probabilities; Statistics; Mathematical optimization; Artificial intelligence; Computer science - Mathematics; Numerical analysis; Probability Theory; Statistical Theory and Methods; Optimization; Artificial Intelligence; Mathematical Applications in Computer Science; Numerical Analysis
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: 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.
• Sommario/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.