Statistical Learning Theory and Stochastic Optimization Ecole d'Eté de Probabilités de Saint-Flour XXXI - 2001 /

• Κύριος συγγραφέας: Catoni, Olivier (Συγγραφέας, http://id.loc.gov/vocabulary/relators/aut)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Άλλοι συγγραφείς: Picard, Jean (Επιμελητής έκδοσης, http://id.loc.gov/vocabulary/relators/edt)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2004.
• Έκδοση: 1st ed. 2004.
• Σειρά: Lecture Notes in Mathematics, 1851
• Θέματα: Probabilities.; Statistics .; Mathematical optimization.; Artificial intelligence.; Information theory.; Numerical analysis.; Probability Theory and Stochastic Processes.; Statistical Theory and Methods.; Optimization.; Artificial Intelligence.; Information and Communication, Circuits.; Numerical Analysis.

 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. 

 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.