Statistical Learning Theory and Stochastic Optimization
Catoni, Olivier.
Statistical Learning Theory and Stochastic Optimization Ecole d’Eté de Probabilités de Saint-Flour XXXI - 2001 / [electronic resource] : by Olivier Catoni ; edited by Jean Picard. - VIII, 284 p. online resource. - Lecture Notes in Mathematics, 1851 0075-8434 ; . - Lecture Notes in Mathematics, 1851 .
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.
9783540445074
10.1007/b99352 doi
Distribution (Probability theory.
Mathematical statistics.
Mathematical optimization.
Artificial intelligence.
Mathematics.
Numerical analysis.
Probability Theory and Stochastic Processes.
Statistical Theory and Methods.
Optimization.
Artificial Intelligence.
Information and Communication, Circuits.
Numerical Analysis.
QA273.A1-274.9 QA274-274.9
519.2
Statistical Learning Theory and Stochastic Optimization Ecole d’Eté de Probabilités de Saint-Flour XXXI - 2001 / [electronic resource] : by Olivier Catoni ; edited by Jean Picard. - VIII, 284 p. online resource. - Lecture Notes in Mathematics, 1851 0075-8434 ; . - Lecture Notes in Mathematics, 1851 .
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.
9783540445074
10.1007/b99352 doi
Distribution (Probability theory.
Mathematical statistics.
Mathematical optimization.
Artificial intelligence.
Mathematics.
Numerical analysis.
Probability Theory and Stochastic Processes.
Statistical Theory and Methods.
Optimization.
Artificial Intelligence.
Information and Communication, Circuits.
Numerical Analysis.
QA273.A1-274.9 QA274-274.9
519.2