Statistical Learning Theory and Stochastic Optimization

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.

• Estimator
• Measure
• Probability theory
• algorithms
• complexity
• information theory
• learning
• learning theory
• optimization
• information and communication, circuits

From the reviews:

"This book is based on a course of lectures given by the author on a circle of ideas lying at the interface of information theory, statistical learning theory and statistical interference. … The book is perhaps the first ever compendium of this circle of ideas and will be a valuable resource for researchers in information theory, statistical learning theory and statistical inference." (Vivek S. Borkar, Mathematical Reviews, Issue 2006 d)

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