Statistical Learning Theory and Stochastic Optimization

Released on by Olivier Catoni
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  • Statistical Learning Theory and Stochastic Optimization Book Detail

  • Author : Olivier Catoni
  • Release Date : 2004-08-30
  • Publisher : Springer
  • Genre : Mathematics
  • Pages : 278
  • ISBN 13 : 3540445072
  • File Size : 69,69 MB
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Statistical Learning Theory and Stochastic Optimization by Olivier Catoni PDF Summary

Book 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.

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Classical Rhetoric in the Middle Ages: The Medieval Rhetors and Their Art 400-1300, with Manuscript Survey to 1500 CE is a completely updated version of John Wa