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    Statistical Learning Theory and Stochastic Optimization

Statistical Learning Theory and Stochastic Optimization

Olivier Catoni
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      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.
      Format: Paperback / softback CONTRIBUTORS: Olivier Catoni EAN: 9783540225720 COUNTRY: Germany PAGES: WEIGHT: 910 g HEIGHT: 235 cm
      PUBLISHED BY: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG DATE PUBLISHED: 2004-08-25 CITY: GENRE: COMPUTERS / Artificial Intelligence / General, MATHEMATICS / Applied, MATHEMATICS / Probability & Statistics / General WIDTH: 155 cm SPINE:

      Book Themes:

      Numerical analysis, Probability and statistics, Optimization, Stochastics, Mathematical theory of computation, Artificial intelligence

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      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.
      Format: Paperback / softback CONTRIBUTORS: Olivier Catoni EAN: 9783540225720 COUNTRY: Germany PAGES: WEIGHT: 910 g HEIGHT: 235 cm
      PUBLISHED BY: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG DATE PUBLISHED: 2004-08-25 CITY: GENRE: COMPUTERS / Artificial Intelligence / General, MATHEMATICS / Applied, MATHEMATICS / Probability & Statistics / General WIDTH: 155 cm SPINE:

      Book Themes:

      Numerical analysis, Probability and statistics, Optimization, Stochastics, Mathematical theory of computation, Artificial intelligence

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