Author | Catoni, Olivier. author |
---|---|

Title | Statistical Learning Theory and Stochastic Optimization [electronic resource] : Ecole d'Etรฉ de Probabilitรฉs de Saint-Flour XXXI - 2001 / by Olivier Catoni ; edited by Jean Picard |

Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 2004 |

Connect to | http://dx.doi.org/10.1007/b99352 |

Descript | VIII, 284 p. online resource |

SUMMARY

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

CONTENT

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

Mathematics
Artificial intelligence
Information theory
Numerical analysis
Mathematical optimization
Probabilities
Statistics
Mathematics
Probability Theory and Stochastic Processes
Statistical Theory and Methods
Optimization
Artificial Intelligence (incl. Robotics)
Information and Communication Circuits
Numerical Analysis