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140122 ||| eng |
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|a 9783540445074
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| 100 |
1 |
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|a Catoni, Olivier
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| 245 |
0 |
0 |
|a Statistical Learning Theory and Stochastic Optimization
|h Elektronische Ressource
|b Ecole d'Eté de Probabilités de Saint-Flour XXXI - 2001
|c by Olivier Catoni ; edited by Jean Picard
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| 250 |
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|a 1st ed. 2004
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| 260 |
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|a Berlin, Heidelberg
|b Springer Berlin Heidelberg
|c 2004, 2004
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| 300 |
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|a VIII, 284 p
|b online resource
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| 505 |
0 |
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|a 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
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| 653 |
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|a Optimization
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| 653 |
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|a Information and Communication, Circuits
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| 653 |
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|a Statistical Theory and Methods
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| 653 |
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|a Statistics
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| 653 |
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|a Artificial Intelligence
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| 653 |
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|a Information theory
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| 653 |
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|a Artificial intelligence
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| 653 |
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|a Numerical analysis
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| 653 |
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|a Numerical Analysis
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| 653 |
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|a Mathematical optimization
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| 653 |
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|a Probability Theory and Stochastic Processes
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| 653 |
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|a Probabilities
|
| 700 |
1 |
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|a Picard, Jean
|e [editor]
|
| 041 |
0 |
7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b SBA
|a Springer Book Archives -2004
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| 490 |
0 |
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|a École d'Été de Probabilités de Saint-Flour
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| 856 |
4 |
0 |
|u https://doi.org/10.1007/b99352?nosfx=y
|x Verlag
|3 Volltext
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| 082 |
0 |
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|a 519.2
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| 520 |
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|a 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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