Statistical learning theory and stochastic optimization Ecole d'Eté de Probabilités de Saint-Flour XXXI, 2001

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1. Verfasser: Catoni, Olivier (VerfasserIn)
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Sprache:English
Veröffentlicht: Berlin [u.a.] Springer 2004
Schriftenreihe:Lecture notes in mathematics 1851
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Datensatz im Suchindex

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adam_text Contents 1 Universal lossless data compression 5 1.1 A link between coding and estimation 5 1.2 Universal coding and mixture codes 13 1.3 Lower bounds for the minimax compression rate 20 1.4 Mixtures of i.i.d. coding distributions 25 1.5 Double mixtures and adaptive compression 33 Appendix 49 1.6 Fano s lemma 49 1.7 Decomposition of the Kullback divergence function 50 2 Links between data compression and statistical estimation . 55 2.1 Estimating a conditional distribution 55 2.2 Least square regression 56 2.3 Pattern recognition 58 3 Non cumulated mean risk 71 3.1 The progressive mixture rule 71 3.2 Estimating a Bernoulli random variable 76 3.3 Adaptive histograms 78 3.4 Some remarks on approximate Monte Carlo computations .... 80 3.5 Selection and aggregation : a toy example pointing out some differences 81 3.6 Least square regression 83 3.7 Adaptive regression estimation in Besov spaces 89 4 Gibbs estimators 97 4.1 General framework 97 4.2 Dichotomic histograms 103 4.3 Mathematical framework for density estimation 113 4.4 Main oracle inequality 117 VIII Contents 4.5 Checking the accuracy of the bounds on the Gaussian shift model 120 4.6 Application to adaptive classification 123 4.7 Two stage adaptive least square regression 131 4.8 One stage piecewise constant regression 136 4.9 Some abstract inference problem 144 4.10 Another type of bound 153 5 Randomized estimators and empirical complexity 155 5.1 A pseudo Bayesian approach to adaptive inference 155 5.2 A randomized rule for pattern recognition 158 5.3 Generalizations of theorem 5.2.3 165 5.4 The non ambiguous case 167 5.5 Empirical complexity bounds for the Gibbs estimator 173 5.6 Non randomized classification rules 176 5.7 Application to classification trees 177 5.8 The regression setting 181 5.9 Links with penalized least square regression 186 5.10 Some elementary bounds 193 5.11 Some refinements about the linear regression case 194 6 Deviation inequalities 199 6.1 Bounded range functional of independent variables 200 6.2 Extension to unbounded ranges 206 6.3 Generalization to Markov chains 210 7 Markov chains with exponential transitions 223 7.1 Model definition 223 7.2 The reduction principle 225 7.3 Excursion from a domain 230 7.4 Fast reduction algorithm 235 7.5 Elevation function and cycle decomposition 237 7.6 Mean hitting times and ordered reduction 244 7.7 Convergence speeds 249 7.8 Generalized simulated annealing algorithm 255 References 261 Index 267 List of participants 271 List of short lectures 273
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publishDate 2004
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publishDateSort 2004
publisher Springer
record_format marc
series Lecture notes in mathematics
series2 Lecture notes in mathematics
spellingShingle Catoni, Olivier
Statistical learning theory and stochastic optimization Ecole d'Eté de Probabilités de Saint-Flour XXXI, 2001
Lecture notes in mathematics
Optimaliseren gtt
Optimisation rasuqam
Probabilités - Congrès
Statistiek gtt
Statistique - Congrès
Statistique mathématique - Congrès
Statistique mathématique rasuqam
Stochastische methoden gtt
Théorie des probabilités rasuqam
Statistik
Combinatorial optimization Congresses
Computational learning theory Congresses
Mathematical statistics Congresses
Probabilities Congresses
Statistics Congresses
Stochastische Optimierung (DE-588)4057625-5 gnd
Mathematische Lerntheorie (DE-588)4169103-9 gnd
subject_GND (DE-588)4057625-5
(DE-588)4169103-9
(DE-588)1071861417
title Statistical learning theory and stochastic optimization Ecole d'Eté de Probabilités de Saint-Flour XXXI, 2001
title_auth Statistical learning theory and stochastic optimization Ecole d'Eté de Probabilités de Saint-Flour XXXI, 2001
title_exact_search Statistical learning theory and stochastic optimization Ecole d'Eté de Probabilités de Saint-Flour XXXI, 2001
title_full Statistical learning theory and stochastic optimization Ecole d'Eté de Probabilités de Saint-Flour XXXI, 2001 Olivier Catoni
title_fullStr Statistical learning theory and stochastic optimization Ecole d'Eté de Probabilités de Saint-Flour XXXI, 2001 Olivier Catoni
title_full_unstemmed Statistical learning theory and stochastic optimization Ecole d'Eté de Probabilités de Saint-Flour XXXI, 2001 Olivier Catoni
title_short Statistical learning theory and stochastic optimization
title_sort statistical learning theory and stochastic optimization ecole d ete de probabilites de saint flour xxxi 2001
title_sub Ecole d'Eté de Probabilités de Saint-Flour XXXI, 2001
topic Optimaliseren gtt
Optimisation rasuqam
Probabilités - Congrès
Statistiek gtt
Statistique - Congrès
Statistique mathématique - Congrès
Statistique mathématique rasuqam
Stochastische methoden gtt
Théorie des probabilités rasuqam
Statistik
Combinatorial optimization Congresses
Computational learning theory Congresses
Mathematical statistics Congresses
Probabilities Congresses
Statistics Congresses
Stochastische Optimierung (DE-588)4057625-5 gnd
Mathematische Lerntheorie (DE-588)4169103-9 gnd
topic_facet Optimaliseren
Optimisation
Probabilités - Congrès
Statistiek
Statistique - Congrès
Statistique mathématique - Congrès
Statistique mathématique
Stochastische methoden
Théorie des probabilités
Statistik
Combinatorial optimization Congresses
Computational learning theory Congresses
Mathematical statistics Congresses
Probabilities Congresses
Statistics Congresses
Stochastische Optimierung
Mathematische Lerntheorie
Konferenzschrift 2001 Saint-Flour
url http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012870262&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link (DE-604)BV000676446
work_keys_str_mv AT catoniolivier statisticallearningtheoryandstochasticoptimizationecoledetedeprobabilitesdesaintflourxxxi2001