Statistical learning theory and stochastic optimization: Ecole d'Eté de Probabilités de Saint-Flour XXXI, 2001
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2004
|
| Series: | Lecture notes in mathematics
1851 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 272 S. |
| ISBN: | 3540225722 |
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| 100 | 1 | |a Catoni, Olivier |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Statistical learning theory and stochastic optimization |b Ecole d'Eté de Probabilités de Saint-Flour XXXI, 2001 |c Olivier Catoni |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2004 | |
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Record in the Search Index
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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
|
| any_adam_object | 1 |
| author | Catoni, Olivier |
| author_facet | Catoni, Olivier |
| author_role | aut |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics 510 - Mathematics |
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| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| format | Book |
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| id | DE-604.BV019408211 |
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| isbn | 3540225722 |
| language | English |
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| series2 | Lecture notes in mathematics |
| spelling | Catoni, Olivier Verfasser aut Statistical learning theory and stochastic optimization Ecole d'Eté de Probabilités de Saint-Flour XXXI, 2001 Olivier Catoni Berlin [u.a.] Springer 2004 VIII, 272 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1851 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 rswk-swf Mathematische Lerntheorie (DE-588)4169103-9 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 2001 Saint-Flour gnd-content Mathematische Lerntheorie (DE-588)4169103-9 s Stochastische Optimierung (DE-588)4057625-5 s DE-604 Lecture notes in mathematics 1851 (DE-604)BV000676446 1851 HBZ Datenaustausch application/pdf 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 Inhaltsverzeichnis |
| 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 |
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