Concentration of measure for the analysis of randomized algorithms:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY, USA
Cambridge University Press
2009
|
| Ausgabe: | 1. publ. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | xiv, 196 Seiten Illustrationen |
| ISBN: | 9780521884273 9781107606609 |
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| 245 | 1 | 0 | |a Concentration of measure for the analysis of randomized algorithms |c Devdatt P. Dubhashi, Chalmers University ; Alessandro Panconesi, Sapienza University of Rome |
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Datensatz im Suchindex
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| adam_text |
Titel: Concentration of measure for the analysis of randomized algorithms
Autor: Dubhashi, Devdatt
Jahr: 2009
Contents
Preface page xi
1
1
2
3
5
6
6
10
10
16
16
17
18
22
23
29
29
34
34
38
39
43
45
1 Chernoff-Hoeffding Bounds
1.1 What Is "Concentration of Measure"?
1.2 The Binomial Distribution
1.3 The Chernoff Bound
1.4 Heterogeneous Variables
1.5 The Hoeffding Extension
1.6 Useful Forms of the Bound
1.7 A Variance Bound
1.8 Pointers to the Literature
1.9 Problems
2 Applications of the Chernoff-Hoeffding Bounds
2.1 Probabilistic Amplification
2.2 Load Balancing
2.3 Skip Lists
2.4 Quicksort
2.5 Low-Distortion Embeddings
2.6 Pointers to the Literature
2.7 Problems
3 Chernoff-Hoeffding Bounds in Dependent Settings
3.1 Negative Dependence
3.2 Local Dependence
3.3 Janson's Inequality
3.4 Limited Independence
3.5 Markov Dependence
viii Contents
3.6 Pointers to the Literature
3.7 Problems
4 Interlude: Probabilistic Recurrences
4.1 Problems
5 Martingales and the Method of Bounded Differences
5.1 Review of Conditional Probabilities and Expectations
5.2 Martingales and Azuma 's Inequality
5.3 Generalising Martingales and Azuma 's Inequality
5.4 The Method of Bounded Differences
5.5 Pointers to the Literature
5.6 Problems
6 The Simple Method of Bounded Differences in Action
6.1 Chernoff-Hoeffding Revisited
6.2 Stochastic Optimisation: Bin Packing
6.3 Balls and Bins
6.4 Distributed Edge Colouring: Take 1
6.5 Models for the Web Graph
6.6 Game Theory and Blackwell's Approachability Theorem
6.7 Pointers to the Literature
6.8 Problems
7 The Method of Averaged Bounded Differences
7.1 Hypergeometric Distribution
7.2 Occupancy in Balls and Bins
7.3 Stochastic Optimisation: Travelling Salesman Problem
7.4 Coupling
7.5 Handling Rare Bad Events
7.6 Quicksort
7.7 Pointers to the Literature
7.8 Problems
8 The Method of Bounded Variances
8.1 A Variance Bound for Martingale Sequences
8.2 Applications
8.3 Pointers to the Literature
8.4 Problems
9 Interlude: The Infamous Upper Tail 121
9.1 Motivation: Non-Lipschitz Functions 121
9.2 Concentration of Multivariate Polynomials 121
Contents ix
9.3 The Deletion Method 123
9.4 Problems 124
10 Isoperimetric Inequalities and Concentration 126
10.1 Isoperimetric Inequalities 126
10.2 Isoperimetry and Concentration 127
10.3 The Hamming Cube 130
10.4 Martingales and Isoperimetric Inequalities 131
10.5 Pointers to the Literature 132
10.6 Problems 133
11 Talagrand's Isoperimetric Inequality 136
11.1 Statement of the Inequality 136
11.2 The Method of Non-Uniformly Bounded Differences 139
11.3 Certifiable Functions 144
11.4 Pointers to the Literature 148
11.5 Problems 148
12 Isoperimetric Inequalities and Concentration via
Transportation Cost Inequalities 151
12.1 Distance between Probability Distributions 151
12.2 Transportation Cost Inequalities Imply Isoperimetric
Inequalities and Concentration 153
12.3 Transportation Cost Inequality in Product Spaces
with the Hamming Distance 154
12.4 An Extension to Non-Product Measures 158
12.5 Pointers to the Literature 159
12.6 Problems 159
13 Quadratic Transportation Cost and Talagrand's Inequality 161
13.1 Introduction 161
13.2 Review and Road Map 161
13.3 An L2 (Pseudo)-Metric on Distributions 163
13.4 Quadratic Transportation Cost 165
13.5 Talagrand's Inequality via Quadratic Transportation Cost 167
13.6 Extension to Dependent Processes 168
13.7 Pointers to the Literature 169
13.8 Problems 169
14 Log-Sobolev Inequalities and Concentration 171
14.1 Introduction 171
14.2 A Discrete Log-Sobolev Inequality on the Hamming Cube 172
Contents
14.3 Tensorisation 174
14.4 Modified Log-Sobolev Inequalities in Product Spaces 175
14.5 The Method of Bounded Differences Revisited 177
14.6 Self-Bounding Functions 179
14.7 Talagrand's Inequality Revisited 179
14.8 Pointers to the Literature 181
14.9 Problems 181
Appendix A Summary of the Most Useful Bounds 185
A.I Chernoff-Hoeffding Bounds 185
A.2 Bounds for Well-Behaved Functions 185
Bibliography 189
Index 195 |
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| discipline | Informatik Mathematik |
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| isbn | 9780521884273 9781107606609 |
| language | English |
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| spelling | Dubhashi, Devdatt Verfasser (DE-588)113742061 aut Concentration of measure for the analysis of randomized algorithms Devdatt P. Dubhashi, Chalmers University ; Alessandro Panconesi, Sapienza University of Rome New York, NY, USA Cambridge University Press 2009 xiv, 196 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Random variables Distribution (Probability theory) Limit theorems (Probability theory) Algorithms Zufallsvariable (DE-588)4129514-6 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Algorithmus (DE-588)4001183-5 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 s Algorithmus (DE-588)4001183-5 s Zufallsvariable (DE-588)4129514-6 s DE-604 Panconesi, Alessandro Verfasser (DE-588)114474397 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017998318&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dubhashi, Devdatt Panconesi, Alessandro Concentration of measure for the analysis of randomized algorithms Random variables Distribution (Probability theory) Limit theorems (Probability theory) Algorithms Zufallsvariable (DE-588)4129514-6 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Algorithmus (DE-588)4001183-5 gnd |
| subject_GND | (DE-588)4129514-6 (DE-588)4079013-7 (DE-588)4001183-5 |
| title | Concentration of measure for the analysis of randomized algorithms |
| title_auth | Concentration of measure for the analysis of randomized algorithms |
| title_exact_search | Concentration of measure for the analysis of randomized algorithms |
| title_full | Concentration of measure for the analysis of randomized algorithms Devdatt P. Dubhashi, Chalmers University ; Alessandro Panconesi, Sapienza University of Rome |
| title_fullStr | Concentration of measure for the analysis of randomized algorithms Devdatt P. Dubhashi, Chalmers University ; Alessandro Panconesi, Sapienza University of Rome |
| title_full_unstemmed | Concentration of measure for the analysis of randomized algorithms Devdatt P. Dubhashi, Chalmers University ; Alessandro Panconesi, Sapienza University of Rome |
| title_short | Concentration of measure for the analysis of randomized algorithms |
| title_sort | concentration of measure for the analysis of randomized algorithms |
| topic | Random variables Distribution (Probability theory) Limit theorems (Probability theory) Algorithms Zufallsvariable (DE-588)4129514-6 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Algorithmus (DE-588)4001183-5 gnd |
| topic_facet | Random variables Distribution (Probability theory) Limit theorems (Probability theory) Algorithms Zufallsvariable Wahrscheinlichkeitstheorie Algorithmus |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017998318&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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