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Cover 1 Front Matter I 3 Front Matter II 5 CAMBRIDGE SERIES IN STATISTICAL AND PROBABILISTIC MATHEMATICS 6 High-Dimensional Probability: An Introduction with Applications in Data Science 7 Copyright 8 Contents 9 Foreword 13 Preface 15 Appetizer: Using Probability to Cover a Geometric Set 17 1 Preliminaries on Random Variables 21 2 Concentration of Sums of Independent Random Variables 27 3 Random Vectors in High Dimensions 54 4 Random Matrices 86 5 ConcentrationWithout Independence 114 6 Quadratic Forms, Symmetrization, and Contraction 143 7 Random Processes 163 8 Chaining 192 9 Deviations of Random Matrices and Geometric Consequences 232 10 Sparse Recovery 248 11 Dvoretzky–Milman Theorem 270 Hints for Exercises 281 References 288 Index 297
- Language
- EN
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