Recent years have seen an explosion in the volume and variety of data collected in scientific disciplines from astronomy to genetics and industrial settings ranging from Amazon to Uber. This graduate text equips readers in statistics, machine learning, and related fields to understand, apply, and adapt modern methods suited to large-scale data.
Author(s): Martin J. Wainwright
Publisher: Cambridge University Press
Year: 2019
Language: English
Pages: 571
Tags: High-Dimensional Statistics; Non-Asymptotic
Cover......Page 1
Frontmatter......Page 2
List of chapters......Page 8
Contents......Page 10
Illustrations......Page 16
Acknowledgements......Page 18
1- introduction......Page 20
2 - Basic tail and concentration bounds......Page 40
3 - Concentration of measure......Page 77
4 - Uniform laws of large numbers......Page 117
5 - Metric entropy and its uses......Page 140
6 - Random matrices and covariance estimation......Page 178
7 - Sparse linear models in high dimensions......Page 213
8 - Principal component analysis in high dimensions......Page 255
9 - Decomposability and restricted strong convexity......Page 278
10 - Matrix estimation with rank constraints......Page 331
11 - Graphical models for high-dimensional data......Page 366
12 - Reproducing kernel Hilbert spaces......Page 402
13 - Nonparametric least squares......Page 435
14 - Localization and uniform laws......Page 472
15 - Minimax lower bounds......Page 504
Subject index......Page 559
reference......Page 543
Author index......Page 567
