Wainwright M. High-Dimensional Statistics: A Non-Asymptotic Viewpoint

Cambridge University Press, 2019. — 572 p. — (Statistical and Probabilistic Mathematics). — ISBN: 978-1-108-49802-9.Recent years have witnessed an explosion in the volume and variety of data collected in all scientific disciplines and industrial settings. Such massive data sets present a number of challenges to researchers in statistics and machine learning. This book provides a self-contained introduction to the area of high-dimensional statistics, aimed at the first-year graduate level. It includes chapters that are focused on core methodology and theory - including tail bounds, concentration inequalities, uniform laws and empirical process, and random matrices - as well as chapters devoted to in-depth exploration of particular model classes - including sparse linear models, matrix models with rank constraints, graphical models, and various types of non-parametric models. With hundreds of worked examples and exercises, this text is intended both for courses and for self-study by graduate students and researchers in statistics, machine learning, and related fields who must understand, apply, and adapt modern statistical methods suited to large-scale data.Illustrations
AcknowledgementsBasic tail and concentration bounds
Concentration of measure
Uniform laws of large numbers
Metric entropy and its uses
Random matrices and covariance estimation
Sparse linear models in high dimensions
Principal component analysis in high dimensions
Decomposability and restricted strong convexity
Matrix estimation with rank constraints
Graphical models for highdimensional data
Reproducing kernel Hilbert spaces
Nonparametric least squares
Localization and uniform laws
Minimax lower bounds
Subject indexAuthor indexTrue PDF