High-dimensional statistics: a non-asymptotic viewpoint

✍ Scribed by Wainwright, Martin J

• Publisher: Cambridge University Press
• Year: 2019
• Tongue: English
• Leaves: 572
• Series: Cambridge series on statistical and probabilistic mathematics 48
• Category: Library

✦ Synopsis

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.  Read more...

Abstract: 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

✦ Table of Contents

Content: Introduction --
Basic 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 high-dimensional data --
Reproducing kernel Hilbert spaces --
Nonparametric least squares --
Localization and uniform laws --
Minimax lower bounds.

✦ Subjects

Mathematical statistics -- Textbooks.;Big data.;Mathematical statistics.