- English
- PDF
- Available on iOS & Android
About this book
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.
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Information
Table of contents
- Cover
- Endorsements
- Half-title
- Series information
- Title page
- Copyright information
- List of chapters
- Contents
- Illustrations
- Acknowledgements
- 1 Introduction
- 2 Basic tail and concentration bounds
- 3 Concentration of measure
- 4 Uniform laws of large numbers
- 5 Metric entropy and its uses
- 6 Random matrices and covariance estimation
- 7 Sparse linear models in high dimensions
- 8 Principal component analysis in high dimensions
- 9 Decomposability and restricted strong convexity
- 10 Matrix estimation with rank constraints
- 11 Graphical models for high-dimensional data
- 12 Reproducing kernel Hilbert spaces
- 13 Nonparametric least squares
- 14 Localization and uniform laws
- 15 Minimax lower bounds
- References
- Subject index
- Author index