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Full Description
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.
Contents
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; Author index; Subject index.
