High-Dimensional Statistics

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.