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伯克利STAT210B讲义所编写的高维统计教材《高维统计:非渐近视角》，内容包括：高维统计背景,集中不等式,一致大数定律,度量熵,随机矩阵,稀疏高维模型，高维PCA,限制特征条件,矩阵估计,图模型,RKHS,非参数OLS,局部与一致律,Minimax下界。 "Highdimensional statistics: A nonasymptotic viewpoint", by M. Wainwright. pdf
完整电子版首发2019.2.15 高清pdf 回复可见
源于https://www.cambridge.org/core/b ... 6DAB53E9FF8757C7A4E
https://people.eecs.berkeley.edu/~jordan/courses/210Bspring17/
Table of 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 highdimensional data
12. Reproducing kernel Hilbert spaces
13. Nonparametric least squares
14. Localization and uniform laws
15. Minimax lower bounds
References
Author index
Subject index.
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 selfcontained introduction to the area of highdimensional statistics, aimed at the firstyear 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 indepth exploration of particular model classes  including sparse linear models, matrix models with rank constraints, graphical models, and various types of nonparametric models. With hundreds of worked examples and exercises, this text is intended both for courses and for selfstudy by graduate students and researchers in statistics, machine learning, and related fields who must understand, apply, and adapt modern statistical methods suited to largescale data.
Almost 200 worked examples support the reader in building practical intuition and understanding the motivation for the theory
Contains over 250 exercises  ranging in difficulty from easy to challenging  which strengthen learning, with solutions available to instructors
The book is organized for teaching and learning, allowing instructors to choose one of several identified paths depending on course length
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Reviews & endorsements
Advance praise: 'Nonasymptotic, highdimensional theory is critical for modern statistics and machine learning. This book is unique in providing a crystal clear, complete and unified treatment of the area. With topics ranging from concentration of measure to graphical models, the author weaves together probability theory and its applications to statistics. Ideal for graduate students and researchers. This will surely be the standard reference on the topic for many years.' Larry Wasserman, Carnegie Mellon University, Pennsylvania
Advance praise: 'Martin J. Wainwright brings his large box of analytical power tools to bear on the problems of the day  the analysis of models for wide data. A broad knowledge of this new area combines with his powerful analytical skills to deliver this impressive and intimidating work  bound to be an essential reference for all the brave souls that try their hand.' Trevor Hastie, Stanford University, California
Advance praise: 'This book provides an excellent treatment of perhaps the fastest growing area within highdimensional theoretical statistics  nonasymptotic theory that seeks to provide probabilistic bounds on estimators as a function of sample size and dimension. It offers the most thorough, clear, and engaging coverage of this area to date, and is thus poised to become the definitive reference and textbook on this topic.' Genevera Allen, William Marsh Rice University, Texas
Advance praise: 'Statistical theory and practice have undergone a renaissance in the past two decades, with intensive study of highdimensional data analysis. No researcher has deepened our understanding of highdimensional statistics more than Martin Wainwright. This book brings the signature clarity and incisiveness of his published research into book form. It will be a fantastic resource for both beginning students and seasoned researchers, as the field continues to make exciting breakthroughs. John Lafferty, Yale University, Connecticut
Advance praise: 'This is an outstanding book on highdimensional statistics, written by a creative and celebrated researcher in the field. It gives comprehensive treatments on many important topics in statistical machine learning and, furthermore, is selfcontained, from introductory materials to most updated results on various research frontiers. This book is a mustread for those who wish to learn and to develop modern statistical machine theory, methods and algorithms.' Jianqing Fan, Princeton University, New Jersey
Advance praise: 'This book provides an indepth mathematical treatment and methodological intuition of highdimensional statistics. The main technical tools from probability theory are carefully developed and the construction and analysis of statistical methods and algorithms for highdimensional problems is presented in an outstandingly clear way. Martin J. Wainwright has written a truly exceptional, inspiring and beautiful masterpiece!' Peter Bühlmann, Eidgenössische Technische Hochschule Zürich
Advance praise: 'This new book by Martin J. Wainwright covers modern topics in highdimensional statistical inference, and focuses primarily on explicit nonasymptotic results related to sparsity and nonparametric estimation. This is a mustread for all graduate students in mathematical statistics and theoretical machine learning, both for the breadth of recent advances it covers and the depth of results which are presented. The exposition is outstandingly clear, starting from the first introductory chapters on the necessary probabilistic tools. Then, the book covers stateoftheart advances in highdimensional statistics, with always a clever choice of results which have the perfect mix of significance and mathematical depth.' Francis Bach, INRIA Paris
Advance praise: 'Wainwright’s book on those parts of probability theory and mathematical statistics critical to understanding of the new phenomena encountered in high dimensions is marked by the clarity of its presentation and the depth to which it travels. In every chapter he starts with intuitive examples and simulations which are systematically developed either into powerful mathematical tools or complete answers to fundamental questions of inference. It is not easy, but elegant and rewarding whether read systematically or dipped into as a reference.' Peter Bickel, University of California, Berkeley

