Skip to content
Register Sign in Wishlist

High-Dimensional Statistics
A Non-Asymptotic Viewpoint

£57.99

Part of Cambridge Series in Statistical and Probabilistic Mathematics

  • Date Published: February 2019
  • availability: Available
  • format: Hardback
  • isbn: 9781108498029

£ 57.99
Hardback

Add to cart Add to wishlist

Other available formats:
eBook


Looking for an inspection copy?

This title is not currently available on inspection

Description
Product filter button
Description
Contents
Resources
Courses
About the Authors
  • 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.

    • 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
    Read more

    Reviews & endorsements

    'Non-asymptotic, high-dimensional 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

    '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

    'This book provides an excellent treatment of perhaps the fastest growing area within high-dimensional theoretical statistics - non-asymptotic 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

    'Statistical theory and practice have undergone a renaissance in the past two decades, with intensive study of high-dimensional data analysis. No researcher has deepened our understanding of high-dimensional 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

    'This is an outstanding book on high-dimensional 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 self-contained, from introductory materials to most updated results on various research frontiers. This book is a must-read for those who wish to learn and to develop modern statistical machine theory, methods and algorithms.' Jianqing Fan, Princeton University, New Jersey

    'This book provides an in-depth mathematical treatment and methodological intuition of high-dimensional statistics. The main technical tools from probability theory are carefully developed and the construction and analysis of statistical methods and algorithms for high-dimensional 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

    'This new book by Martin J. Wainwright covers modern topics in high-dimensional statistical inference, and focuses primarily on explicit non-asymptotic results related to sparsity and non-parametric estimation. This is a must-read 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 state-of-the-art advances in high-dimensional statistics, with always a clever choice of results which have the perfect mix of significance and mathematical depth.' Francis Bach, INRIA Paris

    '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

    '… this is a very valuable book, covering a variety of important topics, self-contained and nicely written.' Fabio Mainardi, MAA Reviews

    See more reviews

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity

    ×

    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?

    ×

    Product details

    • Date Published: February 2019
    • format: Hardback
    • isbn: 9781108498029
    • length: 568 pages
    • dimensions: 260 x 183 x 35 mm
    • weight: 1.2kg
    • contains: 49 b/w illus. 1 table 211 exercises
    • availability: Available
  • 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 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.

  • Author

    Martin J. Wainwright, University of California, Berkeley
    Martin J. Wainwright is a Chancellor's Professor at the University of California, Berkeley, with a joint appointment between the Department of Statistics and the Department of Electrical Engineering and Computer Sciences. His research lies at the nexus of statistics, machine learning, optimization, and information theory, and he has published widely in all of these disciplines. He has written two other books, one on graphical models together with Michael I. Jordan, and one on sparse learning together with Trevor Hastie and Robert Tibshirani. Among other awards, he has received the COPSS Presdients' Award, has been a Medallion Lecturer and Blackwell Lecturer for the Institute of Mathematical Statistics, and has received Best Paper Awards from the Neural Information Processing Systems (NIPS), the International Conference on Machine Learning (ICML), and the Uncertainty in Artificial Intelligence (UAI) conferences, as well as from the Institute of Electrical and Electronics Engineers (IEEE) Information Theory Society.

Sign In

Please sign in to access your account

Cancel

Not already registered? Create an account now. ×

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email lecturers@cambridge.org

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.

Cancel

Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

×
Please fill in the required fields in your feedback submission.
×