Skip to main content Accessibility help
×
×
Home
High-Dimensional Probability
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 1
  • Cited by
    This book has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Gitlin, Andrew Tao, Biaoshuai Balzano, Laura and Lipor, John 2018. Improving <inline-formula> <tex-math notation="LaTeX">$K$</tex-math> </inline-formula>-Subspaces via Coherence Pursuit. IEEE Journal of Selected Topics in Signal Processing, Vol. 12, Issue. 6, p. 1575.

    ×

Book description

High-dimensional probability offers insight into the behavior of random vectors, random matrices, random subspaces, and objects used to quantify uncertainty in high dimensions. Drawing on ideas from probability, analysis, and geometry, it lends itself to applications in mathematics, statistics, theoretical computer science, signal processing, optimization, and more. It is the first to integrate theory, key tools, and modern applications of high-dimensional probability. Concentration inequalities form the core, and it covers both classical results such as Hoeffding's and Chernoff's inequalities and modern developments such as the matrix Bernstein's inequality. It then introduces the powerful methods based on stochastic processes, including such tools as Slepian's, Sudakov's, and Dudley's inequalities, as well as generic chaining and bounds based on VC dimension. A broad range of illustrations is embedded throughout, including classical and modern results for covariance estimation, clustering, networks, semidefinite programming, coding, dimension reduction, matrix completion, machine learning, compressed sensing, and sparse regression.

Reviews

'This is an excellent and very timely text, presenting the modern tools of high-dimensional geometry and probability in a very accessible and applications-oriented manner, with plenty of informative exercises. The book is infused with the author's insights and intuition in this field, and has extensive references to the latest developments in the area. This book will be an extremely useful resource both for newcomers to this subject and for expert researchers.'

Terence Tao - University of California, Los Angeles

'Methods of high-dimensional probability have become indispensable in numerous problems of probability theory and its applications in mathematics, statistics, computer science, and electrical engineering. Roman Vershynin's wonderful text fills a major gap in the literature by providing a highly accessible introduction to this area. Starting with no prerequisites beyond a first course in probability and linear algebra, Vershynin takes the reader on a guided tour through the subject and consistently illustrates the utility of the material through modern data science applications. This book should be essential reading for students and researchers in probability theory, data science, and related fields.'

Ramon van Handel - Princeton University, New Jersey

'This very welcome contribution to the literature gives a concise introduction to several topics in ‘high-dimensional probability’ that are of key relevance in contemporary statistical science and machine learning. The author achieves a fine balance between presenting deep theory and maintaining readability for a non-specialist audience - this book is thus highly recommended for graduate students and researchers alike who wish to learn more about this by now indispensable field of modern mathematics.'

Richard Nickl - University of Cambridge

ershynin is one of the world's leading experts in the area of high-dimensional probability, and his textbook provides a gentle yet thorough treatment of many of the key tools in the area and their applications to the field of data science. The topics covered here are a must-know for anyone looking to do mathematical work in the field, covering subjects important in machine learning, algorithms and theoretical computer science, signal processing, and applied mathematics.'

Jelani Nelson - Harvard University, Massachusetts

'High-Dimensional Probability is an excellent treatment of modern methods in probability and data analysis. Vershynin's perspective is unique and insightful, informed by his expertise as both a probabilist and a functional analyst. His treatment of the subject is gentle, thorough and inviting, providing a great resource for both newcomers and those familiar with the subject. I believe, as the author does, that the topics covered in this book are indeed essential ingredients of the developing foundations of data science.'

Santosh Vempala - Georgia Institute of Technology

'Renowned for his deep contributions to high-dimensional probability, Roman Vershynin is to be commended for the clarity of his progressive exposition of the important concepts, tools and techniques of the field. Advanced students and practitioners interested in the mathematical foundations of data science will enjoy the many relevant worked examples and lively use of exercises. This book is the reference I had been waiting for.'

Rémi Gribonval - IEEE and EURASIP Fellow, Directeur de Recherche, Inria, France

'High-dimensional probability is a fascinating mathematical theory that has rapidly grown in recent years. It is fundamental to high-dimensional statistics, machine learning and data science. In this book, Roman Vershynin, who is a leading researcher in high-dimensional probability and a master of exposition, provides the basic tools and some of the main results and applications of high-dimensional probability. This book is an excellent textbook for a graduate course that will be appreciated by mathematics, statistics, computer science, and engineering students. It will also serve as an excellent reference book for researchers working in high-dimensional probability and statistics.'

Elchanan Mossel - Massachusetts Institute of Technology

'This book on the theory and application of high-dimensional probability is a work of exceptional clarity that will be valuable to students and researchers interested in the foundations of data science. A working knowledge of high dimensional probability is essential for researchers at the intersection of applied mathematics, statistics and computer science. The widely accessible presentation will make this book a classic that everyone in foundational data science will want to have on their bookshelf.'

Alfred Hero - University of Michigan

'Vershynin's book is a brilliant introduction to the mathematics which is at the core of modern signal processing and data science. The focus is on concentration of measure and its applications to random matrices, random graphs, dimensionality reduction, and suprema of random process. The treatment is remarkably clean, and the reader will learn beautiful and deep mathematics without unnecessary formalism.'

Andrea Montanari - Stanford University, California

'The ideas presented here have emerged as the essential core of a modern mathematical education, essential not only for probabilists but also for any researcher interested in high-dimensional statistics, the theory of algorithms, information theory, statistical physics and dynamical systems. Moreover, as Vershynin ably demonstrates, mastering these ideas will provide insight into the essential unity underlying these disciplines.'

Michael Jordan - University of California, Berkeley

Refine List
Actions for selected content:
Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Send to Kindle
  • Send to Dropbox
  • Send to Google Drive
  • Send content to

    To send content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to .

    To send content items to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle.

    Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

    Find out more about the Kindle Personal Document Service.

    Please be advised that item(s) you selected are not available.
    You are about to send
    ×

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
×

Metrics

Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Book summary page views

Total views: 0 *
Loading metrics...

* Views captured on Cambridge Core between #date#. This data will be updated every 24 hours.

Usage data cannot currently be displayed