High-Dimensional Probability

By

Rating

Product Description

Product Details

Preface; Appetizer: using probability to cover a geometric set; 1. Preliminaries on random variables; 2. Concentration of sums of independent random variables; 3. Random vectors in high dimensions; 4. Random matrices; 5. Concentration without independence; 6. Quadratic forms, symmetrization and contraction; 7. Random processes; 8. Chaining; 9. Deviations of random matrices and geometric consequences; 10. Sparse recovery; 11. Dvoretzky-Milman's theorem; Bibliography; Index.

An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.

Roman Vershynin is Professor of Mathematics at the University of California, Irvine. He studies random geometric structures across mathematics and data sciences, in particular in random matrix theory, geometric functional analysis, convex and discrete geometry, geometric combinatorics, high-dimensional statistics, information theory, machine learning, signal processing, and numerical analysis. His honors include an Alfred Sloan Research Fellowship in 2005, an invited talk at the International Congress of Mathematicians in Hyderabad in 2010, and a Bessel Research Award from the Humboldt Foundation in 2013. His 'Introduction to the Non-Asymptotic Analysis of Random Matrices' has become a popular educational resource for many new researchers in probability and data science.

'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.' Remi
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

'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

'Vershynin 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.' Remi
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

Ask a Question About this Product More... |

Look for similar items by category

People also searched for

Item ships from and is sold by Fishpond World Ltd.

↑

Back to top