An Introduction to Matrix Concentration Inequalities

An Introduction to Matrix Concentration Inequalities
Author: Joel Tropp
Publisher:
Total Pages: 256
Release: 2015-05-27
Genre: Computers
ISBN: 9781601988386

Random matrices now play a role in many areas of theoretical, applied, and computational mathematics. It is therefore desirable to have tools for studying random matrices that are flexible, easy to use, and powerful. Over the last fifteen years, researchers have developed a remarkable family of results, called matrix concentration inequalities, that achieve all of these goals. This monograph offers an invitation to the field of matrix concentration inequalities. It begins with some history of random matrix theory; it describes a flexible model for random matrices that is suitable for many problems; and it discusses the most important matrix concentration results. To demonstrate the value of these techniques, the presentation includes examples drawn from statistics, machine learning, optimization, combinatorics, algorithms, scientific computing, and beyond.

Concentration Inequalities

Concentration Inequalities
Author: Stéphane Boucheron
Publisher: Oxford University Press
Total Pages: 492
Release: 2013-02-07
Genre: Mathematics
ISBN: 0199535256

Describes the interplay between the probabilistic structure (independence) and a variety of tools ranging from functional inequalities to transportation arguments to information theory. Applications to the study of empirical processes, random projections, random matrix theory, and threshold phenomena are also presented.

An Introduction to Random Matrices

An Introduction to Random Matrices
Author: Greg W. Anderson
Publisher: Cambridge University Press
Total Pages: 507
Release: 2010
Genre: Mathematics
ISBN: 0521194520

A rigorous introduction to the basic theory of random matrices designed for graduate students with a background in probability theory.

An Introduction to Matrix Concentration Inequalities

An Introduction to Matrix Concentration Inequalities
Author: Joel Aaron Tropp
Publisher:
Total Pages: 230
Release: 2015
Genre: Matrix derivatives
ISBN: 9781601988393

Random matrices now play a role in many areas of theoretical, applied, and computational mathematics. Therefore, it is desirable to have tools for studying random matrices that are flexible, easy to use, and powerful. Over the last fifteen years, researchers have developed a remarkable family of results, called matrix concentration inequalities, that achieve all of these goals. This monograph offers an invitation to the field of matrix concentration inequalities. It begins with some history of random matrix theory; it describes a flexible model for random matrices that is suitable for many problems; and it discusses the most important matrix concentration results. To demonstrate the value of these techniques, the presentation includes examples drawn from statistics, machine learning, optimization, combinatorics, algorithms, scientific computing, and beyond.

High-Dimensional Probability

High-Dimensional Probability
Author: Roman Vershynin
Publisher: Cambridge University Press
Total Pages: 299
Release: 2018-09-27
Genre: Business & Economics
ISBN: 1108415199

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

Large random matrices

Large random matrices
Author: Alice Guionnet
Publisher: Springer Science & Business Media
Total Pages: 296
Release: 2009-03-25
Genre: Mathematics
ISBN: 3540698965

These lectures emphasize the relation between the problem of enumerating complicated graphs and the related large deviations questions. Such questions are closely related with the asymptotic distribution of matrices.

The Random Matrix Theory of the Classical Compact Groups

The Random Matrix Theory of the Classical Compact Groups
Author: Elizabeth S. Meckes
Publisher: Cambridge University Press
Total Pages: 225
Release: 2019-08-01
Genre: Mathematics
ISBN: 1108317995

This is the first book to provide a comprehensive overview of foundational results and recent progress in the study of random matrices from the classical compact groups, drawing on the subject's deep connections to geometry, analysis, algebra, physics, and statistics. The book sets a foundation with an introduction to the groups themselves and six different constructions of Haar measure. Classical and recent results are then presented in a digested, accessible form, including the following: results on the joint distributions of the entries; an extensive treatment of eigenvalue distributions, including the Weyl integration formula, moment formulae, and limit theorems and large deviations for the spectral measures; concentration of measure with applications both within random matrix theory and in high dimensional geometry; and results on characteristic polynomials with connections to the Riemann zeta function. This book will be a useful reference for researchers and an accessible introduction for students in related fields.

High-Dimensional Statistics

High-Dimensional Statistics
Author: Martin J. Wainwright
Publisher: Cambridge University Press
Total Pages: 571
Release: 2019-02-21
Genre: Business & Economics
ISBN: 1108498027

A coherent introductory text from a groundbreaking researcher, focusing on clarity and motivation to build intuition and understanding.

A Dynamical Approach to Random Matrix Theory

A Dynamical Approach to Random Matrix Theory
Author: László Erdős
Publisher: American Mathematical Soc.
Total Pages: 239
Release: 2017-08-30
Genre: Mathematics
ISBN: 1470436485

A co-publication of the AMS and the Courant Institute of Mathematical Sciences at New York University This book is a concise and self-contained introduction of recent techniques to prove local spectral universality for large random matrices. Random matrix theory is a fast expanding research area, and this book mainly focuses on the methods that the authors participated in developing over the past few years. Many other interesting topics are not included, and neither are several new developments within the framework of these methods. The authors have chosen instead to present key concepts that they believe are the core of these methods and should be relevant for future applications. They keep technicalities to a minimum to make the book accessible to graduate students. With this in mind, they include in this book the basic notions and tools for high-dimensional analysis, such as large deviation, entropy, Dirichlet form, and the logarithmic Sobolev inequality. This manuscript has been developed and continuously improved over the last five years. The authors have taught this material in several regular graduate courses at Harvard, Munich, and Vienna, in addition to various summer schools and short courses. Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.

Introduction to Applied Linear Algebra

Introduction to Applied Linear Algebra
Author: Stephen Boyd
Publisher: Cambridge University Press
Total Pages: 477
Release: 2018-06-07
Genre: Business & Economics
ISBN: 1316518965

A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.