An Introduction To Matrix Concentration Inequalities
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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.
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.
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.
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.
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.
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.
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.
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.
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.
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.