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An Introduction To Matrix Concentration Inequalities
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Book Synopsis An Introduction to Matrix Concentration Inequalities by : Joel Tropp
Download or read book An Introduction to Matrix Concentration Inequalities written by Joel Tropp and published by . This book was released on 2015-05-27 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Concentration Inequalities by : Stéphane Boucheron
Download or read book Concentration Inequalities written by Stéphane Boucheron and published by Oxford University Press. This book was released on 2013-02-07 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis An Introduction to Random Matrices by : Greg W. Anderson
Download or read book An Introduction to Random Matrices written by Greg W. Anderson and published by Cambridge University Press. This book was released on 2010 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rigorous introduction to the basic theory of random matrices designed for graduate students with a background in probability theory.
Book Synopsis An Introduction to Matrix Concentration Inequalities by : Joel Aaron Tropp
Download or read book An Introduction to Matrix Concentration Inequalities written by Joel Aaron Tropp and published by . This book was released on 2015 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis High-Dimensional Probability by : Roman Vershynin
Download or read book High-Dimensional Probability written by Roman Vershynin and published by Cambridge University Press. This book was released on 2018-09-27 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.
Book Synopsis Large random matrices by : Alice Guionnet
Download or read book Large random matrices written by Alice Guionnet and published by Springer Science & Business Media. This book was released on 2009-03-25 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Random Matrix Theory of the Classical Compact Groups by : Elizabeth S. Meckes
Download or read book The Random Matrix Theory of the Classical Compact Groups written by Elizabeth S. Meckes and published by Cambridge University Press. This book was released on 2019-08-01 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis High-Dimensional Statistics by : Martin J. Wainwright
Download or read book High-Dimensional Statistics written by Martin J. Wainwright and published by Cambridge University Press. This book was released on 2019-02-21 with total page 571 pages. Available in PDF, EPUB and Kindle. Book excerpt: A coherent introductory text from a groundbreaking researcher, focusing on clarity and motivation to build intuition and understanding.
Book Synopsis A Dynamical Approach to Random Matrix Theory by : László Erdős
Download or read book A Dynamical Approach to Random Matrix Theory written by László Erdős and published by American Mathematical Soc.. This book was released on 2017-08-30 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Topics in Random Matrix Theory by : Terence Tao
Download or read book Topics in Random Matrix Theory written by Terence Tao and published by American Mathematical Soc.. This book was released on 2012-03-21 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of random matrix theory has seen an explosion of activity in recent years, with connections to many areas of mathematics and physics. However, this makes the current state of the field almost too large to survey in a single book. In this graduate text, we focus on one specific sector of the field, namely the spectral distribution of random Wigner matrix ensembles (such as the Gaussian Unitary Ensemble), as well as iid matrix ensembles. The text is largely self-contained and starts with a review of relevant aspects of probability theory and linear algebra. With over 200 exercises, the book is suitable as an introductory text for beginning graduate students seeking to enter the field.
Book Synopsis Random Walks on Reductive Groups by : Yves Benoist
Download or read book Random Walks on Reductive Groups written by Yves Benoist and published by Springer. This book was released on 2016-10-20 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: The classical theory of random walks describes the asymptotic behavior of sums of independent identically distributed random real variables. This book explains the generalization of this theory to products of independent identically distributed random matrices with real coefficients. Under the assumption that the action of the matrices is semisimple – or, equivalently, that the Zariski closure of the group generated by these matrices is reductive - and under suitable moment assumptions, it is shown that the norm of the products of such random matrices satisfies a number of classical probabilistic laws. This book includes necessary background on the theory of reductive algebraic groups, probability theory and operator theory, thereby providing a modern introduction to the topic.
Book Synopsis Oracle Inequalities in Empirical Risk Minimization and Sparse Recovery Problems by : Vladimir Koltchinskii
Download or read book Oracle Inequalities in Empirical Risk Minimization and Sparse Recovery Problems written by Vladimir Koltchinskii and published by Springer. This book was released on 2011-07-29 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of these lecture notes is to provide an introduction to the general theory of empirical risk minimization with an emphasis on excess risk bounds and oracle inequalities in penalized problems. In recent years, there have been new developments in this area motivated by the study of new classes of methods in machine learning such as large margin classification methods (boosting, kernel machines). The main probabilistic tools involved in the analysis of these problems are concentration and deviation inequalities by Talagrand along with other methods of empirical processes theory (symmetrization inequalities, contraction inequality for Rademacher sums, entropy and generic chaining bounds). Sparse recovery based on l_1-type penalization and low rank matrix recovery based on the nuclear norm penalization are other active areas of research, where the main problems can be stated in the framework of penalized empirical risk minimization, and concentration inequalities and empirical processes tools have proved to be very useful.
Download or read book Random Tensors written by Razvan Gurau and published by Oxford University Press. This book was released on 2017 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces "Random Tensors," a framework for studying random geometries in any dimension. It provides a complete derivation of the key results in the field. Whatever form a theory of Quantum Gravity may take, it must incorporate random geometry.
Author :Adrian N. Bishop Publisher :Foundations and Trends (R) in Machine Learning ISBN 13 :9781680835069 Total Pages :134 pages Book Rating :4.8/5 (35 download)
Book Synopsis An Introduction to Wishart Matrix Moments by : Adrian N. Bishop
Download or read book An Introduction to Wishart Matrix Moments written by Adrian N. Bishop and published by Foundations and Trends (R) in Machine Learning. This book was released on 2018-12-07 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, written in lecture note style, provides a comprehensive and self-contained introduction to the analysis of Wishart matrix moments. It can act as an introduction to some particular aspects of random matrix theory, or as a self-contained exposition of Wishart matrix moments.
Book Synopsis A Mathematical Introduction to Compressive Sensing by : Simon Foucart
Download or read book A Mathematical Introduction to Compressive Sensing written by Simon Foucart and published by Springer Science & Business Media. This book was released on 2013-08-13 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the intersection of mathematics, engineering, and computer science sits the thriving field of compressive sensing. Based on the premise that data acquisition and compression can be performed simultaneously, compressive sensing finds applications in imaging, signal processing, and many other domains. In the areas of applied mathematics, electrical engineering, and theoretical computer science, an explosion of research activity has already followed the theoretical results that highlighted the efficiency of the basic principles. The elegant ideas behind these principles are also of independent interest to pure mathematicians. A Mathematical Introduction to Compressive Sensing gives a detailed account of the core theory upon which the field is build. With only moderate prerequisites, it is an excellent textbook for graduate courses in mathematics, engineering, and computer science. It also serves as a reliable resource for practitioners and researchers in these disciplines who want to acquire a careful understanding of the subject. A Mathematical Introduction to Compressive Sensing uses a mathematical perspective to present the core of the theory underlying compressive sensing.
Book Synopsis Linear Matrix Inequalities in System and Control Theory by : Stephen Boyd
Download or read book Linear Matrix Inequalities in System and Control Theory written by Stephen Boyd and published by SIAM. This book was released on 1994-01-01 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book the authors reduce a wide variety of problems arising in system and control theory to a handful of convex and quasiconvex optimization problems that involve linear matrix inequalities. These optimization problems can be solved using recently developed numerical algorithms that not only are polynomial-time but also work very well in practice; the reduction therefore can be considered a solution to the original problems. This book opens up an important new research area in which convex optimization is combined with system and control theory, resulting in the solution of a large number of previously unsolved problems.
Book Synopsis The Concentration of Measure Phenomenon by : Michel Ledoux
Download or read book The Concentration of Measure Phenomenon written by Michel Ledoux and published by American Mathematical Soc.. This book was released on 2001 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: The observation of the concentration of measure phenomenon is inspired by isoperimetric inequalities. This book offers the basic techniques and examples of the concentration of measure phenomenon. It presents concentration functions and inequalities, isoperimetric and functional examples, spectrum and topological applications and product measures.
