An Introduction to Matrix Concentration Inequalities: 25 (Foundations and Trends® in Machine Learning) - Softcover

Tropp, Joel A.

Softcover

ISBN 10: 1601988389 ISBN 13: 9781601988386

Verlag: Now Publishers Inc, 2015

Über diesen Titel

Reseña del editor

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.

Reseña del editor

This book is designed to bring random matrix theory to the people. In recent years, random matrices have come to play a major role in computational mathematics, but most of the classical methods for studying random matrices remain the province of experts. Over the last decade, with the advent of matrix concentration inequalities, research has advanced to the point where we can conquer many (formerly) challenging problems with a page or two of arithmetic. This book describes the most successful methods from this area along with some interesting examples that these techniques can illuminate. The results in these pages are intended to inspire future work on applications of random matrices as well as refinements of the matrix concentration inequalities discussed herein. The book presents a coherent body of results that are based on a generalization of the classical Laplace transform method for establishing scalar concentration inequalities.

Details zur Ausgabe

• Verlag: Now Publishers Inc
• Erscheinungsdatum: 2015
• ISBN 10: 1601988389
• ISBN 13: 9781601988386
• Einband: Tapa blanda
• Sprache: Englisch
• Anzahl der Seiten: 252