Concentration Inequalities For Sums And Martingales
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Concentration Inequalities For Sums And Martingales
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Author : Bernard Bercu
language : en
Publisher: Springer
Release Date : 2015-09-29
Concentration Inequalities For Sums And Martingales written by Bernard Bercu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-29 with Mathematics categories.
The purpose of this book is to provide an overview of historical and recent results on concentration inequalities for sums of independent random variables and for martingales. The first chapter is devoted to classical asymptotic results in probability such as the strong law of large numbers and the central limit theorem. Our goal is to show that it is really interesting to make use of concentration inequalities for sums and martingales. The second chapter deals with classical concentration inequalities for sums of independent random variables such as the famous Hoeffding, Bennett, Bernstein and Talagrand inequalities. Further results and improvements are also provided such as the missing factors in those inequalities. The third chapter concerns concentration inequalities for martingales such as Azuma-Hoeffding, Freedman and De la Pena inequalities. Several extensions are also provided. The fourth chapter is devoted to applications of concentration inequalities in probability and statistics.
Self Normalized Processes
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Author : Victor H. Peña
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-25
Self Normalized Processes written by Victor H. Peña and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-25 with Mathematics categories.
Self-normalized processes are of common occurrence in probabilistic and statistical studies. A prototypical example is Student's t-statistic introduced in 1908 by Gosset, whose portrait is on the front cover. Due to the highly non-linear nature of these processes, the theory experienced a long period of slow development. In recent years there have been a number of important advances in the theory and applications of self-normalized processes. Some of these developments are closely linked to the study of central limit theorems, which imply that self-normalized processes are approximate pivots for statistical inference. The present volume covers recent developments in the area, including self-normalized large and moderate deviations, and laws of the iterated logarithms for self-normalized martingales. This is the first book that systematically treats the theory and applications of self-normalization.
Concentration Inequalities
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Author : Stéphane Boucheron
language : en
Publisher: Oxford University Press
Release Date : 2013-02-07
Concentration Inequalities written by Stéphane Boucheron and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-07 with Mathematics categories.
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 Matrix Concentration Inequalities
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Author : Joel Tropp
language : en
Publisher:
Release Date : 2015-05-27
An Introduction To Matrix Concentration Inequalities written by Joel Tropp and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-27 with Computers categories.
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.
High Dimensional Probability
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Author : Roman Vershynin
language : en
Publisher: Cambridge University Press
Release Date : 2018-09-27
High Dimensional Probability written by Roman Vershynin and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-27 with Business & Economics categories.
An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.
Probabilistic Methods For Algorithmic Discrete Mathematics
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Author : Michel Habib
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-08-19
Probabilistic Methods For Algorithmic Discrete Mathematics written by Michel Habib and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-08-19 with Computers categories.
The book gives an accessible account of modern pro- babilistic methods for analyzing combinatorial structures and algorithms. Each topic is approached in a didactic manner but the most recent developments are linked to the basic ma- terial. Extensive lists of references and a detailed index will make this a useful guide for graduate students and researchers. Special features included: - a simple treatment of Talagrand inequalities and their applications - an overview and many carefully worked out examples of the probabilistic analysis of combinatorial algorithms - a discussion of the "exact simulation" algorithm (in the context of Markov Chain Monte Carlo Methods) - a general method for finding asymptotically optimal or near optimal graph colouring, showing how the probabilistic method may be fine-tuned to explit the structure of the underlying graph - a succinct treatment of randomized algorithms and derandomization techniques
Concentration Of Measure Inequalities In Information Theory Communications And Coding
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Author : Maxim Raginsky
language : en
Publisher:
Release Date : 2014
Concentration Of Measure Inequalities In Information Theory Communications And Coding written by Maxim Raginsky and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Computers categories.
Concentration of Measure Inequalities in Information Theory, Communications, and Coding focuses on some of the key modern mathematical tools that are used for the derivation of concentration inequalities, on their links to information theory, and on their various applications to communications and coding.
Complex Graphs And Networks
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Author : Fan Chung
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Complex Graphs And Networks written by Fan Chung and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Combinatorial analysis categories.
Graph theory is a primary tool for detecting numerous hidden structures in various information networks, including Internet graphs, social networks, biological networks, or any graph representing relations in massive data sets. This book explains the universal and ubiquitous coherence in the structure of these realistic but complex networks.
Martingale Inequalities Seminar Notes On Recent Progress
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Author : Adriano M. Garsia
language : en
Publisher:
Release Date : 1973
Martingale Inequalities Seminar Notes On Recent Progress written by Adriano M. Garsia and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with Inequalities (Mathematics). categories.
The Concentration Of Measure Phenomenon
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Author : Michel Ledoux
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
The Concentration Of Measure Phenomenon written by Michel Ledoux and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Concentration functions categories.
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.