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Concentration Inequalities
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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 Concentration Inequalities for Sums and Martingales by : Bernard Bercu
Download or read book Concentration Inequalities for Sums and Martingales written by Bernard Bercu and published by Springer. This book was released on 2015-09-29 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Concentration of Measure Inequalities in Information Theory, Communications, and Coding by : Maxim Raginsky
Download or read book Concentration of Measure Inequalities in Information Theory, Communications, and Coding written by Maxim Raginsky and published by . This book was released on 2014 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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 and Model Selection by : Pascal Massart
Download or read book Concentration Inequalities and Model Selection written by Pascal Massart and published by Springer. This book was released on 2007-04-26 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concentration inequalities have been recognized as fundamental tools in several domains such as geometry of Banach spaces or random combinatorics. They also turn to be essential tools to develop a non asymptotic theory in statistics. This volume provides an overview of a non asymptotic theory for model selection. It also discusses some selected applications to variable selection, change points detection and statistical learning.
Book Synopsis Concentration Inequalities by : Stéphane Boucheron
Download or read book Concentration Inequalities written by Stéphane Boucheron and published by OUP Oxford. This book was released on 2013-02-08 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concentration inequalities for functions of independent random variables is an area of probability theory that has witnessed a great revolution in the last few decades, and has applications in a wide variety of areas such as machine learning, statistics, discrete mathematics, and high-dimensional geometry. Roughly speaking, if a function of many independent random variables does not depend too much on any of the variables then it is concentrated in the sense that with high probability, it is close to its expected value. This book offers a host of inequalities to illustrate this rich theory in an accessible way by covering the key developments and applications in the field. The authors describe 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. A self-contained introduction to concentration inequalities, it includes a survey of concentration of sums of independent random variables, variance bounds, the entropy method, and the transportation method. Deep connections with isoperimetric problems are revealed whilst special attention is paid to applications to the supremum of empirical processes. Written by leading experts in the field and containing extensive exercise sections this book will be an invaluable resource for researchers and graduate students in mathematics, theoretical computer science, and engineering.
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 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.
Book Synopsis Stochastic Inequalities and Applications by : Evariste Giné
Download or read book Stochastic Inequalities and Applications written by Evariste Giné and published by Springer Science & Business Media. This book was released on 2003-10-24 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concentration inequalities, which express the fact that certain complicated random variables are almost constant, have proven of utmost importance in many areas of probability and statistics. This volume contains refined versions of these inequalities, and their relationship to many applications particularly in stochastic analysis. The broad range and the high quality of the contributions make this book highly attractive for graduates, postgraduates and researchers in the above areas.
Book Synopsis Concentration of Measure for the Analysis of Randomized Algorithms by : Devdatt P. Dubhashi
Download or read book Concentration of Measure for the Analysis of Randomized Algorithms written by Devdatt P. Dubhashi and published by Cambridge University Press. This book was released on 2009-06-15 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a coherent and unified account of classical and more advanced techniques for analyzing the performance of randomized algorithms.
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: Written by the creator of the modern theory of random tensors, this book is the first self-contained introductory text to this rapidly developing theory. Starting from notions familiar to the average researcher or PhD student in mathematical or theoretical physics, the book presents in detail the theory and its applications to physics. The recent detections of the Higgs boson at the LHC and gravitational waves at LIGO mark new milestones in Physics confirming long standing predictions of Quantum Field Theory and General Relativity. These two experimental results only reinforce today the need to find an underlying common framework of the two: the elusive theory of Quantum Gravity. Over the past thirty years, several alternatives have been proposed as theories of Quantum Gravity, chief among them String Theory. While these theories are yet to be tested experimentally, key lessons have already been learned. Whatever the theory of Quantum Gravity may be, it must incorporate random geometry in one form or another. This book introduces a framework for studying random geometries in any dimensions. Building on the resounding success of random matrices as theories of random two dimensional surfaces, random tensors are their natural generalization to theories of random geometry in arbitrary dimension. This book shows that many of the celebrated results in random matrices, most notably 't Hooft's 1/N expansion, can be generalized to higher dimensions. It provides a complete and self-contained derivation of the key results on random tensors.
Book Synopsis Advanced Lectures on Machine Learning by : Olivier Bousquet
Download or read book Advanced Lectures on Machine Learning written by Olivier Bousquet and published by Springer. This book was released on 2011-03-22 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: Machine Learning has become a key enabling technology for many engineering applications, investigating scientific questions and theoretical problems alike. To stimulate discussions and to disseminate new results, a summer school series was started in February 2002, the documentation of which is published as LNAI 2600. This book presents revised lectures of two subsequent summer schools held in 2003 in Canberra, Australia, and in Tübingen, Germany. The tutorial lectures included are devoted to statistical learning theory, unsupervised learning, Bayesian inference, and applications in pattern recognition; they provide in-depth overviews of exciting new developments and contain a large number of references. Graduate students, lecturers, researchers and professionals alike will find this book a useful resource in learning and teaching machine learning.
Book Synopsis Probabilistic Methods for Algorithmic Discrete Mathematics by : Michel Habib
Download or read book Probabilistic Methods for Algorithmic Discrete Mathematics written by Michel Habib and published by Springer Science & Business Media. This book was released on 1998-08-19 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Stochastic Inequalities and Applications by : Evariste Giné
Download or read book Stochastic Inequalities and Applications written by Evariste Giné and published by Birkhäuser. This book was released on 2012-12-06 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concentration inequalities, which express the fact that certain complicated random variables are almost constant, have proven of utmost importance in many areas of probability and statistics. This volume contains refined versions of these inequalities, and their relationship to many applications particularly in stochastic analysis. The broad range and the high quality of the contributions make this book highly attractive for graduates, postgraduates and researchers in the above areas.
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 Stochastic Inequalities by : Moshe Shaked
Download or read book Stochastic Inequalities written by Moshe Shaked and published by IMS. This book was released on 1992 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Unbound written by Heather Boushey and published by . This book was released on 2019 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many fear that efforts to address inequality will undermine the economy as a whole. But the opposite is true: rising inequality has become a drag on growth and an impediment to market competition. Heather Boushey breaks down the problem and argues that we can preserve our nation's economic traditions while promoting shared economic growth.
