concentration-inequalities

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Concentration Inequalities

Author : Stéphane Boucheron
ISBN : 9780199535255
Genre : Mathematics
File Size : 30. 91 MB
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An accessible account of the rich theory surrounding concentration inequalities in probability theory, with applications from machine learning and statistics to high-dimensional geometry. This book introduces key ideas and presents a detailed summary of the state-of-the-art in the area, making it ideal for independent learning and as a reference.

Concentration Inequalities For Sums And Martingales

Author : Bernard Bercu
ISBN : 9783319220994
Genre : Mathematics
File Size : 83. 76 MB
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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.

Concentration Inequalities And Model Selection

Author : Pascal Massart
ISBN : 9783540485032
Genre : Mathematics
File Size : 55. 54 MB
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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.

An Introduction To Matrix Concentration Inequalities

Author : Joel Tropp
ISBN : 1601988389
Genre : Computers
File Size : 46. 18 MB
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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.

Working Paper Series

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ISBN : LCCN:sn86016662
Genre : Management
File Size : 30. 71 MB
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Advanced Lectures On Machine Learning

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ISBN : UOM:39015058886972
Genre : Machine learning
File Size : 57. 16 MB
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Concentration Inequalities In Random Schr?dinger Operators

Author : Christoph Schuhmacher
ISBN : OCLC:1236168757
Genre :
File Size : 56. 87 MB
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Grundbegriffe Der Wahrscheinlichkeitsrechnung

Author : Andrei Nikolaevich Kolmogoroff
ISBN : UCAL:B3534594
Genre : Probabilities
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Annales De L I H P

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ISBN : UOM:39015057370895
Genre : Mathematical statistics
File Size : 87. 31 MB
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Concentration Inequalities For Nonautonomous Stochastic Delay Differential Equations

Author : Daniel Altemeier
ISBN : OCLC:1022218141
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Annales De La Facult? Des Sciences De Toulouse

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ISBN : UOM:39015059073893
Genre : Mathematics
File Size : 77. 63 MB
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Concentration Of Measure For The Analysis Of Randomized Algorithms

Author : Devdatt P. Dubhashi
ISBN : 9781139480994
Genre : Computers
File Size : 84. 11 MB
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Randomized algorithms have become a central part of the algorithms curriculum, based on their increasingly widespread use in modern applications. This book presents a coherent and unified treatment of probabilistic techniques for obtaining high probability estimates on the performance of randomized algorithms. It covers the basic toolkit from the Chernoff–Hoeffding bounds to more sophisticated techniques like martingales and isoperimetric inequalities, as well as some recent developments like Talagrand's inequality, transportation cost inequalities and log-Sobolev inequalities. Along the way, variations on the basic theme are examined, such as Chernoff–Hoeffding bounds in dependent settings. The authors emphasise comparative study of the different methods, highlighting respective strengths and weaknesses in concrete example applications. The exposition is tailored to discrete settings sufficient for the analysis of algorithms, avoiding unnecessary measure-theoretic details, thus making the book accessible to computer scientists as well as probabilists and discrete mathematicians.

Mathematical Reviews

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ISBN : UOM:39015082440762
Genre : Mathematics
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About The Constants In Talagrand S Concentration Inequalities For Empirical Processes

Author : Pascal Massart
ISBN : OCLC:897823574
Genre :
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Estimated Mixing Times

Author : Sharad Chandra Goel
ISBN : CORNELL:31924103605519
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Lectures On Topics In Probability Inequalities

Author : Morris L. Eaton
ISBN : UCAL:B4405673
Genre : Inequalities (Mathematics).
File Size : 62. 98 MB
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Concentration Of Measure Inequalities In Information Theory Communications And Coding

Author : Maxim Raginsky
ISBN : 1601989067
Genre : Computers
File Size : 65. 30 MB
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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.

Cities And Regions In An Enlarging European Union

Author : Ryszard Domański
ISBN : UOM:39015052870931
Genre : Cities and towns
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The Concentration Of Measure Phenomenon

Author : Michel Ledoux
ISBN : 9780821837924
Genre : Mathematics
File Size : 70. 61 MB
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It was undoubtedly a necessary task to collect all the results on the concentration of measure during the past years in a monograph. The author did this very successfully and the book is an important contribution to the topic. It will surely influence further research in this area considerably. The book is very well written, and it was a great pleasure for the reviewer to read it. --Mathematical Reviews The observation of the concentration of measure phenomenon is inspired by isoperimetric inequalities. A familiar example is the way the uniform measure on the standard sphere $S^n$ becomes concentrated around the equator as the dimension gets large. This property may be interpreted in terms of functions on the sphere with small oscillations, an idea going back to Levy. The phenomenon also occurs in probability, as a version of the law of large numbers, due to Emile Borel. This book offers the basic techniques and examples of the concentration of measure phenomenon. The concentration of measure phenomenon was put forward in the early seventies by V. Milman in the asymptotic geometry of Banach spaces. It is of powerful interest in applications in various areas, such as geometry, functional analysis and infinite-dimensional integration, discrete mathematics and complexity theory, and probability theory. Particular emphasis is on geometric, functional, and probabilistic tools to reach and describe measure concentration in a number of settings. The book presents concentration functions and inequalities, isoperimetric and functional examples, spectrum and topological applications, product measures, entropic and transportation methods, as well as aspects of M. Talagrand's deep investigation of concentration in product spaces and its application in discrete mathematics and probability theory, supremum of Gaussian and empirical processes, spin glass, random matrices, etc. Prerequisites are a basic background in measure theory, functional analysis, and probability theory.

Cwi Newsletter

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ISBN : UCAL:B4256304
Genre : Computers
File Size : 69. 87 MB
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