The Generic Chaining
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The Generic Chaining
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Author : Michel Talagrand
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-08
The Generic Chaining written by Michel Talagrand 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 2005-12-08 with Mathematics categories.
Author's Note: The material of this book has been reworked and expanded with a lot more detail and published in the author's 2014 book "Upper and Lower Bounds for Stochastic Processes" (Ergebnisse Vol. 60, ISBN 978-3-642-54074-5). That book is much easier to read and covers everything that is in "The Generic Chaining" book in a more detailed and comprehensible way. ************What is the maximum level a certain river is likely to reach over the next 25 years? (Having experienced three times a few feet of water in my house, I feel a keen personal interest in this question. ) There are many questions of the same nature: what is the likely magnitude of the strongest earthquake to occur during the life of a planned building, or the speed of the strongest wind a suspension bridge will have to stand? All these situations can be modeled in the same manner. The value X of the quantity of interest (be it water t level or speed of wind) at time t is a random variable. What can be said about the maximum value of X over a certain range of t? t A collection of random variables (X ), where t belongs to a certain index t set T, is called a stochastic process, and the topic of this book is the study of the supremum of certain stochastic processes, and more precisely to ?nd upper and lower bounds for the quantity EsupX . (0. 1) t t?T Since T might be uncountable, some care has to be taken to de?ne this quantity. For any reasonable de?nition of Esup X we have t t?T EsupX =sup{EsupX ; F?T,F ?nite} , (0. 2) t t t?T t?F an equality that we will take as the de?nition of the quantity Esup X . t t?T Thus, the crucial case for the estimation of the quantity (0.
Upper And Lower Bounds For Stochastic Processes
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Author : Michel Talagrand
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-02-12
Upper And Lower Bounds For Stochastic Processes written by Michel Talagrand 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 2014-02-12 with Mathematics categories.
The book develops modern methods and in particular the "generic chaining" to bound stochastic processes. This methods allows in particular to get optimal bounds for Gaussian and Bernoulli processes. Applications are given to stable processes, infinitely divisible processes, matching theorems, the convergence of random Fourier series, of orthogonal series, and to functional analysis. The complete solution of a number of classical problems is given in complete detail, and an ambitious program for future research is laid out.
Upper And Lower Bounds For Stochastic Processes
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Author : Michel Talagrand
language : en
Publisher: Springer Nature
Release Date : 2022-01-01
Upper And Lower Bounds For Stochastic Processes written by Michel Talagrand and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-01 with Mathematics categories.
This book provides an in-depth account of modern methods used to bound the supremum of stochastic processes. Starting from first principles, it takes the reader to the frontier of current research. This second edition has been completely rewritten, offering substantial improvements to the exposition and simplified proofs, as well as new results. The book starts with a thorough account of the generic chaining, a remarkably simple and powerful method to bound a stochastic process that should belong to every probabilist’s toolkit. The effectiveness of the scheme is demonstrated by the characterization of sample boundedness of Gaussian processes. Much of the book is devoted to exploring the wealth of ideas and results generated by thirty years of efforts to extend this result to more general classes of processes, culminating in the recent solution of several key conjectures. A large part of this unique book is devoted to the author’s influential work. While many of the results presented are rather advanced, others bear on the very foundations of probability theory. In addition to providing an invaluable reference for researchers, the book should therefore also be of interest to a wide range of readers.
The Generic Chaining
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Author : Michel Talagrand
language : en
Publisher: Springer
Release Date : 2005-03-17
The Generic Chaining written by Michel Talagrand and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-03-17 with Mathematics categories.
The fundamental question of characterizing continuity and boundedness of Gaussian processes goes back to Kolmogorov. After contributions by R. Dudley and X. Fernique, it was solved by the author. This book provides an overview of "generic chaining", a completely natural variation on the ideas of Kolmogorov. It takes the reader from the first principles to the edge of current knowledge and to the open problems that remain in this domain.
Oracle Inequalities In Empirical Risk Minimization And Sparse Recovery Problems
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Author : Vladimir Koltchinskii
language : en
Publisher: Springer
Release Date : 2011-07-29
Oracle Inequalities In Empirical Risk Minimization And Sparse Recovery Problems written by Vladimir Koltchinskii and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-29 with Mathematics categories.
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.
Markov Chains And Stochastic Stability
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Author : Sean Meyn
language : en
Publisher: Cambridge University Press
Release Date : 2009-04-02
Markov Chains And Stochastic Stability written by Sean Meyn 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 2009-04-02 with Mathematics categories.
New up-to-date edition of this influential classic on Markov chains in general state spaces. Proofs are rigorous and concise, the range of applications is broad and knowledgeable, and key ideas are accessible to practitioners with limited mathematical background. New commentary by Sean Meyn, including updated references, reflects developments since 1996.
Learning Java
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Author : Patrick Niemeyer
language : en
Publisher: "O'Reilly Media, Inc."
Release Date : 2002
Learning Java written by Patrick Niemeyer and has been published by "O'Reilly Media, Inc." this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Computers categories.
This updated edition introduces the basics of Java and everything necessary to get up to speed on the new 1.4 version quickly. CD contains the Java 2 SDK for Windows, Linux and Solaris.
Hands On Design Patterns With C
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Author : Fedor G. Pikus
language : en
Publisher: Packt Publishing Ltd
Release Date : 2019-01-30
Hands On Design Patterns With C written by Fedor G. Pikus and has been published by Packt Publishing Ltd this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-30 with Computers categories.
A comprehensive guide with extensive coverage on concepts such as OOP, functional programming, generic programming, and STL along with the latest features of C++ Key FeaturesDelve into the core patterns and components of C++ in order to master application designLearn tricks, techniques, and best practices to solve common design and architectural challenges Understand the limitation imposed by C++ and how to solve them using design patternsBook Description C++ is a general-purpose programming language designed with the goals of efficiency, performance, and flexibility in mind. Design patterns are commonly accepted solutions to well-recognized design problems. In essence, they are a library of reusable components, only for software architecture, and not for a concrete implementation. The focus of this book is on the design patterns that naturally lend themselves to the needs of a C++ programmer, and on the patterns that uniquely benefit from the features of C++, in particular, the generic programming. Armed with the knowledge of these patterns, you will spend less time searching for a solution to a common problem and be familiar with the solutions developed from experience, as well as their advantages and drawbacks. The other use of design patterns is as a concise and an efficient way to communicate. A pattern is a familiar and instantly recognizable solution to specific problem; through its use, sometimes with a single line of code, we can convey a considerable amount of information. The code conveys: "This is the problem we are facing, these are additional considerations that are most important in our case; hence, the following well-known solution was chosen." By the end of this book, you will have gained a comprehensive understanding of design patterns to create robust, reusable, and maintainable code. What you will learnRecognize the most common design patterns used in C++Understand how to use C++ generic programming to solve common design problemsExplore the most powerful C++ idioms, their strengths, and drawbacksRediscover how to use popular C++ idioms with generic programmingUnderstand the impact of design patterns on the program’s performanceWho this book is for This book is for experienced C++ developers and programmers who wish to learn about software design patterns and principles and apply them to create robust, reusable, and easily maintainable apps.
Topics In Random Matrix Theory
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Author : Terence Tao
language : en
Publisher: American Mathematical Soc.
Release Date : 2012-03-21
Topics In Random Matrix Theory written by Terence Tao 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 2012-03-21 with Mathematics categories.
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.