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Author: Michel Talagrand
Publisher: Springer Science & Business Media
ISBN: 9783540245186
Category : Mathematics
Languages : en
Pages : 240
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Book Description
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.
Author: Michel Talagrand
Publisher: Springer Science & Business Media
ISBN: 9783540245186
Category : Mathematics
Languages : en
Pages : 240
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Book Description
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.
Author: Michel Talagrand
Publisher: Springer Science & Business Media
ISBN: 3642540759
Category : Mathematics
Languages : en
Pages : 630
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Book Description
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.
Author: Michel Talagrand
Publisher: Springer
ISBN: 9783540245186
Category : Mathematics
Languages : en
Pages : 0
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Book Description
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.
Author: Michel Talagrand
Publisher: Springer Nature
ISBN: 3030825957
Category : Mathematics
Languages : en
Pages : 727
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Book Description
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.
Author: Roman Vershynin
Publisher: Cambridge University Press
ISBN: 1108415199
Category : Business & Economics
Languages : en
Pages : 299
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Book Description
An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.
Author: Vladimir Koltchinskii
Publisher: Springer
ISBN: 3642221475
Category : Mathematics
Languages : en
Pages : 254
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Book Description
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.
Author: Cheri Fraker
Publisher: Da Capo Press
ISBN: 078673275X
Category : Family & Relationships
Languages : en
Pages : 416
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Book Description
Initially developed by co-author Cheri Fraker in the course of treating an eleven-year-old who ate nothing but peanut butter, bread, and milk,Food Chainingis a breakthrough approach for dealing with picky eating and feeding problems at any age.Food Chainingemphasizes the relationship between foods in regard to taste, temperature, and texture. InFood Chaining, the internationally known feeding team behind this unique method shows how to help your child enjoy new and nutritious foods, no matter what the nature of his picky eating. The guide also includes information on common food allergies, improving eating skills, advice specific to special needs kids, and a pre-chaining program to help prevent food aversions before they develop.Food Chainingwill help you raise a lifelong healthy eater.
Author: Sean Meyn
Publisher: Cambridge University Press
ISBN: 0521731828
Category : Mathematics
Languages : en
Pages : 623
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Book Description
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.
Author: Dave Gurnell
Publisher: Lulu.com
ISBN: 1365613526
Category :
Languages : en
Pages : 116
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Book Description
The best guide to programming in Shapeless to be found anywhere in the galaxy. Learn how to write code that operates across different types and runs entirely at compile-time using the Shapeless library in Scala. This book demystifies Shapeless, unleashing its power to Scala programmers everywhere.
Author: Hadley Wickham
Publisher: CRC Press
ISBN: 1498759807
Category : Mathematics
Languages : en
Pages : 476
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Book Description
An Essential Reference for Intermediate and Advanced R Programmers Advanced R presents useful tools and techniques for attacking many types of R programming problems, helping you avoid mistakes and dead ends. With more than ten years of experience programming in R, the author illustrates the elegance, beauty, and flexibility at the heart of R. The book develops the necessary skills to produce quality code that can be used in a variety of circumstances. You will learn: The fundamentals of R, including standard data types and functions Functional programming as a useful framework for solving wide classes of problems The positives and negatives of metaprogramming How to write fast, memory-efficient code This book not only helps current R users become R programmers but also shows existing programmers what’s special about R. Intermediate R programmers can dive deeper into R and learn new strategies for solving diverse problems while programmers from other languages can learn the details of R and understand why R works the way it does.
