High Dimensional Probability
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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.
High Dimensional Probability
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Author : Ernst Eberlein
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
High Dimensional Probability written by Ernst Eberlein and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
What is high dimensional probability? Under this broad name we collect topics with a common philosophy, where the idea of high dimension plays a key role, either in the problem or in the methods by which it is approached. Let us give a specific example that can be immediately understood, that of Gaussian processes. Roughly speaking, before 1970, the Gaussian processes that were studied were indexed by a subset of Euclidean space, mostly with dimension at most three. Assuming some regularity on the covariance, one tried to take advantage of the structure of the index set. Around 1970 it was understood, in particular by Dudley, Feldman, Gross, and Segal that a more abstract and intrinsic point of view was much more fruitful. The index set was no longer considered as a subset of Euclidean space, but simply as a metric space with the metric canonically induced by the process. This shift in perspective subsequently lead to a considerable clarification of many aspects of Gaussian process theory, and also to its applications in other settings.
High Dimensional Probability Ix
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Author : Radosław Adamczak
language : en
Publisher: Springer Nature
Release Date : 2023-06-05
High Dimensional Probability Ix written by Radosław Adamczak and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-05 with Mathematics categories.
This volume collects selected papers from the Ninth High Dimensional Probability Conference, held virtually from June 15-19, 2020. These papers cover a wide range of topics and demonstrate how high-dimensional probability remains an active area of research with applications across many mathematical disciplines. Chapters are organized around four general topics: inequalities and convexity; limit theorems; stochastic processes; and high-dimensional statistics. High Dimensional Probability IX will be a valuable resource for researchers in this area.
High Dimensional Probability V
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Author : David M. Mason
language : en
Publisher:
Release Date : 2009
High Dimensional Probability V written by David M. Mason and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Gaussian processes categories.
High Dimensional Probability
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Author : Evarist Giné
language : en
Publisher: IMS
Release Date : 2006
High Dimensional Probability written by Evarist Giné and has been published by IMS this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
High Dimensional Probability Viii
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Author : Nathael Gozlan
language : en
Publisher: Springer Nature
Release Date : 2019-11-26
High Dimensional Probability Viii written by Nathael Gozlan and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-26 with Mathematics categories.
This volume collects selected papers from the 8th High Dimensional Probability meeting held at Casa Matemática Oaxaca (CMO), Mexico. High Dimensional Probability (HDP) is an area of mathematics that includes the study of probability distributions and limit theorems in infinite-dimensional spaces such as Hilbert spaces and Banach spaces. The most remarkable feature of this area is that it has resulted in the creation of powerful new tools and perspectives, whose range of application has led to interactions with other subfields of mathematics, statistics, and computer science. These include random matrices, nonparametric statistics, empirical processes, statistical learning theory, concentration of measure phenomena, strong and weak approximations, functional estimation, combinatorial optimization, random graphs, information theory and convex geometry. The contributions in this volume show that HDP theory continues to thrive and develop new tools, methods, techniques and perspectives to analyze random phenomena.
High Dimensional Probability Ii
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Author : Evarist Giné
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
High Dimensional Probability Ii written by Evarist Giné 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 2012-12-06 with Mathematics categories.
High dimensional probability, in the sense that encompasses the topics rep resented in this volume, began about thirty years ago with research in two related areas: limit theorems for sums of independent Banach space valued random vectors and general Gaussian processes. An important feature in these past research studies has been the fact that they highlighted the es sential probabilistic nature of the problems considered. In part, this was because, by working on a general Banach space, one had to discard the extra, and often extraneous, structure imposed by random variables taking values in a Euclidean space, or by processes being indexed by sets in R or Rd. Doing this led to striking advances, particularly in Gaussian process theory. It also led to the creation or introduction of powerful new tools, such as randomization, decoupling, moment and exponential inequalities, chaining, isoperimetry and concentration of measure, which apply to areas well beyond those for which they were created. The general theory of em pirical processes, with its vast applications in statistics, the study of local times of Markov processes, certain problems in harmonic analysis, and the general theory of stochastic processes are just several of the broad areas in which Gaussian process techniques and techniques from probability in Banach spaces have made a substantial impact. Parallel to this work on probability in Banach spaces, classical proba bility and empirical process theory were enriched by the development of powerful results in strong approximations.
High Dimensional Probability Vii
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Author : Christian Houdré
language : en
Publisher: Birkhäuser
Release Date : 2016-09-21
High Dimensional Probability Vii written by Christian Houdré and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-21 with Mathematics categories.
This volume collects selected papers from the 7th High Dimensional Probability meeting held at the Institut d'Études Scientifiques de Cargèse (IESC) in Corsica, France. High Dimensional Probability (HDP) is an area of mathematics that includes the study of probability distributions and limit theorems in infinite-dimensional spaces such as Hilbert spaces and Banach spaces. The most remarkable feature of this area is that it has resulted in the creation of powerful new tools and perspectives, whose range of application has led to interactions with other subfields of mathematics, statistics, and computer science. These include random matrices, nonparametric statistics, empirical processes, statistical learning theory, concentration of measure phenomena, strong and weak approximations, functional estimation, combinatorial optimization, and random graphs. The contributions in this volume show that HDP theory continues to thrive and develop new tools, methods, techniques and perspectives to analyze random phenomena.
High Dimensional Probability Iii
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Author : Joergen Hoffmann-Joergensen
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
High Dimensional Probability Iii written by Joergen Hoffmann-Joergensen and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The title High Dimensional Probability is used to describe the many tributaries of research on Gaussian processes and probability in Banach spaces that started in the early 1970s. Many of the problems that motivated researchers at that time were solved. But the powerful new tools created for their solution turned out to be applicable to other important areas of probability. They led to significant advances in the study of empirical processes and other topics in theoretical statistics and to a new approach to the study of aspects of Lévy processes and Markov processes in general. The papers in this book reflect these broad categories. The volume thus will be a valuable resource for postgraduates and reseachers in probability theory and mathematical statistics.
High Dimensional Probability Vi
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Author : Christian Houdré
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-19
High Dimensional Probability Vi written by Christian Houdré 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 2013-04-19 with Mathematics categories.
This is a collection of papers by participants at High Dimensional Probability VI Meeting held from October 9-14, 2011 at the Banff International Research Station in Banff, Alberta, Canada. High Dimensional Probability (HDP) is an area of mathematics that includes the study of probability distributions and limit theorems in infinite-dimensional spaces such as Hilbert spaces and Banach spaces. The most remarkable feature of this area is that it has resulted in the creation of powerful new tools and perspectives, whose range of application has led to interactions with other areas of mathematics, statistics, and computer science. These include random matrix theory, nonparametric statistics, empirical process theory, statistical learning theory, concentration of measure phenomena, strong and weak approximations, distribution function estimation in high dimensions, combinatorial optimization, and random graph theory. The papers in this volume show that HDP theory continues to develop new tools, methods, techniques and perspectives to analyze the random phenomena. Both researchers and advanced students will find this book of great use for learning about new avenues of research.