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Author: Christian Houdré
Publisher: Springer Science & Business Media
ISBN: 3034804903
Category : Mathematics
Languages : en
Pages : 372
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Book Description
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.
Author: Christian Houdré
Publisher: Springer Science & Business Media
ISBN: 3034804903
Category : Mathematics
Languages : en
Pages : 372
Get Book Here
Book Description
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.
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: Christian Houdré
Publisher: Birkhäuser
ISBN: 3319405195
Category : Mathematics
Languages : en
Pages : 480
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Book Description
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.
Author: Martin J. Wainwright
Publisher: Cambridge University Press
ISBN: 1108498027
Category : Business & Economics
Languages : en
Pages : 571
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Book Description
A coherent introductory text from a groundbreaking researcher, focusing on clarity and motivation to build intuition and understanding.
Author: Christophe Giraud
Publisher: CRC Press
ISBN: 1000408353
Category : Computers
Languages : en
Pages : 410
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Book Description
Praise for the first edition: "[This book] succeeds singularly at providing a structured introduction to this active field of research. ... it is arguably the most accessible overview yet published of the mathematical ideas and principles that one needs to master to enter the field of high-dimensional statistics. ... recommended to anyone interested in the main results of current research in high-dimensional statistics as well as anyone interested in acquiring the core mathematical skills to enter this area of research." —Journal of the American Statistical Association Introduction to High-Dimensional Statistics, Second Edition preserves the philosophy of the first edition: to be a concise guide for students and researchers discovering the area and interested in the mathematics involved. The main concepts and ideas are presented in simple settings, avoiding thereby unessential technicalities. High-dimensional statistics is a fast-evolving field, and much progress has been made on a large variety of topics, providing new insights and methods. Offering a succinct presentation of the mathematical foundations of high-dimensional statistics, this new edition: Offers revised chapters from the previous edition, with the inclusion of many additional materials on some important topics, including compress sensing, estimation with convex constraints, the slope estimator, simultaneously low-rank and row-sparse linear regression, or aggregation of a continuous set of estimators. Introduces three new chapters on iterative algorithms, clustering, and minimax lower bounds. Provides enhanced appendices, minimax lower-bounds mainly with the addition of the Davis-Kahan perturbation bound and of two simple versions of the Hanson-Wright concentration inequality. Covers cutting-edge statistical methods including model selection, sparsity and the Lasso, iterative hard thresholding, aggregation, support vector machines, and learning theory. Provides detailed exercises at the end of every chapter with collaborative solutions on a wiki site. Illustrates concepts with simple but clear practical examples.
Author: Radosław Adamczak
Publisher: Springer Nature
ISBN: 3031269799
Category : Mathematics
Languages : en
Pages : 445
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Book Description
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.
Author: Rick Durrett
Publisher: Cambridge University Press
ISBN: 113949113X
Category : Mathematics
Languages : en
Pages :
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Book Description
This classic introduction to probability theory for beginning graduate students covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a comprehensive treatment concentrating on the results that are the most useful for applications. Its philosophy is that the best way to learn probability is to see it in action, so there are 200 examples and 450 problems. The fourth edition begins with a short chapter on measure theory to orient readers new to the subject.
Author: Nathael Gozlan
Publisher: Springer Nature
ISBN: 3030263916
Category : Mathematics
Languages : en
Pages : 457
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Book Description
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.
Author: Ramsés H. Mena
Publisher: Birkhäuser
ISBN: 3319139843
Category : Mathematics
Languages : en
Pages : 288
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Book Description
This volume features a collection of contributed articles and lecture notes from the XI Symposium on Probability and Stochastic Processes, held at CIMAT Mexico in September 2013. Since the symposium was part of the activities organized in Mexico to celebrate the International Year of Statistics, the program included topics from the interface between statistics and stochastic processes.
Author: Christopher J. Bishop
Publisher: Cambridge University Press
ISBN: 1107134110
Category : Mathematics
Languages : en
Pages : 415
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Book Description
A mathematically rigorous introduction to fractals, emphasizing examples and fundamental ideas while minimizing technicalities.
