High-Dimensional Probability pdf epub mobi txt 电子书下载 2024

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Roman Vershynin

Cambridge University Press

2018-9-27

296

USD 69.99

Hardcover

Cambridge Series in Statistical and Probabilistic Mathematics

9781108415194

图书标签: 数学 Statistics 统计学概率论 Machine_Learning DataScience 统计 statistics

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发表于2024-10-03

High-Dimensional Probability epub 下载 mobi 下载 pdf 下载 txt 电子书下载 2024

High-Dimensional Probability pdf epub mobi txt 电子书下载 2024

图书描述

High-dimensional probability offers insight into the behavior of random vectors, random matrices, random subspaces, and objects used to quantify uncertainty in high dimensions. Drawing on ideas from probability, analysis, and geometry, it lends itself to applications in mathematics, statistics, theoretical computer science, signal processing, optimization, and more. It is the first to integrate theory, key tools, and modern applications of high-dimensional probability. Concentration inequalities form the core, and it covers both classical results such as Hoeffding's and Chernoff's inequalities and modern developments such as the matrix Bernstein's inequality. It then introduces the powerful methods based on stochastic processes, including such tools as Slepian's, Sudakov's, and Dudley's inequalities, as well as generic chaining and bounds based on VC dimension. A broad range of illustrations is embedded throughout, including classical and modern results for covariance estimation, clustering, networks, semidefinite programming, coding, dimension reduction, matrix completion, machine learning, compressed sensing, and sparse regression.

High-Dimensional Probability 下载 mobi epub pdf txt 电子书

著者简介

Roman Vershynin is Professor of Mathematics at the University of California, Irvine. He studies random geometric structures across mathematics and data sciences, in particular in random matrix theory, geometric functional analysis, convex and discrete geometry, geometric combinatorics, high-dimensional statistics, information theory, machine learning, signal processing, and numerical analysis. His honors include an Alfred Sloan Research Fellowship in 2005, an invited talk at the International Congress of Mathematicians in Hyderabad in 2010, and a Bessel Research Award from the Humboldt Foundation in 2013. His 'Introduction to the Non-Asymptotic Analysis of Random Matrices' has become a popular educational resource for many new researchers in probability and data science.

图书目录

High-Dimensional Probability pdf epub mobi txt 电子书下载

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用户评价

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写得很棒！

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这个写得浅显易懂, 为了让更多做应用的人读懂吧. 第1-6章写得很好, 后面就有点意犹未尽草草收尾(特别是第11章). 其实应该多写一点几何泛函分析的, 比如john's ellipsoid什么的. Roman Vershynin其实是从几何泛函分析(他的专长)看这些问题, 与之对应的是van handel的notes, 就更加是从概率论的概率论看这些问题(所以有更多的篇幅讨论更精细的lower bound, 还有hypercontractivity这样的内容). 但是几何泛函分析一般不看hypercontractivity(毕竟主要是boolean cube上的), 即便是ledoux和talagrand的书也不提这个.

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19年刚出的书，对工科背景的学生学习理论工具和数学系学生了解应用背景都有参考价值。想要更严谨地了解这些理论可以去读Handel的notes，还没出版但是挂在Princeton他的个人主页上。

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读后感

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这个书居然作者不给errata也是很不user-friendly了. 根据已经出版的版本, 发现的数学错误或typo错误如下: p58, Exercise 3.5.3: 命题不总成立. 可补充条件"A对角线为0或A是PSD". Online version该处已修正. p83, Exercise 4.3.7(b): t log_2 (e/t) 疑应为 t log_2 (1/t). p96, ...

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