High-Dimensional Probability: An Introduction with Applications in Data Science (Hardcover)

Roman Vershynin

  • 出版商: Cambridge
  • 出版日期: 2018-09-27
  • 售價: $2,930
  • 貴賓價: 9.5$2,784
  • 語言: 英文
  • 頁數: 296
  • 裝訂: Hardcover
  • ISBN: 1108415199
  • ISBN-13: 9781108415194
  • 相關分類: Data Science
  • 海外代購書籍(需單獨結帳)
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商品描述

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.

商品描述(中文翻譯)

高維機率提供了對於隨機向量、隨機矩陣、隨機子空間以及用於量化高維度不確定性的物件行為的洞察。它借鑒了機率、分析和幾何的思想,適用於數學、統計學、理論計算機科學、信號處理、優化等領域的應用。這是第一本整合了高維機率的理論、關鍵工具和現代應用的書籍。集中不等式是其核心,涵蓋了包括Hoeffding和Chernoff不等式在內的經典結果,以及矩陣Bernstein不等式等現代發展。然後介紹了基於隨機過程的強大方法,包括Slepian、Sudakov和Dudley不等式等工具,以及基於VC維度的通用鏈接和界限。全書融入了廣泛的示例,包括協方差估計、聚類、網絡、半定規劃、編碼、降維、矩陣補全、機器學習、壓縮感知和稀疏回歸的經典和現代結果。