The Christoffel-Darboux Kernel for Data Analysis
暫譯: 基於Christoffel-Darboux核的資料分析
Jean Bernard Lasserre , Edouard Pauwels , Mihai Putinar
- 出版商: Cambridge
- 出版日期: 2022-04-07
- 售價: $2,210
- 貴賓價: 9.5 折 $2,100
- 語言: 英文
- 頁數: 188
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 1108838065
- ISBN-13: 9781108838061
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相關分類:
Data Science
海外代購書籍(需單獨結帳)
商品描述
The Christoffel–Darboux kernel, a central object in approximation theory, is shown to have many potential uses in modern data analysis, including applications in machine learning. This is the first book to offer a rapid introduction to the subject, illustrating the surprising effectiveness of a simple tool. Bridging the gap between classical mathematics and current evolving research, the authors present the topic in detail and follow a heuristic, example-based approach, assuming only a basic background in functional analysis, probability and some elementary notions of algebraic geometry. They cover new results in both pure and applied mathematics and introduce techniques that have a wide range of potential impacts on modern quantitative and qualitative science. Comprehensive notes provide historical background, discuss advanced concepts and give detailed bibliographical references. Researchers and graduate students in mathematics, statistics, engineering or economics will find new perspectives on traditional themes, along with challenging open problems.
商品描述(中文翻譯)
克里斯托費爾－達爾布克（Christoffel–Darboux）核是近似理論中的一個核心對象，顯示出在現代數據分析中有許多潛在的應用，包括機器學習的應用。本書是第一本提供該主題快速入門的書籍，展示了一個簡單工具的驚人有效性。作者在詳細介紹該主題的同時，彌合了古典數學與當前不斷發展的研究之間的鴻溝，並採用啟發式的、基於範例的方法，僅假設讀者具備基本的泛函分析、概率論及一些初步的代數幾何概念。他們涵蓋了純數學和應用數學中的新結果，並介紹了對現代定量和定性科學具有廣泛潛在影響的技術。全面的註釋提供了歷史背景，討論了高級概念並給出了詳細的文獻參考。數學、統計學、工程學或經濟學的研究人員和研究生將會在傳統主題上獲得新的視角，並面臨具有挑戰性的開放問題。
作者簡介
ean Bernard Lasserre is Emeritus Directeur de Recherche at the LAAS-CNRS and the Institute of Mathematics at the Université Fédérale Toulouse Midi-Pyrénées. He is Chair of 'Polynomial Optimization' at the Artificial & Natural Intelligence Toulouse Institute. He has won numerous awards for his contributions to the fields of applied mathematics, control, operations research and probability, including the 2015 John von Neumann Theory prize and the 2015 Khachiyan Prize of the INFORMS Optimization Society, for lifetime achievements in the area of optimization. He is the author and co-author of eight books and about 200 articles in international journals.
Edouard Pauwels is Associate Professor at the Institut de Recherche en Informatique de Toulouse, Université Paul Sabatier, and a member of the Artificial & Natural Intelligence Toulouse Institute. His research focuses on numerical optimization and applications in machine learning and data analysis. He received the Bronze Medal of the CNRS in 2021.
Mihai Putinar is Professor in the Mathematics Department at the University of California at Santa Barbara and Professor of Pure Mathematics in the School of Mathematics, Statistics and Physics at Newcastle University. Working in the fields of spectral theory, complex analytic geometry and moment problems, he is the author of three books and more than 200 scientific articles. Over the course of his career, he has been awarded prizes including the Simion Stoilow Prize of the Romanian Academy (1987) and the Romanian National Order of Merit with the rank of Knight (2011).
作者簡介(中文翻譯)
讓·伯納德·拉塞爾（Jean Bernard Lasserre）是法國國家科學研究中心（LAAS-CNRS）及法國聯邦圖盧茲中比利牛斯大學數學研究所的榮譽研究主任。他是圖盧茲人工與自然智慧研究所的「多項式優化」講座教授。他因在應用數學、控制、運籌學和概率領域的貢獻而獲得多項獎項，包括2015年約翰·馮·諾依曼理論獎和2015年INFORMS優化學會的卡恰揚獎，以表彰他在優化領域的終身成就。他是八本書籍的作者和合著者，以及約200篇國際期刊文章的作者。
愛德華·波維爾斯（Edouard Pauwels）是保羅·薩巴提耶大學圖盧茲計算機研究所的副教授，也是圖盧茲人工與自然智慧研究所的成員。他的研究專注於數值優化及其在機器學習和數據分析中的應用。他於2021年獲得法國國家科學研究中心的銅獎。
米哈伊·普提納（Mihai Putinar）是加州大學聖巴巴拉分校數學系的教授，以及紐卡索大學數學、統計與物理學院的純數學教授。他在譜理論、複分析幾何和矩問題等領域工作，是三本書籍和超過200篇科學文章的作者。在他的職業生涯中，他曾獲得包括羅馬尼亞科學院的西米翁·斯托伊洛夫獎（1987年）和羅馬尼亞國家功勳勳章騎士級（2011年）等獎項。
