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The Christoffel-Darboux kernel for data analysis

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	The Christoffel-Darboux kernel for data analysisJean Bernard Lasserre, Edouard Pauwels, Mihai Putinar.
作者:	Lasserre, Jean-Bernard.
其他作者:	Pauwels, Edouard.
出版者:	Cambridge :Cambridge University Press,2022.
面頁冊數:	xv, 168 p. :ill., digital ;23 cm.
附註:	Title from publisher's bibliographic system (viewed on 01 Apr 2022).
標題:	Christoffel-Darboux formula.
電子資源:	https://doi.org/10.1017/9781108937078
ISBN:	9781108937078$q(electronic bk.)

The Christoffel-Darboux kernel for data analysis
Lasserre, Jean-Bernard.

The Christoffel-Darboux kernel for data analysis[electronic resource] /Jean Bernard Lasserre, Edouard Pauwels, Mihai Putinar. - Cambridge :Cambridge University Press,2022. - xv, 168 p. :ill., digital ;23 cm. - Cambridge monographs on applied and computational mathematics ;38. - Cambridge monographs on applied and computational mathematics ;27..

Title from publisher's bibliographic system (viewed on 01 Apr 2022).

Foreword / by Francis Bach -- Positive-definite kernels and moment problems -- Univariate Christoffel-Darboux analysis -- Multivariate Christoffel-Darboux analysis -- Singular supports -- Empirical Christoffel-Darboux analysis -- Applications and occurrences in data analysis -- Further applications -- Transforms of Christoffel-Darboux kernels -- Spectral characterization and extensions of the Christoffel function.

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.

ISBN: 9781108937078$q(electronic bk.)Subjects--Topical Terms:

930615
Christoffel-Darboux formula.

LC Class. No.: QA404.5 / .L375 2022

Dewey Class. No.: 515.55

The Christoffel-Darboux kernel for data analysis
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505 0 $a Foreword / by Francis Bach -- Positive-definite kernels and moment problems -- Univariate Christoffel-Darboux analysis -- Multivariate Christoffel-Darboux analysis -- Singular supports -- Empirical Christoffel-Darboux analysis -- Applications and occurrences in data analysis -- Further applications -- Transforms of Christoffel-Darboux kernels -- Spectral characterization and extensions of the Christoffel function.
520 $a 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.
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