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The Christoffel–Darboux Kernel for Data Analysis

Mihai Putinar author Jean Bernard Lasserre author Edouard Pauwels author

Format:Hardback

Publisher:Cambridge University Press

Published:7th Apr '22

Currently unavailable, and unfortunately no date known when it will be back

The Christoffel–Darboux Kernel for Data Analysis cover

This accessible overview introduces the Christoffel–Darboux kernel as a novel, simple and efficient tool in statistical data analysis.

This book is the first to give an accessible overview of the Christoffel–Darboux kernel as a novel, powerful, yet simple, tool in statistical data analysis. It offers non-expert, graduate-level readers a rapid and informative introduction to an inter-disciplinary subject, with numerous ramifications and intriguing open questions.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.

'This exciting book shows the potential of Christoffel-Darboux (CD) kernels in the context of data analysis … this book allows one to construct new bridges between approximation theory, operator theory, statistics and data science as well as stressing the links between people interested in such scientific domains.' Francisco Marcellan, MathSciNet

ISBN: 9781108838061

Dimensions: 235mm x 157mm x 13mm

Weight: 411g

188 pages