The Christoffel-Darboux Kernel for Data Analysis

The Christoffel–Darboux kernel is a crucial tool in approximation theory and has numerous applications in modern data analysis, such as machine learning. This book provides a rapid introduction to the subject, demonstrating the effectiveness of a simple tool through detailed explanations and example-based approaches. It bridges the gap between classical mathematics and current research, covering new results in pure and applied mathematics and introducing techniques with potential impacts on quantitative and qualitative science. Comprehensive notes offer historical background, advanced concepts, and detailed bibliographical references. Researchers and graduate students in mathematics, statistics, engineering, or economics will find new perspectives on traditional themes and challenging open problems.

Format: Hardback
Length: 188 pages
Publication date: 07 April 2022
Publisher: Cambridge University Press

The Christoffel–Darboux kernel, a fundamental concept in approximation theory, holds immense potential for modern data analysis, particularly in the realm of machine learning. This groundbreaking work is the first to provide a comprehensive and rapid introduction to this topic, showcasing the remarkable effectiveness of a straightforward tool. By bridging the gap between classical mathematics and the rapidly evolving research landscape, the authors present the subject in depth, employing a heuristic, example-based approach that assumes a basic understanding of functional analysis, probability, and some elementary concepts of algebraic geometry. They cover a wide range of novel results in both pure and applied mathematics, while also introducing techniques that have the potential to revolutionize modern quantitative and qualitative science. Extensive notes offer a historical background, delve into advanced concepts, and provide comprehensive bibliographical references for further exploration. Researchers and graduate students in mathematics, statistics, engineering, or economics will discover fresh perspectives on traditional themes, as well as challenging open problems that will stimulate their intellectual curiosity.

ISBN-13: 9781108838061
Edition number: New ed