The Christoffel–Darboux Kernel for Data Analysis

This book presents a comprehensive introduction to the Christoffel–Darboux kernel, highlighting its applications in statistical data analysis and machine learning.

This book provides an accessible overview of the Christoffel–Darboux kernel, presenting it as a novel, powerful, yet simple tool in statistical data analysis. Aimed at non-expert, graduate-level readers, it offers a rapid and informative introduction to an interdisciplinary subject that holds numerous ramifications and intriguing open questions. The authors highlight the significance of the Christoffel–Darboux kernel, a central object in approximation theory, and its potential applications in modern data analysis, including machine learning.

The Christoffel–Darboux Kernel for Data Analysis bridges the gap between classical mathematics and contemporary research. The authors adopt a heuristic, example-based approach, requiring only a basic understanding of functional analysis, probability, and some elementary notions of algebraic geometry. They delve into new results in both pure and applied mathematics, introducing techniques that could significantly impact modern quantitative and qualitative sciences.

Comprehensive notes throughout the book provide historical context, discuss advanced concepts, and include detailed bibliographical references. Researchers and graduate students in mathematics, statistics, engineering, or economics will discover fresh perspectives on traditional themes, along with challenging open problems. This accessible overview illustrates the surprising effectiveness of a simple tool, making it an essential resource for those interested in the intersection of mathematics and data analysis.