The Christoffel–Darboux Kernel for Data Analysis
The Christoffel–Darboux Kernel for Data Analysis
Edouard Pauwels, Institut de Recherche en Informatique, Toulouse
Mihai Putinar, University of California, Santa Barbara
£39.99
GBPThe 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.
- The first comprehensive account of the Christoffel –Darboux kernel, covering a century and a half of discoveries
- Offers a rapid and informative introduction to an inter-disciplinary subject for non-expert readers
- Covers cutting-edge techniques and new results, with a wide range of applications in quantitative and qualitative science
Reviews & endorsements
'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
Product details
April 2022Hardback
9781108838061
188 pages
235 × 157 × 13 mm
0.411kg
Available
Table of Contents
- Foreword Francis Bach
- Preface
- 1. Introduction
- Part I. Historical and Theoretical Background:
- 2. Positive definite kernels and moment problems
- 3. Univariate Christoffel– Darboux analysis
- 4. Multivariate Christoffel– Darboux analysis
- 5. Singular supports
- Part II. Statistics and Applications to Data Analysis:
- 6. Empirical Christoffel–Darboux analysis
- 7. Applications and occurrences in data analysis
- Part III. Complementary Topics:
- 8. Further applications
- 9. Transforms of Christoffel–Darboux kernels
- 10. Spectral characterization and extensions of the Christoffel function
- References
- Index.
