The Christoffel-Darboux Kernel for Data Analysis

ISBN-13: 9781108838061 / Angielski / Twarda / 2022 / 188 str.

Santa Barbara) Putinar Mihai (University of California

Opis

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

Recenzje

'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

Spis treści

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.