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.
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.Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
Jean Bernard Lasserre is Emeritus Directeur de Recherche at the LAAS-CNRS and the Institute of Mathematics at the Université Fédérale Toulouse Midi-Pyrénées. He is Chair of 'Polynomial Optimization' at the Artificial & Natural Intelligence Toulouse Institute. He has won numerous awards for his contributions to the fields of applied mathematics, control, operations research and probability, including the 2015 John von Neumann Theory prize and the 2015 Khachiyan Prize of the INFORMS Optimization Society, for lifetime achievements in the area of optimization. He is the author and co-author of eight books and about 200 articles in international journals.
Inhaltsangabe
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.
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.
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