Description
The 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.
This accessible overview introduces the Christoffel-Darboux kernel as a novel, simple and efficient tool in statistical data analysis.
About the Author
Jean Bernard Lasserre is Emeritus Directeur de Recherche at the LAAS-CNRS and the Institute of Mathematics at the Universite Federale Toulouse Midi-Pyrenees. 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. Edouard Pauwels is Associate Professor at the Institut de Recherche en Informatique de Toulouse, Universite Paul Sabatier, and a member of the Artificial & Natural Intelligence Toulouse Institute. His research focuses on numerical optimization and applications in machine learning and data analysis. He received the Bronze Medal of the CNRS in 2021. Mihai Putinar is Professor in the Mathematics Department at the University of California at Santa Barbara and Professor of Pure Mathematics in the School of Mathematics, Statistics and Physics at Newcastle University. Working in the fields of spectral theory, complex analytic geometry and moment problems, he is the author of three books and more than 200 scientific articles. Over the course of his career, he has been awarded prizes including the Simion Stoilow Prize of the Romanian Academy (1987) and the Romanian National Order of Merit with the rank of Knight (2011).
Reviews
'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
Book Information
ISBN 9781108838061
Author Jean Bernard Lasserre
Format Hardback
Page Count 188
Imprint Cambridge University Press
Publisher Cambridge University Press
Weight(grams) 411g
Dimensions(mm) 235mm * 157mm * 13mm
This accessible overview introduces the Christoffel-Darboux kernel as a novel, simple and efficient tool in statistical data analysis.
About the Author
Jean Bernard Lasserre is Emeritus Directeur de Recherche at the LAAS-CNRS and the Institute of Mathematics at the Universite Federale Toulouse Midi-Pyrenees. 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. Edouard Pauwels is Associate Professor at the Institut de Recherche en Informatique de Toulouse, Universite Paul Sabatier, and a member of the Artificial & Natural Intelligence Toulouse Institute. His research focuses on numerical optimization and applications in machine learning and data analysis. He received the Bronze Medal of the CNRS in 2021. Mihai Putinar is Professor in the Mathematics Department at the University of California at Santa Barbara and Professor of Pure Mathematics in the School of Mathematics, Statistics and Physics at Newcastle University. Working in the fields of spectral theory, complex analytic geometry and moment problems, he is the author of three books and more than 200 scientific articles. Over the course of his career, he has been awarded prizes including the Simion Stoilow Prize of the Romanian Academy (1987) and the Romanian National Order of Merit with the rank of Knight (2011).
Reviews
'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
Book Information
ISBN 9781108838061
Author Jean Bernard Lasserre
Format Hardback
Page Count 188
Imprint Cambridge University Press
Publisher Cambridge University Press
Weight(grams) 411g
Dimensions(mm) 235mm * 157mm * 13mm
