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.
Brief description: 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.
Review Quotes: '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