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  3. The Christoffel–Darboux Kernel for Data Analysis
  • Cited by 19
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    • Publisher:
      Cambridge University Press
      Publication date:
      31 March 2022
      07 April 2022
      ISBN:
      9781108937078
      9781108838061
      DOI:
      https://doi.org/10.1017/9781108937078
      Dimensions:
      (229 x 152 mm)
      Weight & Pages:
      0.411kg, 186 Pages
      Dimensions:
      Weight & Pages:
      • Subjects:
      Mathematics, Algorithmics, Complexity, Computer Algebra, Computational Geometry, Computational Science, Computer Science
      Series:
      Cambridge Monographs on Applied and Computational Mathematics
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    Subjects:
    Mathematics, Algorithmics, Complexity, Computer Algebra, Computational Geometry, Computational Science, Computer Science
    Series:
    Cambridge Monographs on Applied and Computational Mathematics
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    Book 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.

    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 Source: MathSciNet

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