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Learning Theory
An Approximation Theory Viewpoint

$72.00 USD

Part of Cambridge Monographs on Applied and Computational Mathematics

  • Date Published: March 2007
  • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • format: Adobe eBook Reader
  • isbn: 9780511271663

$ 72.00 USD
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About the Authors
  • The goal of learning theory is to approximate a function from sample values. To attain this goal learning theory draws on a variety of diverse subjects, specifically statistics, approximation theory, and algorithmics. Ideas from all these areas blended to form a subject whose many successful applications have triggered a rapid growth during the last two decades. This is the first book to give a general overview of the theoretical foundations of the subject emphasizing the approximation theory, while still giving a balanced overview. It is based on courses taught by the authors, and is reasonably self-contained so will appeal to a broad spectrum of researchers in learning theory and adjacent fields. It will also serve as an introduction for graduate students and others entering the field, who wish to see how the problems raised in learning theory relate to other disciplines.

    • Balanced view, with rigorous approach to issues of practical importance
    • First book to adopt the approximation theory viewpoint
    • Will appeal to mathematicians as well as statisticians and computer scientists
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    Reviews & endorsements

    'The book is well suited for its target audience, which includes researchers and graduate students. They will, no doubt, be reassured to find that each chapter closes with a collection of references and additional remarks, which place the preceding information in a wider context. … Overall, this text is another excellent addition to the Applied and Computational Mathematics series published by Cambridge University Press. It complements other titles in the series without duplicating material and should be of value to anyone interested in learning theory or a neighbouring field.' Mathematics Today

    '… the book under review focuses on the mathematical foundations of learning theory. It is an excellent monograph on the subject. A major novelty is the focus on the point of view of approximation. This distinguishes the book from the majority of previous works on learning theory, which share a prevalent statistics/computer science flavor. However, this doesn't mean at all that the monograph is written only for 'approximation people'. On the contrary, it nicely provides a general overview of the theoretical foundations of the subject also to a broad spectrum of researchers in learning and related fields.' Mathematical Reviews

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    Product details

    • Date Published: March 2007
    • format: Adobe eBook Reader
    • isbn: 9780511271663
    • contains: 20 b/w illus.
    • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • Table of Contents

    Preface
    Foreword
    1. The framework of learning
    2. Basic hypothesis spaces
    3. Estimating the sample error
    4. Polynomial decay approximation error
    5. Estimating covering numbers
    6. Logarithmic decay approximation error
    7. On the bias-variance problem
    8. Regularization
    9. Support vector machines for classification
    10. General regularized classifiers
    Bibliography
    Index.

  • Authors

    Felipe Cucker, City University of Hong Kong
    Felipe Cucker is a Professor of Mathematics at the City University of Hong Kong.

    Ding Xuan Zhou, City University of Hong Kong
    Ding Xuan Zhou is an Associate Professor in the Department of Mathematics at the City University of Hong Kong.

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