Learning theory. An approximation theory viewpoint.

*(English)*Zbl 1274.41001
Cambridge Monographs on Applied and Computational Mathematics 24. Cambridge: Cambridge University Press (ISBN 978-0-521-86559-3/hbk; 978-0-511-27166-3/ebook). xii, 224 p. (2007).

Publisher’s description: 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.

##### MSC:

41-02 | Research exposition (monographs, survey articles) pertaining to approximations and expansions |

62-02 | Research exposition (monographs, survey articles) pertaining to statistics |

68-02 | Research exposition (monographs, survey articles) pertaining to computer science |

41A15 | Spline approximation |

41A65 | Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) |

62H30 | Classification and discrimination; cluster analysis (statistical aspects) |

68Q32 | Computational learning theory |

68T05 | Learning and adaptive systems in artificial intelligence |

93B30 | System identification |

93E35 | Stochastic learning and adaptive control |