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A General Dimension for Approximately Learning Boolean Functions

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Book cover Algorithmic Learning Theory (ALT 2002)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2533))

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Abstract

We extend the notion of general dimension, a combinatorial characterization of learning complexity for arbitrary query protocols, to encompass approximate learning. This immediately yields a characterization of the learning complexity in the statistical query model. As a further application, we consider approximate learning of DNF formulas and we derive close upper and lower bounds on the number of statistical queries needed. In particular, we show that with respect to the uniform distribution, and for any constant error parameter ∈ lt; 1/2, the number of statistical queries needed to approximately learn DNF formulas (over n variables and s terms) with tolerance τ = Θ(1/s) is nΘ(log s).

Work supported by the DFG under project KO 1053/1-1

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Author information

Authors and Affiliations

  1. Institut für Informatik, Humboldt-Universität zu Berlin, 10099, Berlin, Germany

    Johannes Köbler & Wolfgang Lindner

Authors
  1. Johannes Köbler
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  2. Wolfgang Lindner
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Editor information

Editors and Affiliations

  1. Dipartimento di Tecnologie dell’Informazione, Università degli Studi di Milano, via Bramante 65, 26013, Crema (CR), Italy

    Nicolò Cesa-Bianchi

  2. Department of Computer Science, Tokyo Institute of Technology, 2-12-1, Ohokayama Meguro Ward, 152-8552, Tokyo, Japan

    Masayuki Numao

  3. Institut für Theoretische Informatik, Universität zu Lübeck, Wallstr. 40, 23560, Lübeck, Germany

    Rüdiger Reischuk

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© 2002 Springer-Verlag Berlin Heidelberg

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Köbler, J., Lindner, W. (2002). A General Dimension for Approximately Learning Boolean Functions. In: Cesa-Bianchi, N., Numao, M., Reischuk, R. (eds) Algorithmic Learning Theory. ALT 2002. Lecture Notes in Computer Science(), vol 2533. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36169-3_13

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  • DOI: https://doi.org/10.1007/3-540-36169-3_13

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00170-6

  • Online ISBN: 978-3-540-36169-5

  • eBook Packages: Springer Book Archive

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