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Lower Bounds for the Complexity of Learning Half-Spaces with Membership Queries

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Algorithmic Learning Theory (ALT 1998)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1501))

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Abstract

Exact learning of half-spaces over finite subsets of ℝn from membership queries is considered. We describe the minimum set of labelled examples separating the target concept from all the other ones of the concept class under consideration. For a domain consisting of all integer points of some polytope we give non-trivial lower bounds on the complexity of exact identification of half-spaces. These bounds are near to known upper bounds.

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Author information

Authors and Affiliations

  1. Nizhny Novgorod State University, Gagarin ave. 23, Nizhny Novgorod, 603600, Russia

    Valery N. Shevchenko & Nikolai Yu. Zolotykh

Authors
  1. Valery N. Shevchenko
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  2. Nikolai Yu. Zolotykh
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Editor information

Editors and Affiliations

  1. AG Künstliche Intelligenz - Expertensysteme, UniversitÄt Kaiserslautern, Postfach 3049, D-67653, Kaiserslautern, Germany

    Michael M. Richter

  2. Department of Computer Science, University of Maryland, College Park, MD, 20742, USA

    Carl H. Smith

  3. AG Algorithmischesn Lernen, UniversitÄt Kaiserslautern, Postfach 3049, D-67653, Kaiserslautern, Germany

    Rolf Wiehagen

  4. Graduate School of Information Science and Electrical Engineering Department of Informatics, Kyushu University, Kassuga, 816-8580, Japan

    Thomas Zeugmann

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© 1998 Springer-Verlag Berlin Heidelberg

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Shevchenko, V.N., Zolotykh, N.Y. (1998). Lower Bounds for the Complexity of Learning Half-Spaces with Membership Queries. In: Richter, M.M., Smith, C.H., Wiehagen, R., Zeugmann, T. (eds) Algorithmic Learning Theory. ALT 1998. Lecture Notes in Computer Science(), vol 1501. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49730-7_5

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  • DOI: https://doi.org/10.1007/3-540-49730-7_5

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65013-3

  • Online ISBN: 978-3-540-49730-1

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