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On learning disjunctions of zero-one threshold functions with queries

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Algorithmic Learning Theory (ALT 1997)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1316))

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Abstract

We investigate the learnability of the class κ-ZOTFn of disjunctions of (at most) κk zero-one threshold functions with queries. We describe a poly(n)-time algorithm that identifies any concept from 2-ZOTFn with one proper equivalence query and O(n 2) membership queries, propose some techniques that work for larger κ in special cases and via a case analysis obtain an algorithm for learning 3-ZOTFn with O(n 5) membership and proper equivalence queries. Then we prove non-learnability results via exhibiting bounds κ(n) for which polynomial time learnability of κ(n)-ZOTFn with proper equivalence and membership queries becomes presumably intractable. Finally, we provide results on learning a single zero-one threshold function with queries: an efficient membership query algorithm for the case when the target has few relevant attributes, and a parallel algorithm that identifies a zero-one threshold function in constant time with O(n) membership queries.

On leave from Comenius University, Bratislava, Slovakia. Partially supported by the Academy of Finland under grant 22586, and by the Slovak Grant Agency VEGA under grant 14315.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Helsinki, Teollisuuskatu 23, P.O. Box 26, FIN-00014, Finland

    Tibor Hegedüs

  2. Department of Computer Science, Stanford University, Gates Building, 94305, Stanford, CA, USA

    Piotr Indyk

Authors
  1. Tibor Hegedüs
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  2. Piotr Indyk
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Ming Li Akira Maruoka

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© 1997 Springer-Verlag Berlin Heidelberg

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Hegedüs, T., Indyk, P. (1997). On learning disjunctions of zero-one threshold functions with queries. In: Li, M., Maruoka, A. (eds) Algorithmic Learning Theory. ALT 1997. Lecture Notes in Computer Science, vol 1316. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63577-7_60

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  • DOI: https://doi.org/10.1007/3-540-63577-7_60

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63577-2

  • Online ISBN: 978-3-540-69602-5

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