Skip to main content

Optimal attribute-efficient learning of disjunction, parity, and threshold functions

  • Conference paper
  • First Online:
Computational Learning Theory (EuroCOLT 1997)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1208))

Included in the following conference series:

Abstract

Decision trees are a very general computation model. Here the problem is to identify a Boolean function f out of a given set of Boolean functions F by asking for the value of f at adaptively chosen inputs. For classes F consisting of functions which may be obtained from one function g on n inputs by replacing arbitrary n−k inputs by given constants this problem is known as attribute-efficient learning with k essential attributes. Results on general classes of functions are known. More precise and often optimal results are presented for the cases where g is one of the functions disjunction, parity or threshold.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Ahlswede, R. and Wegener, I. (1987). Search Problems. Wiley.

    Google Scholar 

  • Angluin, D. (1988). Queries and concept learning. Machine Learning 2, 319–342.

    Google Scholar 

  • Angluin, D., Hellerstein, L., and Karpinski, M. (1993). Learning read-once formulas with queries. Journal of the ACM 40, 185–210.

    Google Scholar 

  • Bshouty, N. H. and Hellerstein, L. (1996). Attribute-efficient learning in query and mistake-bound models. Proc. of the 9th Conf. on Computational Learning Theory COLT '96, 235–243.

    Google Scholar 

  • Friedman, J. (1984). Constructing (n log n) size monotone formulae for the k-th elementary symmetric polynomial of n Boolean variables. Proc. 25th Symp. on Foundations of Computer Science, 506–515.

    Google Scholar 

  • Håstad, J., Wegener, I., Wurm, N., and Yi, S. (1994). Optimal depth, very small size circuits for symmetric functions in AC 0. Information and Computation 108, 200–211.

    Google Scholar 

  • Heiman, R. and Wigderson, A. (1991). Randomized vs. deterministic decision tree complexity. Computational Complexity 1, 311–329.

    Google Scholar 

  • Hofmeister, T. (1996). Personal communication.

    Google Scholar 

  • Littlestone, N. (1988). Learning quickly when irrelevant attributes abound: a new linear-threshold algorithm. Machine Learning 2, 285–318.

    Google Scholar 

  • Mehlhorn, K. (1982). On the program size of perfect and universal hash functions. Proc. 23rd Symp. on Foundations of Computer Science, 170–175.

    Google Scholar 

  • Motwani, R. and Raghavan, P. (1995). Randomized Algorithms. Cambridge University Press.

    Google Scholar 

  • Naor, M., Schulman, L., and Srinivasan, A. (1995). Splitters and near-optimal decomposition. Proc. 36th Symp. on Foundations of Computer Science, 182–191.

    Google Scholar 

  • Picard, C. (1965). Théorie des Questionnaires. Gauthier-Villars, Paris.

    Google Scholar 

  • Ragde, P. and Widgerson, A. (1991). Linear-size constant-depth polylogthreshold circuits. Information Processing Letters 39, 143–146.

    Google Scholar 

  • Saks, M. and Widgerson, A. (1986). Probabilistic Boolean decision trees and the complexity of evaluating game trees. Proc. of 27th Symp. on Foundations of Computer Science, 29–38.

    Google Scholar 

  • Wegener, I. (1987). The Complexity of Boolean Functions. Wiley-Teubner.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Shai Ben-David

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Uehara, R., Tsuchida, K., Wegener, I. (1997). Optimal attribute-efficient learning of disjunction, parity, and threshold functions. In: Ben-David, S. (eds) Computational Learning Theory. EuroCOLT 1997. Lecture Notes in Computer Science, vol 1208. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62685-9_15

Download citation

  • DOI: https://doi.org/10.1007/3-540-62685-9_15

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62685-5

  • Online ISBN: 978-3-540-68431-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics