Advertisement

Disjunctions of negated counting functions are efficiently learnable with equivalence queries

  • Zhixiang Chen
Session 6A: Parallel Alg./Learning
  • 115 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 959)

Abstract

One open problem regarding learning counting functions is whether disjunctions of negated counting functions with a constant prime modulus p are efficiently learnable with equivalence queries. We give a positive solution to this problem by showing that for any constant prime p, conjunctions of counting functions with modulus p over the domain Z p n is efficiently learnable with at most (n+1)p−1+1 equivalence queries. We further prove that any disjunctions of counting functions and negated counting functions with a constant prime modulus p over the domain Z p n are also efficiently learnable with at most (n+1)p−1+1 equivalence queries.

Keywords

Linear System Target Function Counting Function Membership Query Equivalence Query 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [A]
    D. Angluin, “Queries and concept learning”, Machine Learning, 2, 1988, pages 319–342.Google Scholar
  2. [BCF]
    A. Bertoni, N. Cesa-Bianchi, G. Fiorino, “Efficient learning with equivalence queries of conjunctions of modulo functions”, submitted to Information Processing Letters, 1995.Google Scholar
  3. [B]
    A. Blum, Personal Communication, 1994.Google Scholar
  4. [BCJ]
    A. Blum, P. Chalasani, J. Jackson, “On learning embedded symmetric concepts”, Proc. of the 6th ACM Annual Conference on Computational Learning Theory, pages 337–346, 1993.Google Scholar
  5. [BCDH]
    N. Bshouty, Z, Chen, S. Decatur, S. Homer, “On the learnability of Z N-DNF formulas”, Proc. of the 8th ACM Annual Conference on Computational Learning Theory, 1995.Google Scholar
  6. [CH]
    Z. Chen, S. Homer, “On learning counting functions with queries” Proc. of the 7th ACM Annual Conference on Computational Learning Theory, pages 218–227, 1994.Google Scholar
  7. [HSW]
    D. Helmbold, R. Sloan, M. Warmuth, “Learning integer lattices”, SIAM J. Comput., 1992, pages 240–266.Google Scholar
  8. [R]
    R. Rivest, Personal Communication, 1994.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Zhixiang Chen
    • 1
  1. 1.Computer Science DepartmentBoston UniversityBostonUSA

Personalised recommendations