skip to main content
10.1145/130385.130395acmconferencesArticle/Chapter ViewAbstractPublication PagescoltConference Proceedingsconference-collections
Article
Free Access

Learning DNF formulae under classes of probability distributions

Authors Info & Claims
Published:01 July 1992Publication History

ABSTRACT

We show that 2-term DNF formulae are learnable in quadratic time using only a logarithmic number of positive examples if we assume that examples are drawn from a bounded distribution. We also show that k-term DNF formulae are learnable in polynomial time using positive and negative examples drawn from a bounded distribution.

References

  1. 1.D. Angluin, L.G.Valiant, Fast probabilistic algorithms for Hamiltonian circuits and matchings, J. of Comp. and Syst. Sci., 18, 1979.Google ScholarGoogle Scholar
  2. 2.P.L.Bartlett, R.C.Williamson, Investigating the distribution assumptions in the PAC learning model, Proc. COLT 91, Santa Cruz, Morgan and Kaufman, 1991. Google ScholarGoogle ScholarDigital LibraryDigital Library
  3. 3.A.Blum, M.Singh, Learning functions of k terms, Proc. COLT 90, Morgan and Kaufman, 1990. Google ScholarGoogle ScholarDigital LibraryDigital Library
  4. 4.A. Ehrenfeucht, D. Haussler, L. Kearns, L. Valiant, A general lower bound on the number of examples needed for learning. Information and Computation 82, 1989. Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. 5.T.Hancock, Learning monotone k/l formulas on product distribution, Proc. COLT 91, Santa Cruz, Morgan and Kaufman, 1991. Google ScholarGoogle ScholarDigital LibraryDigital Library
  6. 6.D.Haussler, L. Kearns, N.Littlestone, M. Warmuth, Equivalence of models for polynomial learnability, Proc. $nd Work. on Computational learning Theory, Morgan &: Kauffman, 1988. Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. 7.M. Kearns, M. Li, Learning in the presence of malicious errors, Proc. ~Oih A CM Symposium on Theory of Computing, 1988. Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. 8.M. Kearns, M. Li, L. Pitt, L.G. Valiant, On the learnability of boolean formulae, Proc. 19th ACM Symposium on Theory of Computing, 1987. Google ScholarGoogle ScholarDigital LibraryDigital Library
  9. 9.M. Kearns, L.G. Valiant, Cryptographic limitations on learning boolean formulae and finite automata, Proc. ~1th ACM Symposium on Theory of Computing, 1987. Google ScholarGoogle ScholarDigital LibraryDigital Library
  10. 10.L.Ku6era, A.Marchetti-Spaccamela, M.Protasi, On learning bounded DNF formulae under uniform distribution, Information and Computation, to appear; a preliminary version appeared in Proc. 15 th Conference on Automata, Languages and Programming, Lecture Notes in Computer Science, vol. 317, Springer Verlag, 1988. Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. 11.N.Linial, Y.Mansour, N.Nisan, Constant depth circuits, Fourier transform, and learnability, Proc. 30th IEEE Syrup. on Foundations of Computer Science, 1989.Google ScholarGoogle ScholarDigital LibraryDigital Library
  12. 12.L. Pitt, L.G. Valiant, Computational limitations on learning from examples, J. ACM, 35, 1988. Google ScholarGoogle ScholarDigital LibraryDigital Library
  13. 13.L.G. Valiant, A theory of the learnable, Communications ACM, 27, 1984. Google ScholarGoogle ScholarDigital LibraryDigital Library
  14. 14.K.Verbeurgt, Learning DNF under the uniform distribution in quasi-polynomial time, Proc. COLT 90, Morgan and Kaufman, 1990. Google ScholarGoogle ScholarDigital LibraryDigital Library

Index Terms

  1. Learning DNF formulae under classes of probability distributions

        Recommendations

        Comments

        Login options

        Check if you have access through your login credentials or your institution to get full access on this article.

        Sign in
        • Published in

          cover image ACM Conferences
          COLT '92: Proceedings of the fifth annual workshop on Computational learning theory
          July 1992
          452 pages
          ISBN:089791497X
          DOI:10.1145/130385

          Copyright © 1992 ACM

          Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

          Publisher

          Association for Computing Machinery

          New York, NY, United States

          Publication History

          • Published: 1 July 1992

          Permissions

          Request permissions about this article.

          Request Permissions

          Check for updates

          Qualifiers

          • Article

          Acceptance Rates

          Overall Acceptance Rate35of71submissions,49%

        PDF Format

        View or Download as a PDF file.

        PDF

        eReader

        View online with eReader.

        eReader