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International Conference on Algorithmic Learning Theory

ALT 1998: Algorithmic Learning Theory pp 385–399Cite as

Learning Sub-classes of Monotone DNF on the Uniform Distribution

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

Abstract

In this paper, we give learning algorithms for two new sub-class of DNF formulas: poly-disjoint One-read-once Monotone DNF; and Read-once Factorable Monotone DNF, which is a generalization of Read-once Monotone DNF formulas. Our result uses Fourier analysis to construct the terms of the target formula based on the Fourier coeficients corresponding to these terms. To facilitate this result, we give a novel theorem on the approximation of Read-once Factorable Monotone DNF formulas, in which we show that if a set of terms of the target formula have polynomially small mutually disjoint satisfying sets, then the set of terms can be approximated with small error by the greatest common factor of the set of terms. This approximation theorem may be of independent interest.

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References

  1. Aizenstein, H., Pitt, L.: On the Learnability of Disjunctive Normal Form Formulas. Machine Learning 19 (1995) 183–208

    MATH  Google Scholar 

  2. Angluin, D., Valiant, L.: Fast Probabilistic Algorithms for Hamiltonian Circuits and Matchings. Journal of Computer and Systems Sciences 18 (1979) 155–193

    Article  MATH  MathSciNet  Google Scholar 

  3. Angluin, D., Hellerstein, L., Karpinski, M.: Learning Read-Once Formulas with Queries. Journal of the ACM 40 (1993) 185–210

    Article  MATH  MathSciNet  Google Scholar 

  4. Chernoff, H.: A measure of Asymptotic Eficiency for Tests of a Hypothesis Based on the Sum of Observations. Annals of Mathematical Statistics 23 (1952) 493–509

    Article  MathSciNet  MATH  Google Scholar 

  5. Goldman, S., Kearns, M., Schapire, R.: Exact Identification of Circuits Using Fixed Points of Amplification Functions. Proceedings of the 31st Annual Symposium on Foundations of Computer Science (1990) 193–202

    Google Scholar 

  6. Hancock, T.R.: The Complexity of Learning Formulas and Decision Trees that have Restricted Reads. PhD Thesis, Department of Computer Science, Harvard University, Technical Report TR-15-92 (1992)

    Google Scholar 

  7. Haussler, D., Kearns, M., Littlestone, N., Warmuth, M.K.: Equivalence of Models for Polynomial Learnability. Proceedings of the 1988 Workshop on Computational Learning Theory (1988)

    Google Scholar 

  8. Jackson, J.: An Eficient Membership-Query Algorithm for Learning DNF with Respect to the Uniform Distribution. Proceedings of the 35th Annual Symposium on Foundations of Computer Science (1994) 42–53

    Google Scholar 

  9. Kearns, M., Li, M., Pitt, L., Valiant, L.: On the Learnability of Boolean Formulae. Proceedings of the 19th Annual ACM Symposium on the Theory of Computing (1987) 285–295

    Google Scholar 

  10. Kearns, M., Li, M., Valiant, L.: Learning Boolean Formulas. Journal of the ACM 41-6 (1994) 1298–1328

    Article  MathSciNet  Google Scholar 

  11. Kearns, M., Valiant, L.G.: Learning Boolean Formulae or Finite Automata is As Hard as Factoring. Tech Report TR-14-88, Aiken Computer Laboratory, Harvard University (1988)

    Google Scholar 

  12. Khardon, R.: On using the Fourier transform to learn Disjoint DNF. Information Processing Letters, 49 (1994) 219–222

    Article  MATH  Google Scholar 

  13. Linial, N., Mansour, Y., Nisan, N.: Constant Depth Circuits, Fourier Transform, and Learnability. Proceedings of the 30th Annual IEEE Symposium on Foundations of Computer Science (1989) 574–579

    Google Scholar 

  14. Lund, C., Yannakakis, Y.: On the Hardness of Approximating Minimization Problems. Proceedings of the 25th Annual ACM Symposium on the Theory of Computing (1993) 286–293

    Google Scholar 

  15. Mansour, Y.: An O(n log log n) Learning Algorithm for DNF under the Uniform Distribution. Proceedings of the 5th Annual Workshop on Computational Learning Theory (1992) 53–61

    Google Scholar 

  16. Pitt, L., Valiant, L.: Computational Limits on Learning from Examples. Tech. Rep. TR-05-86, Aiken Computer Laboratory, Harvard University (1986)

    Google Scholar 

  17. Schapire, R.: The Design and Analysis of Eficient Learning Algorithms. Doctoral Dissertation, MIT, The MIT Press (1992)

    Google Scholar 

  18. Valiant, L.: A Theory of the Learnable. Communications of the ACM 27-11 (1984) 1134–1142

    Article  Google Scholar 

  19. Verbeurgt, K.: On the Learnability of DNF Formulae. Master’s Thesis, University of Toronto (1990)

    Google Scholar 

  20. Verbeurgt, K.: Learning DNF Under the Uniform Distribution in Quasipolynomial Time. Proceedings of the 3rd Annual Workshop on Computational Learning Theory (1990) 314–326

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada

    Karsten A. Verbeurgt

Authors
  1. Karsten A. Verbeurgt
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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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Verbeurgt, K.A. (1998). Learning Sub-classes of Monotone DNF on the Uniform Distribution. 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_27

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  • DOI: https://doi.org/10.1007/3-540-49730-7_27

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65013-3

  • Online ISBN: 978-3-540-49730-1

  • eBook Packages: Springer Book Archive

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