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Stochastic Refinement

  • Alireza Tamaddoni-Nezhad
  • Stephen Muggleton
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6489)

Abstract

The research presented in this paper is motivated by the following question. How can the generality order of clauses and the relevant concepts such as refinement be adapted to be used in a stochastic search? To address this question we introduce the concept of stochastic refinement operators and adapt a framework, called stochastic refinement search. In this paper we introduce stochastic refinements of a clause as a probability distribution over a set of clauses. This probability distribution can be viewed as a prior in a stochastic ILP search. We study the properties of a stochastic refinement search as two well known Markovian approaches: 1) Gibbs sampling algorithm and 2) random heuristic search. As a Gibbs sampling algorithm, a stochastic refinement search iteratively generates random samples from the hypothesis space according to a posterior distribution. We show that a minimum sample size can be set so that in each iteration a consistent clause is generated with a high probability. We study the stochastic refinement operators within the framework of random heuristic search and use this framework to characterise stochastic search methods in some ILP systems. We also study a special case of stochastic refinement search where refinement operators are defined with respect to subsumption order relative to a bottom clause. This paper also provided some insights to explain the relative advantages of using stochastic lgg-like operators as in the ILP systems Golem and ProGolem.

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References

  1. 1.
    Gelman, A., Carlin, J., Stern, H., Rubin, D.: Bayesian Data Analysis. Chapman and Hall/CRC, Boca Raton (2003)Google Scholar
  2. 2.
    Haussler, D., Kearns, M., Shapire, R.: Bounds on the sample complexity of Bayesian learning using information theory and the VC dimension. Machine Learning 14(1), 83–113 (1994)MATHGoogle Scholar
  3. 3.
    Mitchell, T.: Machine Learning. McGraw-Hill, New York (1997)MATHGoogle Scholar
  4. 4.
    Muggleton, S., Feng, C.: Efficient induction of logic programs. In: Muggleton, S. (ed.) Inductive Logic Programming, pp. 281–298. Academic Press, London (1992)Google Scholar
  5. 5.
    Muggleton, S., Marginean, F.: Binary refinement. In: Proceedings of Workshop on Logic-Based Artificial Intelligence (1999)Google Scholar
  6. 6.
    Muggleton, S., Santos, J., Tamaddoni-Nezhad, A.: ProGolem: a system based on relative minimal generalisation. In: De Raedt, L. (ed.) ILP 2009. LNCS, vol. 5989, pp. 131–148. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  7. 7.
    Muggleton, S.H.: Stochastic logic programs. In: de Raedt, L. (ed.) Advances in Inductive Logic Programming, pp. 254–264. IOS Press, Amsterdam (1996)Google Scholar
  8. 8.
    Muggleton, S.H., Tamaddoni-Nezhad, A.: QG/GA: A stochastic search for Progol. Machine Learning 70(2-3), 123–133 (2007)Google Scholar
  9. 9.
    Nienhuys-Cheng, S.-H., de Wolf, R.: Foundations of Inductive Logic Programming. LNCS (LNAI), vol. 1228. Springer, Heidelberg (1997)Google Scholar
  10. 10.
    Paes, A., Zelezny, F., Zaverucha, G., Page, D., Srinivasan, A.: ILP Through Propositionalization and Stochastic k-Term DNF Learning. In: Muggleton, S.H., Otero, R., Tamaddoni-Nezhad, A. (eds.) ILP 2006. LNCS (LNAI), vol. 4455, pp. 379–393. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  11. 11.
    Pompe, U., Kovacic, M., Kononenko, I.: SFOIL: Stochastic approach to inductive logic programming. In: Proceedings of the Second Electrotechnical and Computer Science Conference ERK, vol. 93, pp. 189–192. Citeseer (1993)Google Scholar
  12. 12.
    Ruckert, U., Kramer, S.: Stochastic Local Search in k-term DNF Learning. In: Proc. 20th International Conf. on Machine Learning, pp. 648–655 (2003)Google Scholar
  13. 13.
    Serrurier, M., Prade, H., Richard, G.: A simulated annealing framework for ILP. In: Camacho, R., King, R., Srinivasan, A. (eds.) ILP 2004. LNCS (LNAI), vol. 3194, pp. 288–304. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  14. 14.
    Srinivasan, A.: The Aleph Manual. University of Oxford, Oxford (2007)Google Scholar
  15. 15.
    Tamaddoni-Nezhad, A., Muggleton, S.H.: A genetic algorithms approach to ILP. In: Matwin, S., Sammut, C. (eds.) ILP 2002. LNCS (LNAI), vol. 2583, pp. 285–300. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  16. 16.
    Tamaddoni-Nezhad, A., Muggleton, S.H.: The lattice structure and refinement operators for the hypothesis space bounded by a bottom clause. Machine Learning 76(1), 37–72 (2009)CrossRefGoogle Scholar
  17. 17.
    Vose, M.D.: Random heuristic search. Theoretical Computer Science 229(1), 103–142 (1999)MathSciNetMATHCrossRefGoogle Scholar
  18. 18.
    Zelezny, F., Srinivasan, A., Page, D.: Randomised restarted search in ILP. Machine Learning, 64 1(3), 183–208 (2006)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Alireza Tamaddoni-Nezhad
    • 1
  • Stephen Muggleton
    • 1
  1. 1.Department of ComputingImperial College LondonUK

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