Learning Discriminant Rules as a Minimal Saturation Search

  • Matthieu Lopez
  • Lionel Martin
  • Christel Vrain
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6489)


It is well known that for certain relational learning problems, traditional top-down search falls into blind search. Recent works in Inductive Logic Programming about phase transition and crossing plateau show that no general solution can face to all these difficulties. In this context, we introduce the notion of “minimal saturation” to build non-blind refinements of hypotheses in a bidirectional approach.

We present experimental results of this approach on some benchmarks inspired by constraint satisfaction problems. These problems can be specified in first order logic but most existing ILP systems fail to learn a correct definition, especially because they fall into blind search.


Constraint Programming Constraint Satisfaction Problem Target Concept Inductive Logic Programming Constraint Problem 
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.


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  1. 1.
    Alphonse, É., Osmani, A.: A model to study phase transition and plateaus in relational learning. In: Železný, F., Lavrač, N. (eds.) ILP 2008. LNCS (LNAI), vol. 5194, pp. 6–23. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  2. 2.
    Alphonse, É., Osmani, A.: On the connection between the phase transition of the covering test and the learning success rate in ilp. Machine Learning 70(2-3), 135–150 (2008)CrossRefGoogle Scholar
  3. 3.
    Alphonse, E., Osmani, A.: Empirical study of relational learning algorithms in the phase transition framework. In: Buntine, W., Grobelnik, M., Mladenić, D., Shawe-Taylor, J. (eds.) ECML PKDD 2009. LNCS, vol. 5781, pp. 51–66. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  4. 4.
    Alphonse, É., Rouveirol, C.: Lazy propositionalisation for relational learning. In: Horn, W. (ed.) ECAI, pp. 256–260. IOS Press, Amsterdam (2000)Google Scholar
  5. 5.
    Alphonse, É., Rouveirol, C.: Extension of the top-down data-driven strategy to ILP. In: Muggleton, S.H., Otero, R.P., Tamaddoni-Nezhad, A. (eds.) ILP 2006. LNCS (LNAI), vol. 4455, pp. 49–63. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  6. 6.
    Botta, M., Giordana, A., Saitta, L., Sebag, M.: Relational learning: Hard problems and phase transitions. In: Lamma, E., Mello, P. (eds.) AI*IA 1999. LNCS (LNAI), vol. 1792, pp. 178–189. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  7. 7.
    Botta, M., Giordana, A., Saitta, L., Sebag, M.: Relational learning as search in a critical region. Journal of Machine Learning Research 4, 431–463 (2003)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Lallouet, A., Lopez, M., Martin, L., Vrain, C.: On learning constraint problems. In: 22th IEEE International Conference on Tools with Artificial Intelligence, ICTAI 2010 (2010)Google Scholar
  9. 9.
    Lodhi, H., Muggleton, S.: Is mutagenesis still challenging. In: ILP - Late-Breaking Papers (2005)Google Scholar
  10. 10.
    Muggleton, S.: Inverse entailment and progol. New Generation Computing, Special issue on Inductive Logic Programming 13(3-4), 245–286 (1995)Google Scholar
  11. 11.
    Ross Quinlan, J., Mike Cameron-Jones, R.: Foil: A midterm report. In: Brazdil, P.B. (ed.) ECML 1993. LNCS, vol. 667, Springer, Heidelberg (1993)Google Scholar
  12. 12.
    De Raedt, L., Van Laer, W.: Inductive constraint logic. In: ALT, pp. 80–94 (1995)Google Scholar
  13. 13.
    Rouveirol, C.: Extensions of inversion of resolution applied to theory completion. In: Muggleton, S. (ed.) ILP, pp. 63–92. AP (1992)Google Scholar
  14. 14.
    Serra, A., Giordana, A., Saitta, L.: Learning on the phase transition edge. In: IJCAI, pp. 921–926 (2001)Google Scholar
  15. 15.
    Srinivasan, A.: A learning engine for proposing hypotheses (Aleph),
  16. 16.
    Tang, L.P.R.: Integrating top-down and bottom-up approaches in inductive logic programming: applications in natural language processing and relational data mining. PhD thesis, University of Texas, Supervisor-Mooney (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Matthieu Lopez
    • 1
  • Lionel Martin
    • 1
  • Christel Vrain
    • 1
  1. 1.LIFOUniversity of OrléansOrléansFrance

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