Advertisement

Fast Parameter Learning for Markov Logic Networks Using Bayes Nets

  • Hassan Khosravi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7842)

Abstract

Markov Logic Networks (MLNs) are a prominent statistical relational model that have been proposed as a unifying framework for statistical relational learning. As part of this unification, their authors proposed methods for converting other statistical relational learners into MLNs. For converting a first order Bayes net into an MLN, it was suggested to moralize the Bayes net to obtain the structure of the MLN and then use the log of the conditional probability table entries to calculate the weight of the clauses. This conversion is exact for converting propositional Markov networks to propositional Bayes nets however, it fails to perform well for the relational case. We theoretically analyze this conversion and introduce new methods of converting a Bayes net into an MLN. An extended imperial evaluation on five datasets indicates that our conversion method outperforms previous methods.

Keywords

Inductive Logic Programming Descriptive Attribute Ground Atom Markov Network Conditional Probability Table 
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. 1.
    Getoor, L., Tasker, B.: Introduction to statistical relational learning. MIT Press (2007)Google Scholar
  2. 2.
    Domingos, P., Richardson, M.: Markov logic: A unifying framework for statistical relational learning. In: [1]Google Scholar
  3. 3.
    Kok, S., Summer, M., Richardson, M., Singla, P., Poon, H., Lowd, D., Wang, J., Domingos, P.: The Alchemy system for statistical relational AI. Technical report, University of Washington, Version 30 (2009)Google Scholar
  4. 4.
    Schulte, O., Khosravi, H.: Learning graphical models for relational data via lattice search. Machine Learning, 41 pages (2012) (to appear)Google Scholar
  5. 5.
    Schulte, O., Khosravi, H.: Learning directed relational models with recursive dependencies. Machine Learning (2012) (Forthcoming. Extended Abstract)Google Scholar
  6. 6.
    Khosravi, H., Schulte, O., Hu, J., Gao, T.: Learning compact markov logic networks with decision trees. Machine Learning (2012) (Forthcoming. Extended Abstract. Acceptance Rate?)Google Scholar
  7. 7.
    Lowd, D., Domingos, P.: Efficient weight learning for Markov logic networks. In: Kok, J.N., Koronacki, J., Lopez de Mantaras, R., Matwin, S., Mladenič, D., Skowron, A. (eds.) PKDD 2007. LNCS (LNAI), vol. 4702, pp. 200–211. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  8. 8.
    Kok, S., Domingos, P.: Learning Markov logic networks using structural motifs. In: ICML, pp. 551–558 (2010)Google Scholar
  9. 9.
    Taskar, B., Abbeel, P., Koller, D.: Discriminative probabilistic models for relational data. In: UAI, pp. 485–492 (2002)Google Scholar
  10. 10.
    Khosravi, H., Schulte, O., Man, T., Xu, X., Bina, B.: Structure learning for Markov logic networks with many descriptive attributes. In: AAAI, pp. 487–493 (2010)Google Scholar
  11. 11.
    Kersting, K., de Raedt, L.: Bayesian logic programming: Theory and tool. In: [1], ch. 10, pp. 291–318Google Scholar
  12. 12.
    Friedman, N., Getoor, L., Koller, D., Pfeffer, A.: Learning probabilistic relational models. In: IJCAI, pp. 1300–1309. Springer (1999)Google Scholar
  13. 13.
    Ramon, J., Croonenborghs, T., Fierens, D., Blockeel, H., Bruynooghe, M.: Generalized ordering-search for learning directed probabilistic logical models. Machine Learning 70, 169–188 (2008)CrossRefGoogle Scholar
  14. 14.
    Pearl, J.: Probabilistic Reasoning in Intelligent Systems. Morgan Kaufmann (1988)Google Scholar
  15. 15.
    Poole, D.: First-order probabilistic inference. In: IJCAI, pp. 985–991 (2003)Google Scholar
  16. 16.
    Boutilier, C., Friedman, N., Goldszmidt, M., Koller, D.: Context-specific independence in bayesian networks. In: UAI, pp. 115–123 (1996)Google Scholar
  17. 17.
    Khosravi, H., Schulte, O., Hu, J., Gao, T.: Learning compact markov logic networks with decision trees. In: Muggleton, S.H., Tamaddoni-Nezhad, A., Lisi, F.A. (eds.) ILP 2011. LNCS, vol. 7207, pp. 20–25. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  18. 18.
    Srinivasan, A., Muggleton, S., Sternberg, M., King, R.: Theories for mutagenicity: A study in first-order and feature-based induction. Artificial Intelligence 85, 277–299 (1996)CrossRefGoogle Scholar
  19. 19.
    Frank, R., Moser, F., Ester, M.: A method for multi-relational classification using single and multi-feature aggregation functions. In: Kok, J.N., Koronacki, J., Lopez de Mantaras, R., Matwin, S., Mladenič, D., Skowron, A. (eds.) PKDD 2007. LNCS (LNAI), vol. 4702, pp. 430–437. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  20. 20.
    She, R., Wang, K., Xu, Y.: Pushing feature selection ahead of join. In: SIAM SDM (2005)Google Scholar
  21. 21.
    Chickering, D.: Optimal structure identification with greedy search. Journal of Machine Learning Research 3, 507–554 (2003)MathSciNetzbMATHGoogle Scholar
  22. 22.
    The Tetrad Group: The Tetrad project (2008), http://www.phil.cmu.edu/projects/tetrad/
  23. 23.
    Domingos, P., Lowd, D.: Markov Logic: An Interface Layer for Artificial Intelligence. Morgan and Claypool Publishers (2009)Google Scholar
  24. 24.
    Poon, H., Domingos, P.: Sound and efficient inference with probabilistic and deterministic dependencies. In: AAAI (2006)Google Scholar
  25. 25.
    Lodhi, H., Muggleton, S.: Is mutagenesis still challenging? In: Inductive Logic Programming, pp. 35–40 (2005)Google Scholar
  26. 26.
    Quinlan, J.: Boosting first-order learning. In: Arikawa, S., Sharma, A.K. (eds.) ALT 1996. LNCS, vol. 1160, pp. 143–155. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  27. 27.
    Sebag, M., Rouveirol, C.: Tractable induction and classification in first order logic via stochastic matching. In: IJCAI, pp. 888–893 (1997)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Hassan Khosravi
    • 1
  1. 1.School of Computing ScienceSimon Fraser UniversityVancouver-BurnabyCanada

Personalised recommendations