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Learning Directed Relational Models with Recursive Dependencies

  • Oliver Schulte
  • Hassan Khosravi
  • Tong Man
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7207)

Abstract

Recently, there has been an increasing interest in generative relational models that represent probabilistic patterns over both links and attributes. A key characteristic of relational data is that the value of a predicate often depends on values of the same predicate for related entities. In this paper we present a new approach to learning directed relational models which utilizes two key concepts: a pseudo likelihood measure that is well defined for recursive dependencies, and the notion of stratification from logic programming. An issue for modelling recursive dependencies with Bayes nets are redundant edges that increase the complexity of learning. We propose a new normal form for 1st-order Bayes nets that removes the redundancy, and prove that assuming stratification, the normal form constraints involve no loss of modelling power. We incorporate these constraints in the learn-and-join algorithm of Khosravi et al., which is a state-of-the art structure learning algorithm that upgrades propositional Bayes net learners for relational data. Emprical evaluation compares our approach to learning recursive dependencies with undirected models (Markov Logic Networks). The Bayes net approach is orders of magnitude faster, and learns more recursive dependencies, which lead to more accurate predictions.

Keywords

Logic Programming Ground Atom Main Functor Main Node Functor Node 
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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References

  1. 1.
    Poole, D.: First-order probabilistic inference. In: Gottlob, G., Walsh, T. (eds.) IJCAI, pp. 985–991. Morgan Kaufmann (2003)Google Scholar
  2. 2.
    Khosravi, H., Schulte, O., Man, T., Xu, X., Bina, B.: Structure learning for Markov logic networks with many descriptive attributes. In: Proceedings of the Twenty-Fourth Conference on Artificial Intelligence (AAAI), pp. 487–493 (2010)Google Scholar
  3. 3.
    Schulte, O.: A tractable pseudo-likelihood function for bayes nets applied to relational data. In: Proceedings of SIAM Conference on Data Mining (SIAM SDM), pp. 462–473 (2011)Google Scholar
  4. 4.
    Fierens, D., Ramon, J., Bruynooghe, M., Blockeel, H.: Learning Directed Probabilistic Logical Models: Ordering-Search Versus Structure-Search. In: Kok, J.N., Koronacki, J., Lopez de Mantaras, R., Matwin, S., Mladenič, D., Skowron, A. (eds.) ECML 2007. LNCS (LNAI), vol. 4701, pp. 567–574. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  5. 5.
    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
  6. 6.
    Friedman, N., Getoor, L., Koller, D., Pfeffer, A.: Learning probabilistic relational models. In: IJCAI, pp. 1300–1309. Springer (1999)Google Scholar
  7. 7.
    Kersting, K., de Raedt, L.: Bayesian logic programming: Theory and tool. In: Introduction to Statistical Relational Learning, pp. 291–318. MIT Press (2007)Google Scholar
  8. 8.
    Apt, K.R., Bezem, M.: Acyclic programs. New Generation Comput. 9, 335–364 (1991)CrossRefGoogle Scholar
  9. 9.
    Fierens, D.: On the Relationship between Logical Bayesian Networks and Probabilistic Logic Programming Based on the Distribution Semantics. In: De Raedt, L. (ed.) ILP 2009. LNCS, vol. 5989, pp. 17–24. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  10. 10.
    Lifschitz, V.: Foundations of logic programming. In: Principles of Knowledge Representation. CSLI Publications (1996)Google Scholar
  11. 11.
    Kok, S., Domingos, P.: Learning markov logic network structure via hypergraph lifting. In: Danyluk, A.P., Bottou, L., Littman, M.L. (eds.) ICML, pp. 64–71. ACM (2009)Google Scholar
  12. 12.
    Kok, S., Domingos, P.: Learning markov logic networks using structural motifs. In: Fürnkranz, J., Joachims, T. (eds.) ICML, pp. 551–558. Omni Press (2010)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Oliver Schulte
    • 1
  • Hassan Khosravi
    • 1
  • Tong Man
    • 1
  1. 1.School of Computing ScienceSimon Fraser UniversityVancouver-BurnabyCanada

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