Extending Markov Logic to Model Probability Distributions in Relational Domains

  • Dominik Jain
  • Bernhard Kirchlechner
  • Michael Beetz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4667)

Abstract

Markov logic, as a highly expressive representation formalism that essentially combines the semantics of probabilistic graphical models with the full power of first-order logic, is one of the most intriguing representations in the field of probabilistic logical modelling. However, as we will show, models in Markov logic often fail to generalize because the parameters they contain are highly domain-specific. We take the perspective of generative stochastic processes in order to describe probability distributions in relational domains and illustrate the problem in this context by means of simple examples.

We propose an extension of the language that involves the specification of a priori independent attributes and that furthermore introduces a dynamic parameter adjustment whenever a model in Markov logic is instantiated for a certain domain (set of objects). Our extension removes the corresponding restrictions on processes for which models can be learned using standard methods and thus enables Markov logic networks to be practically applied to a far greater class of generative stochastic processes.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Nilsson, N.J.: Probabilistic Logic. Artif. Intell. 28, 71–87 (1986)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Halpern, J.Y.: An analysis of first-order logics of probability. In: Proceedings of IJCAI-89, 11th International Joint Conference on Artificial Intelligence, Detroit, US, pp. 1375–1381 (1989)Google Scholar
  3. 3.
    Bacchus, F.: Representing and Reasoning with Probabilistic Knowledge. MIT Press, Cambridge (1990)Google Scholar
  4. 4.
    Friedman, N., Getoor, L., Koller, D., Pfeffer, A.: Learning probabilistic relational models. In: IJCAI 1999, pp. 1300–1309 (1999)Google Scholar
  5. 5.
    Milch, B., Marthi, B., Russell, S.J., Sontag, D., Ong, D.L., Kolobov, A.: BLOG: Probabilistic Models with Unknown Objects. In: IJCAI, pp. 1352–1359 (2005)Google Scholar
  6. 6.
    Kersting, K., Raedt, L.D.: Bayesian Logic Programming: Theory and Tool. In: Getoor, L., Taskar, B. (eds.) An Introduction to Statistical Relational Learning, MIT Press, Cambridge (2005)Google Scholar
  7. 7.
    Neville, J., Jensen, D.: Dependency networks for relational data. In: ICDM 2004, pp. 170–177. IEEE Computer Society, Los Alamitos (2004)Google Scholar
  8. 8.
    Richardson, M., Domingos, P.: Markov Logic Networks. Mach. Learn. 62(1-2), 107–136 (2006)CrossRefGoogle Scholar
  9. 9.
    Domingos, P., Richardson, M.: Markov Logic: A Unifying Framework for Statistical Relational Learning. In: Proceedings of the ICML 2004 Workshop on Statistical Relational Learning and its Connections to Other Fields, pp. 49–54 (2004)Google Scholar
  10. 10.
    Kok, S., Singla, P., Richardson, M., Domingos, P.: The Alchemy system for statistical relational AI (2004), http://alchemy.cs.washington.edu/
  11. 11.
    Domingos, P.: What’s Missing in AI: The Interface Layer. In: Cohen, P. (ed.) Artificial Intelligence: The First Hundred Years, AAAI Press (2006)Google Scholar
  12. 12.
    Beetz, M., Gedikli, S., Bandouch, J., von Hoyningen-Huene, N., Kirchlechner, B., Perzylo, A.: Visually Tracking Football Games Based on TV Broadcasts. In: IJCAI. Proceedings of the Twentieth International Joint Conference on Artificial Intelligence (2007)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Dominik Jain
    • 1
  • Bernhard Kirchlechner
    • 1
  • Michael Beetz
    • 1
  1. 1.Intelligent Autonomous Systems Group, Department of Informatics, Technische Universität München 

Personalised recommendations