Constraint Propagation for Efficient Inference in Markov Logic

  • Tivadar Papai
  • Parag Singla
  • Henry Kautz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6876)

Abstract

Many real world problems can be modeled using a combination of hard and soft constraints. Markov Logic is a highly expressive language which represents the underlying constraints by attaching realvalued weights to formulas in first order logic. The weight of a formula represents the strength of the corresponding constraint. Hard constraints are represented as formulas with infinite weight. The theory is compiled into a ground Markov network over which probabilistic inference can be done. For many problems, hard constraints pose a significant challenge to the probabilistic inference engine. However, solving the hard constraints (partially or fully) before hand outside of the probabilistic engine can hugely simplify the ground Markov network and speed probabilistic inference. In this work, we propose a generalized arc consistency algorithm that prunes the domains of predicates by propagating hard constraints. Our algorithm effectively performs unit propagation at a lifted level, avoiding the need to explicitly ground the hard constraints during the pre-processing phase, yielding a potentially exponential savings in space and time. Our approach results in much simplified domains, thereby, making the inference significantly more efficient both in terms of time and memory. Experimental evaluation over one artificial and two real-world datasets show the benefit of our approach.

Keywords

Constraint Satisfaction Problem Constraint Propagation Soft Constraint Hard Constraint Probabilistic Inference 
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.
    Dechter, R.: Constraint Processing. Morgan Kaufmann, San Francisco (2003)MATHGoogle Scholar
  2. 2.
    Domingos, P., Lowd, D.: Markov Logic: An Interface Layer for Artificial Intelligence. Morgan & Claypool, San Rafael (2009)MATHGoogle Scholar
  3. 3.
    Garcia-Molina, H., Ullman, J.D., Widom, J.D.: Database Systems: The Complete Book, 2nd edn. Prentice Hall, Englewood Cliffs (2008)Google Scholar
  4. 4.
    Getoor, L., Taskar, B. (eds.): Introduction to Statistical Relational Learning. MIT Press, Cambridge (2007)MATHGoogle Scholar
  5. 5.
    Gogate, V., Dechter, R.: SampleSearch: Importance sampling in presence of determinism. Artificial Intelligence 175, 694–729 (2011)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Jha, A., Gogate, V., Meliou, A., Suciu, D.: Lifted inference seen from the other side: The tractable features. In: Advances in Neural Information Processing Systems 23 (NIPS 2010), pp. 973–981 (2010)Google Scholar
  7. 7.
    Kautz, H., Selman, B., Jiang, Y.: A general stochastic approach to solving problems with hard and soft constraints. In: Gu, D., Du, J., Pardalos, P. (eds.) The Satisfiability Problem: Theory and Applications. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 35, pp. 573–586. American Mathematical Society, New York (1997)CrossRefGoogle Scholar
  8. 8.
    Kisyński, J., Poole, D.: Constraint processing in lifted probabilistic inference. In: Proceedings of 25th Conference on Uncertainty in Artificial Intelligence (UAI 2009), pp. 292–302 (2009)Google Scholar
  9. 9.
    Kok, S., Sumner, M., Richardson, M., Singla, P., Poon, H., Lowd, D., Wang, J., Nath, A., Domingos, P.: The Alchemy system for statistical relational AI. Tech. rep., Department of Computer Science and Engineering, University of Washington (2010), http://alchemy.cs.washington.edu
  10. 10.
    McCallum, A.: Efficiently inducing features of conditional random fields. In: Proceedings of 19th Conference on Uncertainty in Artificial Intelligence (UAI 2003), Acapulco, Mexico, pp. 403–410 (August 2003)Google Scholar
  11. 11.
    Poon, H., Domingos, P.: Sound and efficient inference with probabilistic and deterministic dependencies. In: Proceedings of the Twenty-First National Conference on Artificial Intelligence (AAAI 2006), Boston, MA (2006)Google Scholar
  12. 12.
    Russell, S., Norvig, P.: Artificial Intelligence: A Modern Approach, 2nd edn. Prentice Hall, Upper Saddle River (2003)MATHGoogle Scholar
  13. 13.
    Sadilek, A., Kautz, H.: Recognizing mutli-agent activities from GPS data. In: Proceedings of the 25th AAAI Conference on Artificial Intelligence, AAAI 2010 (2010)Google Scholar
  14. 14.
    Shavlik, J., Natarajan, S.: Speeding up inference in Markov logic networks by preprocessing to reduce the size of the resulting grounded network. In: Proceedings of the Twenty First International Joint Conference on Artificial Intelligence (IJCAI 2009), Hyederabad, India, pp. 1951–1956 (2009)Google Scholar
  15. 15.
    Singla, P., Domingos, P.: Discriminative training of Markov logic networks. In: Proceedings of the Twentieth National Conference on Artificial Intelligence (AAAI 2005), Pittsburgh, PA, pp. 868–873 (2005)Google Scholar
  16. 16.
    Singla, P., Domingos, P.: Lifted first-order belief propagation. In: Proceedings of the 23rd AAAI Conference on Artificial Intelligence (AAAI 2008), Chicago, IL, pp. 1094–1099 (2008)Google Scholar
  17. 17.
    Taskar, B., Abbeel, P., Koller, D.: Discriminative probabilistic models for relational data. In: Proceedings of 18th Conference on Uncertainty in Artificial Intelligence (UAI 2002), Edmonton, Canada, pp. 485–492 (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Tivadar Papai
    • 1
  • Parag Singla
    • 2
  • Henry Kautz
    • 1
  1. 1.University of RochesterRochesterUSA
  2. 2.University of TexasAustinUSA

Personalised recommendations