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Machine Learning

, Volume 62, Issue 1–2, pp 7–31 | Cite as

PRL: A probabilistic relational language

  • Lise GetoorEmail author
  • John Grant
Article

Abstract

In this paper, we describe the syntax and semantics for a probabilistic relational language (PRL). PRL is a recasting of recent work in Probabilistic Relational Models (PRMs) into a logic programming framework. We show how to represent varying degrees of complexity in the semantics including attribute uncertainty, structural uncertainty and identity uncertainty. Our approach is similar in spirit to the work in Bayesian Logic Programs (BLPs), and Logical Bayesian Networks (LBNs). However, surprisingly, there are still some important differences in the resulting formalism; for example, we introduce a general notion of aggregates based on the PRM approaches. One of our contributions is that we show how to support richer forms of structural uncertainty in a probabilistic logical language than have been previously described. Our goal in this work is to present a unifying framework that supports all of the types of relational uncertainty yet is based on logic programming formalisms. We also believe that it facilitates understanding the relationship between the frame-based approaches and alternate logic programming approaches, and allows greater transfer of ideas between them.

Keywords

Probabilistic relational models Logic programming Uncertainty 

References

  1. Bhattacharya, I. & Getoor, L. (2004). Iterative record linkage for cleaning and integration. In 9th ACM SIGMOD Workshop on Research Issues in Data Mining and Knowledge Discovery.Google Scholar
  2. Blockeel, H. (2003). Prolog for bayesian networks: A meta-interpreter approach. In Proceedings of the 2nd Workshop on Multi-Relational Data Mining.Google Scholar
  3. Costa, V. S., Page, D. Qazi, & M. Cussens, J. (2003). CLP (BN): Constraint logic programming for probabilistic knowledge. In Proceedings of the Conference on Uncertainty in Artificial Intelligence. (pp. 517–524).Google Scholar
  4. DeGroot, M. H. (1970)., Optimal Statistical Decisions. New York: McGraw-Hill.zbMATHGoogle Scholar
  5. Fierens, D., Blockeel, H., Bruynooghe, & M. Ramon, J. (2004). Logical bayesian networks. In Proceedings of the 3rd Workshop on Multi-Relational Data Mining.Google Scholar
  6. Fierens, D., Blockeel, H., Bruynooghe, M. & Ramon, J. (2005). Logical bayesian networks and their relation to other probabilistic logical models. In Proceedings of the Inductive Logic Programming Conference.Google Scholar
  7. Friedman, N., Getoor, L., Koller, D. & Pfeffer, A. (1999). Learning probabilistic relational models. In Proceedings of the International Joint Conference on Artificial Intelligence. Stockholm, Sweden (pp. 1300–1307) Morgan Kaufman.Google Scholar
  8. Gaifman, H. (1964). Concerning measures in first order calculi. Israel Journal of Mathematics, 2, 1–18.zbMATHMathSciNetGoogle Scholar
  9. Getoor, L. (2001). Learning Statistical Models of Relational Data. Ph.D. thesis, Stanford University.Google Scholar
  10. Getoor, L., Friedman, N., Koller, D. & Pfeffer, A. (2001a) Learning probabilistic relational models. In S. Dzeroski and N. Lavrac (eds.), Relational Data Mining Kluwer (pp. 307–335).Google Scholar
  11. Getoor, L., Friedman. N., Koller, D. & Taskar, B. (2001b). Learning probabilistic relational models with structural uncertainty. In Proceedings of the International Conference on Machine Learning. Morgan Kaufman (pp. 170—l177).Google Scholar
  12. Getoor, L., Friedman, N., Koller, D. & Taskar, B. (2002). Learning probabilistic models with link structure. Journal of Machine Learning Research, 3, 679–707.MathSciNetCrossRefGoogle Scholar
  13. Getoor, L., Rhee, J., Koller, D. & Small, P. (2004). Understanding tuberculosis epidemiology using probabilistic relational models. Artificial Integllicence in Medicine, 30 (233–256).CrossRefGoogle Scholar
  14. Getoor, L., Segal, E., Taskar, B., & Koller, D. (2001c). Probabilistic models of text and link structure for hypertext classification. In IJCAI Workshop on Text Learning: Beyond Supervision.Google Scholar
  15. Getoor, L., Taskar, B., & Koller, D. (2001d). Using probabilistic models for selectivity estimation. In Proceedings of ACM SIGMOD International Conference on Management of Data. ACM Press (pp. 461–472).Google Scholar
  16. Halpern, J. (1990). An analysis of first-order logics of probability. Artificial Intelligence Journal, 46, 311–350.zbMATHMathSciNetCrossRefGoogle Scholar
  17. Heckerman, D., Meek, C. & Koller, D. (2004). Probabilistic models for relational data. Technical Report 30, Microsoft Research, Microsoft Corporation.Google Scholar
  18. Jaeger, M. (1998). Reasoning about infinite random structures with relational Bayesian networks. In Proceedings of the Knowledge Representations Conference (pp. 570–581).Google Scholar
  19. Kersting, K. & De Raedt, L. (2001a). Adaptive Bayesian logic programs. In Proceedings of the Inductive Logic Programming Conference.Google Scholar
  20. Kersting, K. & De Raedt, L. (2001b). Bayesian logic programs. Technical Report 151, Institute for Computer Science, University of Freiburg, Germany.Google Scholar
  21. Koller, D., McAllester, D. & Pfeffer, A. (1997). Effective Bayesian inference for stochastic programs. In Proceedings of the National Conference on Artificial Intelligence (pp. 740–747).Google Scholar
  22. Koller, D. & Pfeffer, A. (1998). Probabilistic frame-based systems. In Proceedings of American Artificial Intelligence Conference.Google Scholar
  23. Laskey, K. B. (2003). MEBN: A logic for open-world probabilistic reasoning. Technical report, Department of Systems Engineering and Operations Research, George Mason University.Google Scholar
  24. Lloyd, J. W. (1989). Foundations of Logic Programming. Springer.Google Scholar
  25. McCallum, A. & Wellner, B. (2003). Toward conditional models of identity uncertainty with application to proper noun coreference. In IJCAI Workshop on Information Integration on the Web.Google Scholar
  26. Milch, B., Marthi, B. & Russell, S. (2004). BLOG: Relational modeling with unknown objects. In ICML 2004 Workshop on Statistical Relational Learning and Its Connections to Other Fields.Google Scholar
  27. Muggleton, S. (1996). Stochastic logic programs. In Advnaces in Inductive Logic Programming (pp. 254–264).Google Scholar
  28. Pasula, H., Marthi, B., Milch, B., Russell, S. & Shpitser, I. (2003). Identity uncertainty and citation matching. In Advances in Neural Information Processing.Google Scholar
  29. Pasula, H. & Russell, S. (2001). Approximate inference for first-order probabilistic languages. In Proceedings of the International Joint Conference on Artificial Intelligence (pp. 741–748).Google Scholar
  30. Pearl, J. (1988). Probabilistic Reasoning in Intelligent Systems. Morgan Kaufmann.Google Scholar
  31. Pfeffer, A. (2000). Probabilistic reasoning for complex systems. Ph.D. thesis, Stanford University.Google Scholar
  32. Pfeffer, A., Koller, D., Milch, B. & Takusagawa, K. (1999). SPOOK: A system for probabilistic object-oriented knowledge representation. In Proceedings of the Conference on Uncertainty in Artificial Intelligence.Google Scholar
  33. Poole, D. (1993). Probabilistic horn abduction and Bayesian networks. Artificial Intelligence Journal, 64 (1), 81–129.zbMATHCrossRefGoogle Scholar
  34. Russell, S. (2001). Identity uncertainty. In Proceedings of International Fuzzy Systems Association.Google Scholar
  35. Sato, T. & Kameya, Y. (1997) PRISM: A symbolic-statistical modeling language. In Proceedings of the International Joint Conference on Artificial Intelligence (pp. 1330–1335).Google Scholar
  36. Wellman, M., Breese, J. & Goldman, R. (1992). From knowledge bases to decision models. Knowledge Engineering Review, 7 (1), 35–53.CrossRefGoogle Scholar

Copyright information

© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Department of Computer Science and UMIACSUniversity of MarylandCollege Park
  2. 2.Department of Computer and Information Sciences and Department of MathematicsTowson UniversityTowson

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