Generative Modeling by PRISM

  • Taisuke Sato
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5649)

Abstract

PRISM is a probabilistic extension of Prolog. It is a high level language for probabilistic modeling capable of learning statistical parameters from observed data. After reviewing it from various viewpoints, we examine some technical details related to logic programming, including semantics, search and program synthesis.

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References

  1. 1.
    Poole, D.: Probabilistic Horn abduction and Bayesian networks. Artificial Intelligence 64(1), 81–129 (1993)CrossRefMATHGoogle Scholar
  2. 2.
    Sato, T.: A statistical learning method for logic programs with distribution semantics. In: Proceedings of the 12th International Conference on Logic Programming (ICLP 1995), pp. 715–729 (1995)Google Scholar
  3. 3.
    Muggleton, S.: Stochastic logic programs. In: De Raedt, L. (ed.) Advances in Inductive Logic Programming, pp. 254–264. IOS Press, Amsterdam (1996)Google Scholar
  4. 4.
    Poole, D.: The independent choice logic for modeling multiple agents under uncertainty. Artificial Intelligence 94(1-2), 7–56 (1997)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Sato, T., Kameya, Y.: Parameter learning of logic programs for symbolic-statistical modeling. Journal of Artificial Intelligence Research 15, 391–454 (2001)MathSciNetMATHGoogle Scholar
  6. 6.
    Kersting, K., De Raedt, L.: Basic principles of learning bayesian logic programs. Technical Report Technical Report No. 174, Institute for Computer Science, University of Freiburg (2002)Google Scholar
  7. 7.
    Blockeel, H.: Prolog for Bayesian networks: a meta-interpreter approach. In: Proceedings of the 2nd International Workshop on Multi-Relational Data Mining (MRDM 2003), pp. 1–13 (2003)Google Scholar
  8. 8.
    Vennekens, J., Verbaeten, S., Bruynooghe, M.: Logic programs with annotated disjunctions. In: Demoen, B., Lifschitz, V. (eds.) ICLP 2004. LNCS, vol. 3132, pp. 431–445. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  9. 9.
    Fierens, D., Blockeel, H., Bruynooghe, M., Ramon, J.: Logical Bayesian networks and their relation to other probabilistic logical models. In: Kramer, S., Pfahringer, B. (eds.) ILP 2005. LNCS, vol. 3625, pp. 121–135. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  10. 10.
    De Raedt, L., Kimmig, A., Toivonen, H.: ProbLog: A probabilistic Prolog and its application in link discoverry. In: Proceedings of the 20th International Joint Conference on Artificial Intelligence (IJCAI 2007), pp. 2468–2473 (2007)Google Scholar
  11. 11.
    Baral, C., Gelfond, M., Rushton, N.: Probabilistic reasoning with answer sets. Theory and Practice of Logic Programming (TPLP) 9(1), 57–144 (2009)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    De Raedt, L., Kersting, K.: Probabilistic inductive logic programming. In: De Raedt, L., Frasconi, P., Kersting, K., Muggleton, S. (eds.) Probabilistic Inductive Logic Programming - Theory and Applications. LNCS, pp. 1–27. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  13. 13.
    Breese, J.S.: Construction of belief and decision networks. Computational Intelligence 8(4), 624–647 (1992)CrossRefGoogle Scholar
  14. 14.
    Koller, D., Pfeffer, A.: Learning probabilities for noisy first-order rules. In: Proceedings of the 15th International Joint Conference on Artificial Intelligence (IJCAI 1997), pp. 1316–1321 (1997)Google Scholar
  15. 15.
    Friedman, N., Getoor, L., Koller, D., Pfeffer, A.: Learning probabilistic relational models. In: Proceedings of the 16th International Joint Conference on Artificial Intelligence (IJCAI 1999), pp. 1300–1309 (1999)Google Scholar
  16. 16.
    Pfeffer, A.: IBAL: A probabilistic rational programming language. In: Proceedings of the 17th International Conference on Artificial Intelligence (IJCAI 2001), pp. 733–740 (2001)Google Scholar
  17. 17.
    Jaeger, J.: Complex probabilistic modeling with recursive relational Bayesian networks. Annals of Mathematics and Artificial Intelligence 32(1-4), 179–220 (2001)MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Getoor, L., Friedman, N., Koller, D., Taskar, B.: Learning Probabilistic Models of Relational Structure. Journal of Machine Learning Research 3, 679–707 (2002)MATHGoogle Scholar
  19. 19.
    Costa, V., Page, D., Qazi, M., Cussens, J.: CLP(BN): Constraint logic programming for probabilistic knowledge. In: Proceedings of the 19th Conference on Uncertainty in Artificial Intelligence (UAI 2003), pp. 517–524 (2003)Google Scholar
  20. 20.
    Milch, B., Marthi, B., Russell, S., Sontag, D., Ong, D., Kolobov, A.: BLOG: Probabilistic models with unknown objects. In: Proceedings of the 19th International Joint Conference on Artificial Intelligence (IJCAI 2005), pp. 1352–1359 (2005)Google Scholar
  21. 21.
    Laskey, K.: MEBN: A logic for open-world probabilistic reasoning. C4I Center Technical Report C4I06-01, George Mason University Department of Systems Engineering and Operations Research (2006)Google Scholar
  22. 22.
    Richardson, M., Domingos, P.: Markov logic networks. Machine Learning 62, 107–136 (2006)CrossRefGoogle Scholar
  23. 23.
    Getoor, L., Grant, J.: PRL: A probabilistic relational language. Journal of Machine Learning 62(1-2), 7–31 (2006)CrossRefGoogle Scholar
  24. 24.
    Getoor, L., Taskar, B. (eds.): Introduction to Statistical Relational Learning. MIT Press, Cambridge (2007)MATHGoogle Scholar
  25. 25.
    Sato, T., Kameya, Y.: Statistical abduction with tabulation. In: Kakas, A., Sadri, F. (eds.) Computational Logic: Logic Programming and Beyond. LNCS (LNAI), vol. 2408, pp. 567–587. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  26. 26.
    Zhou, N.F., Sato, T., Shen, Y.D.: Linear tabling strategies and optimization. Theory and Practice of Logic Programming 8(1), 81–109 (2008)MathSciNetCrossRefMATHGoogle Scholar
  27. 27.
    Sato, T.: First Order Compiler: A deterministic logic program synthesis algorithm. Journal of Symbolic Computation 8, 605–627 (1989)MathSciNetCrossRefMATHGoogle Scholar
  28. 28.
    Fenstad, J.E.: Representation of probabilities defined on first order languages. In: Crossley, J.N. (ed.) Sets, Models and Recursion Theory, pp. 156–172. North-Holland, Amsterdam (1967)CrossRefGoogle Scholar
  29. 29.
    Milch, B., Marthi, B., Sontag, D., Russell, S., Ong, D., Kolobov, A.: Approximate Inference for Infinite Contingent Bayesian Networks. In: Proceedings of the 10th International Workshop on Artificial Intelligence and Statistics (AISTATS 2005), pp. 1352–1359 (2005)Google Scholar
  30. 30.
    Domingos, P., Singla, P.: Markov logic in infinite domains. In: De Raedt, L., Dietterich, T., Getoor, L., Kersting, K., Muggleton, S. (eds.) Probabilistic, Logical and Relational Learning - A Further Synthesis. Dagstuhl Seminar Proceedings, vol. 07161 (2008)Google Scholar
  31. 31.
    Stolcke, A.: An efficient probabilistic context-free parsing algorithm that computes prefix probabilities. Computational Linguistics 21(2), 165–201 (1995)MathSciNetGoogle Scholar
  32. 32.
    Gelfond, M., Lifshcitz, V.: The stable model semantics for logic programming, pp. 1070–1080 (1988)Google Scholar
  33. 33.
    Van Gelder, A., Ross, K., Schlipf, J.: The well-founded semantics for general logic programs. The journal of ACM (JACM) 38(3), 620–650 (1991)MathSciNetMATHGoogle Scholar
  34. 34.
    Tamaki, H., Sato, T.: OLD resolution with tabulation. In: Shapiro, E. (ed.) ICLP 1986. LNCS, vol. 225, pp. 84–98. Springer, Heidelberg (1986)CrossRefGoogle Scholar
  35. 35.
    Sagonas, K., Swift, T., Warren, D.: XSB as an efficient deductive database engine. In: Proceedings of the 1994 ACM SIGMOD International Conference on Management of Data, pp. 442–453 (1994)Google Scholar
  36. 36.
    Ramakrishnan, I., Rao, P., Sagonas, K., Swift, T., Warren, D.: Efficient tabling mechanisms for logic programs. In: Proceedings of the 12th International Conference on Logic Programming (ICLP 1995), pp. 687–711. The MIT Press, Cambridge (1995)Google Scholar
  37. 37.
    Guo, H.F., Gupta, G.: A simple scheme for implementing tabled logic programming systems based on dynamic reordering of alternatives. In: Codognet, P. (ed.) ICLP 2001. LNCS, vol. 2237, pp. 181–196. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  38. 38.
    Sagonas, K., Stuckey, J.: Just enough tabling. In: Proceedings of the 6th ACM SIGPLAN international conference on Principles and practice of declarative programming (PPDP 2004), pp. 78–89. ACM, New York (2004)Google Scholar
  39. 39.
    Rabiner, L.R., Juang, B.: Foundations of Speech Recognition. Prentice-Hall, Englewood Cliffs (1993)MATHGoogle Scholar
  40. 40.
    Baker, J.K.: Trainable grammars for speech recognition. In: Proceedings of Spring Conference of the Acoustical Society of America, pp. 547–550 (1979)Google Scholar
  41. 41.
    Pearl, J.: Probabilistic Reasoning in Intelligent Systems. Morgan Kaufmann, San Francisco (1988)MATHGoogle Scholar
  42. 42.
    Sato, T.: Inside-Outside probability computation for belief propagation. In: Proceedings of the 20th International Joint Conference on Artificial Intelligence (IJCAI 2007), pp. 2605–2610 (2007)Google Scholar
  43. 43.
    Sato, T., Kameya, Y., Kurihara, K.: Variational bayes via propositionalized probability computation in prism. Annals of Mathematics and Artificial Intelligence (to appear)Google Scholar
  44. 44.
    Cussens, J.: Parameter estimation in stochastic logic programs. Machine Learning 44(3), 245–271 (2001)MathSciNetCrossRefMATHGoogle Scholar
  45. 45.
    Sato, T., Kameya, Y.: PRISM: a language for symbolic-statistical modeling. In: Proceedings of the 15th International Joint Conference on Artificial Intelligence (IJCAI 1997), pp. 1330–1335 (1997)Google Scholar
  46. 46.
    Sato, T., Kameya, Y., Zhou, N.F.: Generative modeling with failure in PRISM. In: Proceedings of the 19th International Joint Conference on Artificial Intelligence (IJCAI 2005), pp. 847–852 (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Taisuke Sato
    • 1
  1. 1.Tokyo Institute of TechnologyTokyoJapan

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