Machine Learning

, Volume 70, Issue 2–3, pp 151–168 | Cite as

Compressing probabilistic Prolog programs

  • L. De Raedt
  • K. Kersting
  • A. Kimmig
  • K. Revoredo
  • H. Toivonen
Article

Abstract

ProbLog is a recently introduced probabilistic extension of Prolog (De Raedt, et al. in Proceedings of the 20th international joint conference on artificial intelligence, pp. 2468–2473, 2007). A ProbLog program defines a distribution over logic programs by specifying for each clause the probability that it belongs to a randomly sampled program, and these probabilities are mutually independent. The semantics of ProbLog is then defined by the success probability of a query in a randomly sampled program.

This paper introduces the theory compression task for ProbLog, which consists of selecting that subset of clauses of a given ProbLog program that maximizes the likelihood w.r.t. a set of positive and negative examples. Experiments in the context of discovering links in real biological networks demonstrate the practical applicability of the approach.

Keywords

Probabilistic logic Inductive logic programming Theory revision Compression Network mining Biological applications Statistical relational learning 

References

  1. Bryant, R. E. (1986). Graph-based algorithms for boolean function manipulation. IEEE Transactions on Computers, 35(8), 677–691. MATHCrossRefGoogle Scholar
  2. Chavira, M., & Darwiche, A. (2007). Compiling Bayesian networks using variable elimination. In M. Veloso (Ed.), Proceedings of the 20th international joint conference on artificial intelligence (pp. 2443–2449). Menlo Park: AAAI Press. Google Scholar
  3. De Raedt, L., & Kersting, K. (2003). Probabilistic logic learning. SIGKDD Explorations, 5(1), 31–48. CrossRefGoogle Scholar
  4. De Raedt, L., Kimmig, A., & Toivonen, H. (2007). ProbLog: a probabilistic Prolog and its application in link discovery. In M. Veloso (Ed.), Proceedings of the 20th international joint conference on artificial intelligence (pp. 2468–2473). Menlo Park: AAAI Press. Google Scholar
  5. Flach, P. A. (1994). Simply logical: intelligent reasoning by example. New York: Wiley. MATHGoogle Scholar
  6. Fuhr, N. (2000). Probabilistic datalog: implementing logical information retrieval for advanced applications. Journal of the American Society for Information Science, 51, 95–110. CrossRefGoogle Scholar
  7. Getoor, L., & Taskar, B. (Eds.). (2007). Statistical relational learning. Cambridge: MIT Press. Google Scholar
  8. Koppel, M., Feldman, R., & Segre, A. M. (1994). Bias-driven revision of logical domain theories. Journal of Artificial Intelligence Research, 1, 159–208. MATHMathSciNetGoogle Scholar
  9. Minato, S., Satoh, K., & Sato, T. (2007). Compiling Bayesian networks by symbolic probability calculation based on zero-suppressed BDDs. In M. Veloso (Ed.), Proceedings of the 20th international joint conference on artificial intelligence (pp. 2550–2555). Menlo Park: AAAI Press. Google Scholar
  10. Muggleton, S. H. (1996). Stochastic logic programs. In L. De Raedt (Ed.), Advances in inductive logic programming. Amsterdam: IOS Press. Google Scholar
  11. Perez-Iratxeta, C., Bork, P., & Andrade, M. A. (2002). Association of genes to genetically inherited diseases using data mining. Nature Genetics, 31, 316–319. Google Scholar
  12. Poole, D. (1992). Logic programming, abduction and probability. In Fifth generation computing systems (pp. 530–538). Google Scholar
  13. Poole, D. (1993). Probabilistic Horn abduction and Bayesian networks. Artificial Intelligence, 64, 81–129. MATHCrossRefGoogle Scholar
  14. Sato, T., & Kameya, Y. (2001). Parameter learning of logic programs for symbolic-statistical modeling. Journal of AI Research, 15, 391–454. MATHMathSciNetGoogle Scholar
  15. Sevon, P., Eronen, L., Hintsanen, P., Kulovesi, K., & Toivonen, H. (2006). Link discovery in graphs derived from biological databases. In U. Leser, F. Naumann, & B. Eckman (Eds.), Lecture notes in bioinformatics : Vol. 4075. Data integration in the life sciences 2006. Berlin: Springer. CrossRefGoogle Scholar
  16. Valiant, L. G. (1979). The complexity of enumeration and reliability problems. SIAM Journal of Computing, 8, 410–411. MATHCrossRefMathSciNetGoogle Scholar
  17. Wrobel, S. (1996). First Order Theory Refinement. In L. De Raedt (Ed.), Advances in inductive logic programming. Amsterdam: IOS Press. Google Scholar
  18. Zelle, J. M., & Mooney, R. J. (1994). Inducing deterministic Prolog parsers from treebanks: a machine learning approach. In Proceedings of the 12th national conference on artificial intelligence (AAAI-94) (pp. 748–753). Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • L. De Raedt
    • 2
  • K. Kersting
    • 1
  • A. Kimmig
    • 2
  • K. Revoredo
    • 1
  • H. Toivonen
    • 3
  1. 1.Institut für InformatikAlbert-Ludwigs-UniversitätFreiburg im BreisgauGermany
  2. 2.Departement ComputerwetenschappenK.U. LeuvenHeverleeBelgium
  3. 3.Department of Computer ScienceUniversity of HelsinkiHelsinkiFinland

Personalised recommendations