Variational Bayes Inference for Logic-Based Probabilistic Models on BDDs

  • Masakazu Ishihata
  • Yoshitaka Kameya
  • Taisuke Sato
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7207)


Abduction is one of the basic logical inferences (deduction, induction and abduction) and derives the best explanations for our observation. Statistical abduction attempts to define a probability distribution over explanations and to evaluate them by their probabilities. Logic-based probabilistic models (LBPMs) have been developed as a way to combine probabilities and logic, and it enables us to perform statistical abduction. However non-deterministic knowledge like preference and frequency seems difficult to represent by logic. Bayesian inference can reflect such knowledge on a prior distribution, and variational Bayes (VB) is known as an approximation method for it. In this paper, we propose VB for logic-based probabilistic models and show that our proposed method is efficient in evaluating abductive explanations about failure in a logic circuit and a metabolic pathway.


Boolean Function Bayesian Inference Logic Program Variable Node Dirichlet Distribution 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Poole, D.: Probabilistic Horn abduction and Bayesian networks. Artificial Intelligence 64(1), 81–129 (1993)zbMATHCrossRefGoogle Scholar
  2. 2.
    Ishihata, M., Kameya, Y., Sato, T., Minato, S.: An EM algorithm on BDDs with order encoding for logic-based probabilistic models. In: Proc. of ACML 2010 (2010)Google Scholar
  3. 3.
    Singla, P., Mooney, R.J.: Abductive Markov Logic for Plan Recognition. In: Proc. of AAAI 2011 (2011)Google Scholar
  4. 4.
    Raghavan, S., Mooney, R.J.: Abductive Plan Recognition by Extending Bayesian Logic Programs. In: Gunopulos, D., Hofmann, T., Malerba, D., Vazirgiannis, M. (eds.) ECML PKDD 2011. LNCS, vol. 6912, pp. 629–644. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  5. 5.
    Inoue, K., Sato, T., Ishihata, M., Kameya, Y., Nabeshima, H.: Evaluating abductive hypotheses using an EM algorithm on BDDs. In: Proc. of IJCAI 2009 (2009)Google Scholar
  6. 6.
    Synnaeve, G., Inoue, K., Doncescu, A., Nabeshima, H., Kameya, Y., Ishihata, M., Sato, T.: Kinetic Models and Qualitative Abstraction for Relational Learning in Systems Biology. In: BIOSTEC Bioinformatics 2011 (2011)Google Scholar
  7. 7.
    Getoor, L., Taskar, B.: Introduction to Statistical Relational Learning (Adaptive Computation and Machine Learning). The MIT Press (2007)Google Scholar
  8. 8.
    Muggleton, S.: Stochastic Logic Programs. In: New Generation Computing. Academic Press (1996)Google Scholar
  9. 9.
    Poole, D.: The Independent Choice Logic for modelling multiple agents under uncertainty. Artificial Intelligence 94, 7–56 (1997)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Sato, T., Kameya, Y.: Parameter Learning of Logic Programs for Symbolic-statistical Modeling. Journal of Artificial Intelligence Research 15, 391–454 (2001)MathSciNetzbMATHGoogle Scholar
  11. 11.
    Kersting, K., De Raedt, L.: Towards Combining Inductive Logic Programming with Bayesian Networks. In: Rouveirol, C., Sebag, M. (eds.) ILP 2001. LNCS (LNAI), vol. 2157, pp. 118–131. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  12. 12.
    Richardson, M., Domingos, P.: Markov logic networks. Machine Learning 62(1), 107–136 (2006)CrossRefGoogle Scholar
  13. 13.
    De Raedt, L., Kimming, A., Toivonen, H.: ProbLog: A probabilistic Prolog and its application in link discovery. In: Proc. of IJCAI 2007, pp. 2468–2473 (2007)Google Scholar
  14. 14.
    Raghavan, S., Mooney, R.: Bayesian Abductive Logic Programs. In: Proc. of AAAI 2010 Workshop on Star-AI 2010 (2010)Google Scholar
  15. 15.
    Sato, T., Kameya, Y., Kurihara, K.: Variational Bayes via propositionalized probability computation in PRISM. Annals of Mathematics and Artificial Inteligence 54(1-3), 135–158 (2009)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Sato, T.: A General MCMC Method for Bayesian Inference in Logic-based Probabilistic Modeling. In: Proceedings of the 22nd International Joint Conference on Artificial Intelligence, IJCAI 2011 (2011)Google Scholar
  17. 17.
    Beal, M., Ghahramani, Z.: The Variational Bayesian EM Algorithm for Incomplete Data: with Application to Scoring Graphical Model Structures. Bayesian Statistics 7 (2003)Google Scholar
  18. 18.
    Akers, S.B.: Binary decision diagrams. IEEE Transaction on Computers 27(6), 509–516 (1978)zbMATHCrossRefGoogle Scholar
  19. 19.
    Tamaddoni-Nezhad, A., Chaleil, R., Kakas, A., Muggleton, S.: Application of abductive ILP to learning metabolic network inhibition from temporal data. Machine Learning 64, 209–230 (2006)zbMATHCrossRefGoogle Scholar
  20. 20.
    Gutmann, B., Thon, I., De Raedt, L.: Learning the parameters of probabilistic logic programs from interpretations, Dept. of Computer Science, K.U.Leuven (2010)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Masakazu Ishihata
    • 1
  • Yoshitaka Kameya
    • 1
  • Taisuke Sato
    • 1
  1. 1.Tokyo institute of TechnologyMeguro-kuJapan

Personalised recommendations