Bayesian Logic Networks and the Search for Samples with Backward Simulation and Abstract Constraint Learning

  • Dominik Jain
  • Klaus von Gleissenthall
  • Michael Beetz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7006)


With Bayesian logic networks (BLNs), we present a practical representation formalism for statistical relational knowledge. Based on the concept of mixed networks with probabilistic and deterministic constraints, BLNs combine the probabilistic semantics of (relational) Bayesian networks with constraints in first-order logic. In practical applications, efficient inference in statistical relational models such as BLNs is a key concern. Motivated by the inherently mixed nature of models instantiated from BLNs, we investigate two novel importance sampling methods: The first combines backward simulation, i.e. sampling backward from the evidence, with systematic search, while the second explores the possibility of recording abstract constraints during the search for samples.


Bayesian Network Importance Sampling Constraint Satisfaction Problem Importance Function Likelihood Weighting 
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.
    Richardson, M., Domingos, P.: Markov Logic Networks. Mach. Learn. 62, 107–136 (2006)CrossRefGoogle Scholar
  2. 2.
    Jain, D., Kirchlechner, B., Beetz, M.: Extending Markov Logic to Model Probability Distributions in Relational Domains. In: Hertzberg, J., Beetz, M., Englert, R. (eds.) KI 2007. LNCS (LNAI), vol. 4667, pp. 129–143. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  3. 3.
    Getoor, L., Friedman, N., Koller, D., Pfeffer, A., Taskar, B.: Probabilistic Relational Models. In: Getoor, L., Taskar, B. (eds.) An Introduction to Statistical Relational Learning. MIT Press, Cambridge (2007)Google Scholar
  4. 4.
    Kersting, K., Raedt, L.D.: Bayesian Logic Programming: Theory and Tool. In: Getoor, L., Taskar, B. (eds.) Introduction to Statistical Relational Learning. MIT Press, Cambridge (2007)Google Scholar
  5. 5.
    Laskey, K.B.: MEBN: A Language for First-Order Bayesian Knowledge Bases. Artif. Intell. 172, 140–178 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Jaeger, M.: Model-Theoretic Expressivity Analysis. In: Raedt, L.D., Frasconi, P., Kersting, K., Muggleton, S. (eds.) Probabilistic Inductive Logic Programming. LNCS (LNAI), vol. 4911, pp. 325–339. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  7. 7.
    Mateescu, R., Dechter, R.: Mixed Deterministic and Probabilistic Networks. Ann. Math. Artif. Intel. (2008)Google Scholar
  8. 8.
    Poon, H., Domingos, P.: Sound and Efficient Inference with Probabilistic and Deterministic Dependencies. In: AAAI. AAAI Press, Menlo Park (2006)Google Scholar
  9. 9.
    Rubinstein, R.: Simulation and the Monte Carlo Method. John Wiley & Sons, Inc., Chichester (1981)CrossRefzbMATHGoogle Scholar
  10. 10.
    Fung, R.M., Favero, B.D.: Backward Simulation in Bayesian Networks. In: UAI, pp. 227–234 (1994)Google Scholar
  11. 11.
    Gogate, V., Dechter, R.: SampleSearch: A Scheme that Searches for Consistent Samples. In: AISTATS (2007)Google Scholar
  12. 12.
    Dechter, R., Frost, D.: Backjump-Based Backtracking for Constraint Satisfaction Problems. Artif. Intell. 136, 147–188 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Gogate, V., Domingos, P.: Formula-Based Probabilistic Inference. In: UAI (2010)Google Scholar
  14. 14.
    Kersting, K., Ahmadi, B., Natarajan, S.: Counting Belief Propagation. In: UAI (2009)Google Scholar
  15. 15.
    Parkes, A.J.: Lifted Search Engines for Satisfiability. PhD thesis (1999)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Dominik Jain
    • 1
  • Klaus von Gleissenthall
    • 1
  • Michael Beetz
    • 1
  1. 1.Intelligent Autonomous Systems, Department of InformaticsTechnische Universität MünchenGermany

Personalised recommendations