Efficient Sequential Clamping for Lifted Message Passing

  • Fabian Hadiji
  • Babak Ahmadi
  • Kristian Kersting
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7006)


Lifted message passing approaches can be extremely fast at computing approximate marginal probability distributions over single variables and neighboring ones in the underlying graphical model. They do, however, not prescribe a way to solve more complex inference tasks such as computing joint marginals for k-tuples of distant random variables or satisfying assignments of CNFs. A popular solution in these cases is the idea of turning the complex inference task into a sequence of simpler ones by selecting and clamping variables one at a time and running lifted message passing again after each selection. This naive solution, however, recomputes the lifted network in each step from scratch, therefore often canceling the benefits of lifted inference. We show how to avoid this by efficiently computing the lifted network for each conditioning directly from the one already known for the single node marginals. Our experiments show that significant efficiency gains are possible for lifted message passing guided decimation for SAT and sampling.


Relational Probabilistic Models Relational Learning Probabilistic Inference Satisfiability 


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  1. 1.
    Acar, U., Ihler, A., Mettu, R., Sumer, O.: Adaptive inference on general graphical models. In: Proc. of the Twenty-Fourth Conference on Uncertainty in Artificial Intelligence (UAI 2008). AUAI Press, Corvallis (2008)Google Scholar
  2. 2.
    Braunstein, A., Mézard, M., Zecchina, R.: Survey propagation: An algorithm for satisfiability. Random Structures and Algorithms 27(2), 201–226 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Delcher, A.L., Grove, A.J., Kasif, S., Pearl, J.: Logarithmic-time updates and queries in probabilistic networks. JAIR 4, 37–59 (1996)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Gomes, C.P., Hoffmann, J., Sabharwal, A., Selman, B.: From sampling to model counting. In: 20th IJCAI, Hyderabad, India, pp. 2293–2299 (January 2007)Google Scholar
  5. 5.
    Ihler, A.T., Fisher III, J.W., Willsky, A.S.: Loopy belief propagation: Convergence and effects of message errors. JMLR 6, 905–936 (2005)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Kersting, K., Ahmadi, B., Natarajan, S.: Counting belief propagation. In: Proc. of the 25th Conf. on Uncertainty in AI (UAI 2009), Montreal, Canada (2009)Google Scholar
  7. 7.
    Kschischang, F.R., Frey, B.J., Loeliger, H.-A.: Factor graphs and the sum-product algorithm. IEEE Transactions on Information Theory 47 (2001)Google Scholar
  8. 8.
    Mezard, M., Montanari, A.: Information, Physics, and Computation. Oxford University Press, Inc., New York (2009)CrossRefzbMATHGoogle Scholar
  9. 9.
    Milch, B., Zettlemoyer, L., Kersting, K., Haimes, M., Pack Kaelbling, L.: Lifted Probabilistic Inference with Counting Formulas. In: Proc. of the 23rd AAAI Conf. on Artificial Intelligence, AAAI 2008 (July 13–17, 2008)Google Scholar
  10. 10.
    Montanari, A., Ricci-Tersenghi, F., Semerjian, G.: Solving constraint satisfaction problems through belief propagation-guided decimation. In: Proc. of the 45th Allerton Conference on Communications, Control and Computing (2007)Google Scholar
  11. 11.
    Nath, A., Domingos, P.: Efficient lifting for online probabilistic inference. In: Proceedings of the Twenty-Fourth AAAI Conference on AI, AAAI 2010 (2010)Google Scholar
  12. 12.
    Pearl, J.: Reasoning in Intelligent Systems: Networks of Plausible Inference, 2nd edn. Morgan Kaufmann, San Francisco (1991)zbMATHGoogle Scholar
  13. 13.
    Richardson, M., Domingos, P.: Markov Logic Networks. MLJ 62, 107–136 (2006)Google Scholar
  14. 14.
    Selman, B., Kautz, H., Cohen, B.: Local search strategies for satisfiability testing. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, pp. 521–532 (1995)Google Scholar
  15. 15.
    Sen, P., Deshpande, A., Getoor, L.: Bisimulation-based approximate lifted inference. In: Proc. of the 25th Conf. on Uncertainty in AI, UAI 2009 (2009)Google Scholar
  16. 16.
    Singla, P., Domingos, P.: Lifted First-Order Belief Propagation. In: Proc. of the 23rd AAAI Conf. on AI (AAAI 2008), pp. 1094–1099 (2008)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Fabian Hadiji
    • 1
  • Babak Ahmadi
    • 1
  • Kristian Kersting
    • 1
  1. 1.Knowledge Discovery DepartmentFraunhofer IAISSankt AugustinGermany

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