Advertisement

Preventing Groundings and Handling Evidence in the Lifted Junction Tree Algorithm

  • Tanya Braun
  • Ralf Möller
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10505)

Abstract

For inference in probabilistic formalisms with first-order constructs, lifted variable elimination (LVE) is one of the standard approaches for single queries. To handle multiple queries efficiently, the lifted junction tree algorithm (LJT) uses a specific representation of a first-order knowledge base and LVE in its computations. Unfortunately, LJT induces unnecessary groundings in cases where the standard LVE algorithm, GC-FOVE, has a fully lifted run. Additionally, LJT does not handle evidence explicitly. We extend LJT (i) to identify and prevent unnecessary groundings and (ii) to effectively handle evidence in a lifted manner. Given multiple queries, e.g., in machine learning applications, our extension computes answers faster than LJT and GC-FOVE.

Keywords

Probabilistic logical models Reasoning Lifting 

References

  1. 1.
    Ahmadi, B., Kersting, K., Mladenov, M., Natarajan, S.: Exploiting symmetries for scaling loopy belief propagation and relational training. In: Machine Learning, vol. 92, pp. 91–132. Kluwer Academic Publishers, Hingham (2013)Google Scholar
  2. 2.
    Bellodi, E., Lamma, E., Riguzzi, F., Santos Costa, V., Zese, R.: Lifted variable elimination for probabilistic logic programming. Theory Pract. Logic Program. 14(4–5), 681–695 (2014). Cambridge University Press, CambridgeCrossRefzbMATHGoogle Scholar
  3. 3.
    Braun, T., Möller, R.: Lifted junction tree algorithm. In: Friedrich, G., Helmert, M., Wotawa, F. (eds.) KI 2016. LNCS, vol. 9904, pp. 30–42. Springer, Cham (2016). doi: 10.1007/978-3-319-46073-4_3 CrossRefGoogle Scholar
  4. 4.
    Van den Broeck, G.: Lifted Inference and Learning in Statistical Relational Models. Ph.D. Thesis, KU Leuven (2013)Google Scholar
  5. 5.
    Choi, J., Amir, E., Hill, D.J.: Lifted inference for relational continuous models. In: Proceedings of the 26th Conference on Artificial Intelligence. The AAAI Press, Menlo Park (2012)Google Scholar
  6. 6.
    Darwiche, A.: Recursive conditioning. In: Artificial Intelligence, vol. 2, pp. 4–41. Elsevier Science Publishers, Essex (2001)Google Scholar
  7. 7.
    Darwiche, A.: Modeling and Reasoning with Bayesian Networks. Cambridge University Press, Cambridge (2009)CrossRefzbMATHGoogle Scholar
  8. 8.
    Das, M., Wu, Y., Khot, T., Kersting, K., Natarajan, S.: Scaling lifted probabilistic inference and learning via graph databases. In: Proceedings of the SIAM International Conference on Data Mining, pp. 738–746. Society for Industrial and Applied Mathematics, Philadelphia (2016)Google Scholar
  9. 9.
    Gogate, V., Domingos, P.: Exploiting logical structure in lifted probabilistic inference. In: Working Note of the Workshop on Statistical Relational Artificial Intelligence at the 24th Conference on Artificial Intelligence. The AAAI Press, Menlo Park (2010)Google Scholar
  10. 10.
    Gogate, V., Domingos, P.: Probabilistic theorem proving. In: Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence, pp. 256–265. AUAI Press, Arlington (2011)Google Scholar
  11. 11.
    Jensen, F.V., Lauritzen, S.L., Oleson, K.G.: Bayesian updating in recursive graphical models by local computations. In: Computational Statistics Quarterly, vol. 4, pp. 269–282. Physica-Verlag, Vienna (1990)Google Scholar
  12. 12.
    Lauritzen, S.L., Spiegelhalter, D.J.: Local computations with probabilities on graphical structures and their application to expert systems. J. Roy. Stat. Soc.: Ser. B (Stat. Methodol.) 50, 157–224 (1988). Wiley-Blackwell, OxfordMathSciNetzbMATHGoogle Scholar
  13. 13.
    Milch, B., Zettlemoyer, L.S., Kersting, K., Haimes, M., Pack Kaelbling, L.: Lifted probabilistic inference with counting formulas. In: Proceedings of the 23rd Conference on Artificial Intelligence, pp. 1062–1068. The AAAI Press, Menlo Park (2008)Google Scholar
  14. 14.
    Poole, D.: First-order probabilistic inference. In: Proceedings of the 18th International Joint Conference on Artificial Intelligence, pp. 985–991. Morgan Kaufman Publishers Inc., San Francisco (2003)Google Scholar
  15. 15.
    de Salvo Braz, R.: Lifted First-Order Probabilistic Inference. Ph.D. Thesis, University of Illinois at Urbana-Champaign (2007)Google Scholar
  16. 16.
    Shafer, G.R., Shenoy, P.P.: Probability propagation. Ann. Math. Artif. Intell. 2, 327–351 (1989). Springer, HeidelbergMathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Singla, P., Domingos, P.: Lifted first-order belief propagation. In: Proceedings of the 23rd Conference on Artificial Intelligence, pp. 1094–1099. The AAAI Press, Menlo Park (2008)Google Scholar
  18. 18.
    Taghipour, N.: Lifted Probabilistic Inference by Variable Elimination. Ph.D. Thesis, KU Leuven (2013)Google Scholar
  19. 19.
    Taghipour, N., Davis, J., Blockeel, H.: First-order decomposition trees. In: Advances in Neural Information Processing Systems 26, pp. 1052–1060. Curran Associates, Red Hook (2013)Google Scholar
  20. 20.
    Vlasselaer, J., Meert, W., van den Broeck, G., de Raedt, L.: Exploiting local and repeated structure in dynamic baysian networks. In: Artificial Intelligence, vol. 232, pp. 43–53. Elsevier, Amsterdam (2016)Google Scholar
  21. 21.
    Zhang, N.L., Poole, D.: A simple approach to bayesian network computations. In: Proceedings of the 10th Canadian Conference on Artificial Intelligence, pp. 171–178. Morgan Kaufman Publishers, San Francisco (1994)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Institute of Information SystemsUniversität zu LübeckLübeckGermany

Personalised recommendations