Advertisement

Lifted Most Probable Explanation

  • Tanya Braun
  • Ralf Möller
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10872)

Abstract

Standard approaches for inference in probabilistic formalisms with first-order constructs include lifted variable elimination (LVE) for single queries, boiling down to computing marginal distributions. To handle multiple queries efficiently, the lifted junction tree algorithm (LJT) uses a first-order cluster representation of a knowledge base and LVE in its computations. Another type of query asks for a most probable explanation (MPE) for given events. The purpose of this paper is twofold: (i) We formalise how to compute an MPE in a lifted way with LVE and LJT. (ii) We present a case study in the area of IT security for risk analysis. A lifted computation of MPEs exploits symmetries, while providing a correct and exact result equivalent to one computed on ground level.

Keywords

Probabilistic logical model Lifting MPE MAP Abduction 

References

  1. 1.
    Braun, T., Möller, R.: Lifted junction tree algorithm. In: Friedrich, G., Helmert, M., Wotawa, F. (eds.) KI 2016. LNCS (LNAI), vol. 9904, pp. 30–42. Springer, Cham (2016).  https://doi.org/10.1007/978-3-319-46073-4_3CrossRefGoogle Scholar
  2. 2.
    Ceylan, İ.İ., Borgwardt, S., Lukasiewicz, T.: Most probable explanations for probabilistic database queries. In: Proceedings of the 26th International Joint Conference on Artificial Intelligence (2017)Google Scholar
  3. 3.
    Chen, H., Erol, Y., Shen, E., Russell, S.: Probabilistic model-based approach for heart beat detection. Physiol. Measur. 37(9), 1404 (2016)CrossRefGoogle Scholar
  4. 4.
    Dawid, A.P.: Applications of a general propagation algorithm for probabilistic expert systems. Stat. Comput. 2(1), 25–36 (1992)CrossRefGoogle Scholar
  5. 5.
    Dechter, R.: Bucket elimination: a unifying framework for probabilistic inference. In: Learning and Inference in Graphical Models, pp. 75–104. MIT Press (1999)CrossRefGoogle Scholar
  6. 6.
    Gribkoff, E., van den Broeck, G., Suciu, D.: The most probable database problem. In: Proceedings of the 1st International Workshop on Big Uncertain Data (2014)Google Scholar
  7. 7.
    Lauritzen, S.L., Spiegelhalter, D.J.: Local computations with probabilities on graphical structures and their application to expert systems. J. R. Stat. Soc. Ser. B: Methodol. 50, 157–224 (1988)MathSciNetMATHGoogle Scholar
  8. 8.
    Milch, B., Zettelmoyer, L.S., Kersting, K., Haimes, M., Kaelbling, L.P.: Lifted probabilistic inference with counting formulas. In: Proceedings of the 23rd Conference on Artificial Intelligence, AAAI 2008, pp. 1062–1068 (2008)Google Scholar
  9. 9.
    Muñoz-González, L., Sgandurra, D., Barrère, M., Lupu, E.C.: Exact inference techniques for the analysis of Bayesian attack graphs. IEEE Trans. Dependable Secure Comput. PP(99), 1–14 (2017)CrossRefGoogle Scholar
  10. 10.
    Nilsson, D.: An efficient algorithm for finding the M most probable configurations in probabilistic expert systems. Stat. Comput. 8(2), 159–173 (1998)CrossRefGoogle Scholar
  11. 11.
    Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, Burlington (1988)MATHGoogle Scholar
  12. 12.
    Poole, D.: First-order probabilistic inference. In: Proceedings of the 18th International Joint Conference on Artificial Intelligence, IJCAI 2003 (2003)Google Scholar
  13. 13.
    de Salvo Braz, R.: Lifted first-order probabilistic inference. Ph.D. thesis, University of Illinois at Urbana Champaign (2007)Google Scholar
  14. 14.
    de Salvo Braz, R., Amir, E., Roth, D.: MPE and partial inversion in lifted probabilistic variable elimination. In: Proceedings of the 21st Conference on Artificial Intelligence, AAAI 2006 (2006)Google Scholar
  15. 15.
    Schröder, M., Lüdtke, S., Bader, S., Krüger, F., Kirste, T.: LiMa: sequential lifted marginal filtering on multiset state descriptions. In: Kern-Isberner, G., Fürnkranz, J., Thimm, M. (eds.) KI 2017. LNCS (LNAI), vol. 10505, pp. 222–235. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-67190-1_17CrossRefGoogle Scholar
  16. 16.
    Shenoy, P.P., Shafer, G.R.: Axioms for probability and belief-function propagation. Uncertain. Artif. Intell. 4(9), 169–198 (1990)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Shterionov, D., Renkens, J., Vlasselaer, J., Kimmig, A., Meert, W., Janssens, G.: The most probable explanation for probabilistic logic programs with annotated disjunctions. In: Davis, J., Ramon, J. (eds.) ILP 2014. LNCS (LNAI), vol. 9046, pp. 139–153. Springer, Cham (2015).  https://doi.org/10.1007/978-3-319-23708-4_10CrossRefGoogle Scholar
  18. 18.
    Taghipour, N., Davis, J., Blockeel, H.: First-order decomposition trees. In: Advances in Neural Information Processing Systems 26, pp. 1052–1060. Curran Associates, Inc. (2013)Google Scholar
  19. 19.
    Taghipour, N., Fierens, D., Davis, J., Blockeel, H.: Lifted variable elimination: decoupling the operators from the constraint language. J. Artif. Intell. Res. 47(1), 393–439 (2013)MathSciNetMATHGoogle Scholar
  20. 20.
    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 (1994)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Information SystemsUniversität zu LübeckLübeckGermany

Personalised recommendations