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.
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References
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_3
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)
Chen, H., Erol, Y., Shen, E., Russell, S.: Probabilistic model-based approach for heart beat detection. Physiol. Measur. 37(9), 1404 (2016)
Dawid, A.P.: Applications of a general propagation algorithm for probabilistic expert systems. Stat. Comput. 2(1), 25–36 (1992)
Dechter, R.: Bucket elimination: a unifying framework for probabilistic inference. In: Learning and Inference in Graphical Models, pp. 75–104. MIT Press (1999)
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)
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)
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)
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)
Nilsson, D.: An efficient algorithm for finding the M most probable configurations in probabilistic expert systems. Stat. Comput. 8(2), 159–173 (1998)
Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, Burlington (1988)
Poole, D.: First-order probabilistic inference. In: Proceedings of the 18th International Joint Conference on Artificial Intelligence, IJCAI 2003 (2003)
de Salvo Braz, R.: Lifted first-order probabilistic inference. Ph.D. thesis, University of Illinois at Urbana Champaign (2007)
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)
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_17
Shenoy, P.P., Shafer, G.R.: Axioms for probability and belief-function propagation. Uncertain. Artif. Intell. 4(9), 169–198 (1990)
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_10
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)
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)
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)
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Braun, T., Möller, R. (2018). Lifted Most Probable Explanation. In: Chapman, P., Endres, D., Pernelle, N. (eds) Graph-Based Representation and Reasoning. ICCS 2018. Lecture Notes in Computer Science(), vol 10872. Springer, Cham. https://doi.org/10.1007/978-3-319-91379-7_4
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DOI: https://doi.org/10.1007/978-3-319-91379-7_4
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