Abstract
Probabilistic models involving relational and temporal aspects need exact and efficient inference algorithms. Existing approaches are approximative, include unnecessary grounding, or do not consider the relational and temporal aspects of the models. One approach for efficient reasoning on relational static models given multiple queries is the lifted junction tree algorithm. In addition, for propositional temporal models, the interface algorithm allows for efficient reasoning. To leverage the advantages of the two algorithms for relational temporal models, we present the lifted dynamic junction tree algorithm, an exact algorithm to answer multiple queries efficiently for probabilistic relational temporal models with known domains by reusing computations for multiple queries and multiple time steps. First experiments show computational savings while appropriately accounting for relational and temporal aspects of models.
This research originated from the Big Data project being part of Joint Lab 1, funded by Cisco Systems Germany, at the centre COPICOH, University of Lübeck.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Ahmadi, B., Kersting, K., Mladenov, M., Natarajan, S.: Exploiting symmetries for scaling loopy belief propagation and relational training. Mach. Learn. 92(1), 91–132 (2013)
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
Braun, T., Möller, R.: Counting and conjunctive queries in the lifted junction tree algorithm. In: Croitoru, M., Marquis, P., Rudolph, S., Stapleton, G. (eds.) 5th International Workshop on Graph Structures for Knowledge Representation and Reasoning. LNCS, vol. 10775, pp. 54–72. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-78102-0_3
Darwiche, A.: Modeling and Reasoning with Bayesian Networks. Cambridge University Press, Cambridge (2009)
Dignös, A., Böhlen, M.H., Gamper, J.: Temporal alignment. In: Proceedings of the 2012 ACM SIGMOD International Conference on Management of Data, pp. 433–444. ACM (2012)
Dylla, M., Miliaraki, I., Theobald, M.: A temporal-probabilistic database model for information extraction. Proc. VLDB Endow. 6(14), 1810–1821 (2013)
Geier, T., Biundo, S.: Approximate online inference for dynamic Markov logic networks. In: Proceedings of the 23rd IEEE International Conference on Tools with Artificial Intelligence (ICTAI), pp. 764–768. IEEE (2011)
Kanagal, B., Deshpande, A.: Lineage processing over correlated probabilistic databases. In: Proceedings of the 2010 ACM SIGMOD International Conference on Management of data, pp. 675–686. ACM (2010)
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)
Manfredotti, C.E.: Modeling and Inference with Relational Dynamic Bayesian Networks. Ph.D. thesis, Ph.D. Dissertation, University of Milano-Bicocca (2009)
Milch, B., Zettlemoyer, L.S., Kersting, K., Haimes, M., Kaelbling, L.P.: Lifted probabilistic inference with counting formulas. In: Proceedings of AAAI, vol. 8, pp. 1062–1068 (2008)
Murphy, K., Weiss, Y.: The factored frontier algorithm for approximate inference in DBNs. In: Proceedings of the Seventeenth conference on Uncertainty in artificial intelligence, pp. 378–385. Morgan Kaufmann Publishers Inc. (2001)
Murphy, K.P.: Dynamic Bayesian Networks: Representation, Inference and Learning. Ph.D. thesis, University of California, Berkeley (2002)
Nitti, D., De Laet, T., De Raedt, L.: A particle filter for hybrid relational domains. In: Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 2764–2771. IEEE (2013)
Papai, T., Kautz, H., Stefankovic, D.: Slice normalized dynamic Markov logic networks. In: Proceedings of the Advances in Neural Information Processing Systems, pp. 1907–1915 (2012)
Poole, D.: First-order probabilistic inference. In: Proceedings of IJCAI, vol. 3, pp. 985–991 (2003)
Richardson, M., Domingos, P.: Markov logic networks. Mach. Learn. 62(1), 107–136 (2006)
de Salvo Braz, R.: Lifted First-Order Probabilistic Inference. Ph.D. thesis, Ph.D. Dissertation, University of Illinois at Urbana Champaign (2007)
Taghipour, N., Davis, J., Blockeel, H.: First-order decomposition trees. In: Proceedings of the Advances in Neural Information Processing Systems, pp. 1052–1060 (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)
Thon, I., Landwehr, N., De Raedt, L.: Stochastic relational processes: efficient inference and applications. Mach. Learn. 82(2), 239–272 (2011)
Vlasselaer, J., Van den Broeck, G., Kimmig, A., Meert, W., De Raedt, L.: TP-Compilation for inference in probabilistic logic programs. Int. J. Approx. Reason. 78, 15–32 (2016)
Vlasselaer, J., Meert, W., Van den Broeck, G., De Raedt, L.: Efficient probabilistic inference for dynamic relational models. In: AAAIWS’14-13 Proceedings of the 13th AAAI Conference on Statistical Relational AI, pp. 131–132. AAAI Press (2014)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Gehrke, M., Braun, T., Möller, R. (2018). Lifted Dynamic Junction Tree Algorithm. 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_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-91379-7_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-91378-0
Online ISBN: 978-3-319-91379-7
eBook Packages: Computer ScienceComputer Science (R0)