Abstract
Large probabilistic models are often shaped by a pool of known individuals (a universe) and relations between them. Lifted inference algorithms handle sets of known individuals for tractable inference. Universes may not always be known, though, or may only described by assumptions such as “small universes are more likely”. Without a universe, inference is no longer possible for lifted algorithms, losing their advantage of tractable inference. The aim of this paper is to define a semantics for models with unknown universes decoupled from a specific constraint language to enable lifted and thereby, tractable inference.
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References
Acar, U.A., Ihler, A.T., Mettu, R.R., Sümer, Ö.: Adaptive inference on general graphical models. In: UAI-08 Proceedings of the 24th Conference on Uncertainty in Artificial Intelligence, pp. 1–8. AUAI Press (2008)
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.: Preventing groundings and handling evidence in the lifted junction tree algorithm. In: Kern-Isberner, G., Fürnkranz, J., Thimm, M. (eds.) KI 2017. LNCS (LNAI), vol. 10505, pp. 85–98. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-67190-1_7
Braun, T., Möller, R.: Adaptive inference on probabilistic relational models. In: Mitrovic, T., Xue, B., Li, X. (eds.) AI 2018. LNCS (LNAI), vol. 11320, pp. 487–500. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-03991-2_44
Brewka, G., Eiter, T., Truszczynski, M.: Answer set programming at a glance. Commun. ACM 15(12), 92–103 (2011)
Ceylan, İ.İ., Darwiche, A., Van den Broeck, G.: Open-world probabilistic databases. In: KR-16 Proceedings of the 15th International Conference on Principles of Knowledge Representation and Reasoning, pp. 339–348. AAAI Press (2016)
De Raedt, L., Kimmig, A., Toivonen, H.: ProbLog: a probabilistic prolog and its application in link discovery. In: IJCAI-07 Proceedings of 20th International Joint Conference on Artificial Intelligence, pp. 2062–2467. IJCAI Organization (2007)
Fagin, R.: Combining fuzzy information from multiple systems. J. Comput. Syst. Sci. 58(1), 83–99 (1999)
Fuhr, N.: Probabilistic datalog - a logic for powerful retrieval methods. In: SIGIR-95 Proceedings of the 18th Annual International ACM SIGIR Conference on Research and Development in Information Retrieval, pp. 282–290. ACM (1995)
Gogate, V., Domingos, P.: Probabilistic theorem proving. In: UAI-11 Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence, pp. 256–265. AUAI Press (2011)
Kazemi, S.M., Poole, D.: Knowledge compilation for lifted probabilistic inference: compiling to a low-level language. In: KR-16 Proceedings of the 15th International Conference on Principles of Knowledge Representation and Reasoning, pp. 561–564 (2016)
LeCun, Y.: Learning World Models: the Next Step Towards AI. Invited Talk at IJCAI-ECAI 2018 (2018). https://www.youtube.com/watch?v=U2mhZ9E8Fk8. Accessed 19 Nov 2018
Milch, B., Marthi, B., Russell, S., Sontag, D., Long, D.L., Kolobov, A.: BLOG: probabilistic models with unknown objects. In: IJCAI-05 Proceedings of the 19th International Joint Conference on Artificial Intelligence, pp. 1352–1359. IJCAI Organization (2005)
Niepert, M., Van den Broeck, G.: Tractability through exchangeability: a new perspective on efficient probabilistic inference. In: AAAI-14 Proceedings of the 28th AAAI Conference on Artificial Intelligence, pp. 2467–2475. AAAI Press (2014)
Poole, D.: First-order probabilistic inference. In: IJCAI-03 Proceedings of the 18th International Joint Conference on Artificial Intelligence, pp. 985–991. IJCAI Organization (2003)
Richardson, M., Domingos, P.: Markov logic networks. Mach. Learn. 62(1–2), 107–136 (2006)
Srivastava, S., Russell, S., Ruan, P., Cheng, X.: First-order open-universe POMDPs. In: UAI-14 Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence, pp. 742–751. AUAI Press (2014)
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)
Van den Broeck, G., Taghipour, N., Meert, W., Davis, J., De Raedt, L.: Lifted probabilistic inference by first-order knowledge compilation. In: IJCAI-11 Proceedings of the 22nd International Joint Conference on Artificial Intelligence, pp. 2178–2185. IJCAI Organization (2011)
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Braun, T., Möller, R. (2019). Exploring Unknown Universes in Probabilistic Relational Models. In: Liu, J., Bailey, J. (eds) AI 2019: Advances in Artificial Intelligence. AI 2019. Lecture Notes in Computer Science(), vol 11919. Springer, Cham. https://doi.org/10.1007/978-3-030-35288-2_8
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