Abstract
Probabilistic Logic Learning (PLL) aims at learning probabilistic logical frameworks on the basis of data. Such frameworks combine expressive knowledge representation formalisms with reasoning mechanisms grounded in probability theory. Numerous frameworks have already addressed this issue. Therefore, there is a real need to compare these frameworks in order to be able to unify them. This paper provides a comparison of Relational Markov Models (RMMs) and Bayesian Logic Programs (BLPs). We demonstrate relations between BLPs’ and RMMs’ semantics, arguing that RMMs encode the same knowledge as a sub-class of BLPs. We fully describe a translation from a sub-class of BLPs into RMMs and provide complexity results which demonstrate an exponential expansion in formula size, showing that RMMs are less compact than their equivalent BLPs with respect to this translation. The authors are unaware of any more compact translation between BLPs and RMMs. A full implementation has already been realized, consisting of meta-interpreters for both BLPs and RMMs and a translation engine. The equality of BLPs’ and corresponding RMMs’ probability distributions has been proven on practical examples.
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References
Anderson, C., et al.: Relational Markov models and their application to adaptive Web navigation. In: 8th Intl. Conf. on Knowledge Discovery and Data Mining (2002)
April2 Blackforest Workshop 2006 (2006), palermo.informatik.uni-freiburg.de/bfw/
de Raedt, L., et al.: Probabilistic logic learning. ACM-SIGKDD Explorations (2004)
Getoor, L., et al.: PRL: A Probabilistic relational language. Machine Learning (2006)
Jaeger, M.: Importance sampling on relational bayesian networks. In: Dagstuhl Seminar Proceeding 05051 (2006)
Jaeger, M.: Expressivity Analysis for PL-Languages. In: Online Proceedings of the ICML06 Workshop on Statistical Relational Learning (2006)
Kersting, K., et al.: Bayesian Logic Programs. In: Proceedings of the Work-in-Progress Track at the 10th INtl. Conf. on Inductive Logic Programming (2000)
Koller, D., Pfeffer, A.: Learning Probabilities for Noisy First-Order Rules. IJCAI (1997)
Lloyd, J.W.: Foundations of Logic Programming, 2nd edn. Springer, Heidelberg (1987)
Pahlavi, N.: Probabilistic Logic Learning, A Comparative Study. Technical Report. Imperial College London (2005)
Pahlavi, N.: Comparing RMMs with SLPs and BLPs. Technical Report. Imperial College London (2006)
Pahlavi, N.: The Complexity of Translating BLPs to RMMs. Technical Report. Imperial College London (2006)
Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, San Francisco (1988)
Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of plausible Inference. Morgan Kaufmann, San Francisco (1988)
Puech, A., Muggleton, S.H.: A Comparison of Stochastic Logic Programs and Bayesian Logic Programs. IJCAI03 Workshop on Learning Statistical Models from Relational Data (2003)
Rabiner, L.R.: A tutorial on Hidden Markov Models and selected applications in speech recognition. In: Proceedings of the IEEE, IEEE Computer Society Press, Los Alamitos (1989)
Vennekens, J., et al.: A general view on probabilistic logic programming. In: Proceedings of BNAIC-03 (2003)
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Muggleton, S., Pahlavi, N. (2007). The Complexity of Translating BLPs to RMMs. In: Muggleton, S., Otero, R., Tamaddoni-Nezhad, A. (eds) Inductive Logic Programming. ILP 2006. Lecture Notes in Computer Science(), vol 4455. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73847-3_33
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DOI: https://doi.org/10.1007/978-3-540-73847-3_33
Publisher Name: Springer, Berlin, Heidelberg
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