Abstract
For relational probabilistic conditionals, the so-called aggregation semantics has been proposed recently. Applying the maximum entropy principle for reasoning under aggregation semantics requires solving a complex optimization problem. Here, we improve an approach to solving this optimization problem by Generalized Iterative Scaling (GIS). After showing how the method of Lagrange multipliers can also be used for aggregation semantics, we exploit that possible worlds are structurally equivalent with respect to a knowledge base \(\mathcal R\) if they have the same verification and falsification properties. We present a GIS algorithm operating on the induced equivalence classes of worlds; its implementation yields significant performance improvements.
The research reported here was partially supported by the DFG (grant BE 1700/7-2).
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References
Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, New York (2004)
Darroch, J.N., Ratcliff, D.: Generalized iterative scaling for log-linear models. In: Annals of Mathematical Statistics. Institute of Mathematical Statistics (1972)
De Raedt, L., Kersting, K.: Probabilistic Inductive Logic Programming. In: De Raedt, L., Frasconi, P., Kersting, K., Muggleton, S. (eds.) Probabilistic ILP 2007. LNCS (LNAI), vol. 4911, pp. 1–27. Springer, Heidelberg (2008)
Finthammer, M.: An Iterative Scaling Algorithm for Maximum Entropy Reasoning in Relational Probabilistic Conditional Logic. In: Hüllermeier, E., Link, S., Fober, T., Seeger, B. (eds.) SUM 2012. LNCS (LNAI), vol. 7520, pp. 351–364. Springer, Heidelberg (2012)
Finthammer, M., Thimm, M.: An integrated development environment for probabilistic relational reasoning. Logic Journal of the IGPL (to appear, 2012)
Fisseler, J.: Learning and Modeling with Probabilistic Conditional Logic. Dissertations in Artificial Intelligence, vol. 328. IOS Press, Amsterdam (2010)
Geman, S., Geman, D.: Stochastic relaxation, gibbs distributions, and the bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence 6, 721–741 (1984)
Getoor, L., Taskar, B. (eds.): Introduction to Statistical Relational Learning. MIT Press (2007)
Kern-Isberner, G.: Conditionals in Nonmonotonic Reasoning and Belief Revision. LNCS (LNAI), vol. 2087. Springer, Heidelberg (2001)
Kern-Isberner, G., Lukasiewicz, T.: Combining probabilistic logic programming with the power of maximum entropy. Artificial Intelligence, Special Issue on Nonmonotonic Reasoning 157(1-2), 139–202 (2004)
Kern-Isberner, G., Thimm, M.: A ranking semantics for first-order conditionals. In: Proc. 20th European Conference on Artificial Intelligence (to appear, 2012)
Kern-Isberner, G., Thimm, M.: Novel semantical approaches to relational probabilistic conditionals. In: Proc. of KR 2010, pp. 382–392. AAAI Press (May 2010)
Paris, J.: The uncertain reasoner’s companion – A mathematical perspective. Cambridge University Press (1994)
Poole, D.: First-order probabilistic inference. In: Gottlob, G., Walsh, T. (eds.) Proc. of IJCAI 2003, pp. 985–991. Morgan Kaufmann (2003)
de Salvo Braz, R., Amir, E., Roth, D.: Lifted first-order probabilistic inference. In: Proc. of IJCAI 2005 (2005)
Thimm, M.: Probabilistic Reasoning with Incomplete and Inconsistent Beliefs. Ph.D. thesis, Technische Universität Dortmund (2011)
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Finthammer, M., Beierle, C. (2012). Using Equivalences of Worlds for Aggregation Semantics of Relational Conditionals. In: Glimm, B., Krüger, A. (eds) KI 2012: Advances in Artificial Intelligence. KI 2012. Lecture Notes in Computer Science(), vol 7526. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33347-7_5
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DOI: https://doi.org/10.1007/978-3-642-33347-7_5
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