Abstract
The principle of maximum entropy allows to define the semantics of a knowledge base consisting of a set of probabilistic relational conditionals by a unique model having maximum entropy. Using the concept of a conditional structure of a world, we define the notion of weighted conditional impacts and present a two-level approach for maximum entropy model computation based on them. Once the weighted conditional impact of a knowledge base has been determined, a generalized iterative scaling algorithm is used that fully abstracts from concrete worlds. The weighted conditional impact may be reused when only the quantitative aspects of the knowledge base are changed. As a further extension of previous work, also deterministic conditionals may be present in the knowledge base, and a special treatment of such conditionals reduces the problem size.
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
Preview
Unable to display preview. Download preview PDF.
References
Adams, E.: The Logic of Conditionals. D. Reidel, Dordrecht (1975)
Beierle, C., Finthammer, M., Kern-Isberner, G., Thimm, M.: Evaluation and comparison criteria for approaches to probabilistic relational knowledge representation. In: Bach, J., Edelkamp, S. (eds.) KI 2011. LNCS, vol. 7006, pp. 63–74. Springer, Heidelberg (2011)
Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, New York (2004)
Fagin, R., Halpern, J.Y.: Reasoning about knowledge and probability. J. ACM 41(2), 340–367 (1994)
Finthammer, M., Beierle, C.: Using equivalences of worlds for aggregation semantics of relational conditionals. In: Glimm, B., Krüger, A. (eds.) KI 2012. LNCS, vol. 7526, pp. 49–60. Springer, Heidelberg (2012)
Finthammer, M., Thimm, M.: An integrated development environment for probabilistic relational reasoning. Logic Journal of the IGPL 20(5), 831–871 (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)
Halpern, J.: Reasoning About Uncertainty. MIT Press (2005)
Kern-Isberner, G.: Conditionals in Nonmonotonic Reasoning and Belief Revision. LNCS (LNAI), vol. 2087, p. 27. Springer, Heidelberg (2001)
Kern-Isberner, G., Lukasiewicz, T.: Combining probabilistic logic programming with the power of maximum entropy. Artif. Intell. 157(1-2), 139–202 (2004)
Kern-Isberner, G., Thimm, M.: A ranking semantics for first-order conditionals. In: ECAI 2012, pp. 456–461. IOS Press (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)
Milch, B., Zettlemoyer, L., Kersting, K., Haimes, M., Kaelbling, L.P.: Lifted probabilistic inference with counting formulas. In: AAAI 2008, pp. 1062–1068. AAAI Press (2008)
Nilsson, N.: Probabilistic logic. Artificial Intelligence 28, 71–87 (1986)
Nute, D., Cross, C.: Conditional logic. In: Gabbay, D., Guenther, F. (eds.) Handbook of Philosophical Logic, 2nd edn., vol. 4, pp. 1–98. Kluwer Academic Publishers (2002)
Paris, J.: The uncertain reasoner’s companion – A mathematical perspective. Cambridge University Press (1994)
Pearl, J.: Probabilistic Reasoning in Intelligent Systems. Morgan Kaufmann, San Mateo (1988)
de Salvo Braz, R., Amir, E., Roth, D.: Lifted first-order probabilistic inference. In: IJCAI 2005, pp. 1319–1325. Professional Book Center (2005)
Shore, J., Johnson, R.: Axiomatic derivation of the principle of maximum entropy and the principle of minimum cross-entropy. IEEE Transactions on Information Theory IT-26, 26–37 (1980)
Zhu, C., Byrd, R.H., Lu, P., Nocedal, J.: Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization. ACM Trans. Math. Softw. 23(4), 550–560 (1997), http://doi.acm.org/10.1145/279232.279236
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Finthammer, M., Beierle, C. (2014). A Two-Level Approach to Maximum Entropy Model Computation for Relational Probabilistic Logic Based on Weighted Conditional Impacts. In: Straccia, U., Calì, A. (eds) Scalable Uncertainty Management. SUM 2014. Lecture Notes in Computer Science(), vol 8720. Springer, Cham. https://doi.org/10.1007/978-3-319-11508-5_14
Download citation
DOI: https://doi.org/10.1007/978-3-319-11508-5_14
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-11507-8
Online ISBN: 978-3-319-11508-5
eBook Packages: Computer ScienceComputer Science (R0)