Abstract
Semantics in Bayesian network inference has received an increasing level of interest in recent years. This paper considers the use of semantics in Bayesian network inference using Lazy Propagation. In particular, we describe how the semantics of potentials created during belief update can be determined using the Semantics in Inference algorithm. This includes a description of the necessary properties of Semantics in Inference to make the task feasible to be performed as part of belief update. The paper also reports on the results of an experimental analysis designed to determine the average number of potentials and distributions created during belief update on a set of real-world Bayesian networks.
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References
Butz, C.J., de S. Oliveira, J., Madsen, A.L.: Bayesian network inference using marginal trees. In: van der Gaag, L.C., Feelders, A.J. (eds.) PGM 2014. LNCS (LNAI), vol. 8754, pp. 81–96. Springer, Heidelberg (2014)
Butz, C.J., Konkel, K., Lingras, P.: Join tree propagation utilizing both arc reversal and variable elimination. Intl. J. Approx. Rea. 52(7), 948–959 (2011)
Butz, C.J., Yan, W., Madsen, A.L.: d-separation:strong completeness of semantics in bayesian network inference. In: Zaïane, O.R., Zilles, S. (eds.) Canadian AI 2013. LNCS (LNAI), vol. 7884, pp. 13–24. Springer, Heidelberg (2013)
Butz, C.J., Yan, W., Madsen, A.L.: On semantics of inference in bayesian networks. In: van der Gaag, L.C. (ed.) ECSQARU 2013. LNCS (LNAI), vol. 7958, pp. 73–84. Springer, Heidelberg (2013)
Butz, C.J., Yao, H., Hua, S.: A join tree probability propagation architecture for semantic modelling. J. Int. Info. Sys. 33(2), 145–178 (2009)
Cooper, G.F.: The computational complexity of probabilistic inference using Bayesian belief networks. Artificial Intelligence 42(2–3), 393–405 (1990)
Cowell, R.G., Dawid, A.P., Lauritzen, S.L., Spiegelhalter, D.J.: Probabilistic Networks and Expert Systems. Springer (1999)
Dagum, P., Luby, M.: Approximating probabilistic inference in Bayesian belief netwoks is NP-hard. Artificial Intelligence 60, 141–153 (1993)
Darwiche, A.: Modeling and Reasoning with Bayesian Networks. Cambridge University Press (2009)
Jensen, F.: HUGIN API Reference Manual, Version 8.1 (2014). www.hugin.com
Jensen, F.V., Jensen, F.: Optimal junction trees. In: Proc. of UAI, pp. 360–366 (1994)
Jensen, F.V., Lauritzen, S.L., Olesen, K.G.: Bayesian updating in causal probabilistic networks by local computations. Computational Statistics Quarterly 4, 269–282 (1990)
Jensen, F.V., Nielsen, T.D.: Bayesian Networks and Decision Graphs, 2nd (edn.). Springer (2007)
Kjærulff, U.B.: Graph triangulation – algorithms giving small total state space. Technical Report R 90–09, University of Aalborg, Denmark (1990)
Kjærulff, U.B., Madsen, A.L.: Bayesian Networks and Influence Diagrams: A Guide to Construction and Analysis, 2nd (edn.). Springer (2013)
Koller, D., Friedman, N.: Probabilistic Graphical Models – Principles and Techniques. MITPress (2009)
Lauritzen, S.L., Spiegelhalter, D.J.: Local computations with probabilities on graphical structures and their application to expert systems. JRSS, B 50(2), 157–224 (1988)
Madsen, A.L.: A differential semantics of lazy propagation. In: Proc. of UAI, pp. 364–371 (2005)
Madsen, A.L.: Variations Over the Message Computation Algorithm of Lazy Propagation. IEEE Transactions on Systems, Man. and Cybernetics Part B 36(3), 636–648 (2006)
Madsen, A.L., Butz, C.J.: Ordering arc-reversal operations when eliminating variables in lazy ar propagation. International Journal of Approximate Reasoning 54(8), 1182–1196 (2013)
Madsen, A.L., Jensen, F., Kjærulff, U.B., Lang, M.: HUGIN - The Tool for Bayesian Networks and Influence Diagrams. International Journal on Artificial Intelligence Tools 14(3), 507–543 (2005)
Madsen, A.L., Jensen, F.V.: Lazy propagation: A junction tree inference algorithm based on lazy evaluation. Artificial Intelligence 113(1–2), 203–245 (1999)
Neapolitan, R.: Learning Bayesian Networks. Prentice Hall (2003)
Park, J.D., Darwiche, A.: A differential semantics for jointree algorithms. Artificial Intelligence 156(2), 197–216 (2004)
Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Series in Representation and Reasoning. Morgan Kaufmann Publishers, San Mateo (1988)
Shachter, R.D.: Evaluating influence diagrams. Operations Research 34(6), 871–882 (1986)
Shafer, G.R.: Probabilistic Expert Systems. SIAM (1996)
Shafer, G.R., Shenoy, P.P.: Probability Propagation. Annals of Mathematics and Artificial Intelligence 2, 327–351 (1990)
Zhang, N.L., Poole, D.: A simple approach to bayesian network computations. In: Proc. Canadian Conference on AI, pp. 171–178 (1994)
Zhang, N.L., Poole, D.: Intercausal independence and heterogeneous factorization. In: Proc. of UAI, pp. 606–614 (1994)
Zhu, M., Liu, S., Yang, Y.: Propagation in CLG Bayesian networks based on semantic modeling. Artificial Intelligence Review 38(2), 149–162 (2012)
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Madsen, A.L., Butz, C.J. (2015). Exploiting Semantics in Bayesian Network Inference Using Lazy Propagation. In: Barbosa, D., Milios, E. (eds) Advances in Artificial Intelligence. Canadian AI 2015. Lecture Notes in Computer Science(), vol 9091. Springer, Cham. https://doi.org/10.1007/978-3-319-18356-5_1
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DOI: https://doi.org/10.1007/978-3-319-18356-5_1
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