Abstract
Lazy Propagation (LP) is a propagation scheme for belief update in Bayesian networks based upon Shenoy-Shafer propagation. So far the secondary computational structure has been a junction tree (or strong junction tree). This paper describes and shows how different tree structures can be used for LP. This includes the use of different junction trees and the maximal prime subgraph decomposition organised as a tree. The paper reports on the results of an empirical evaluation on a set of real-world Bayesian networks of the performance impact of using different tree structures in LP. The results indicate that the tree structure can have a significant impact on both time and space performance of belief update.
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Bloemeke, M., Valtorta, M.: A Hybrid Algorithm to compute Marginal and Joint Beliefs in Bayesian Networks and Its Complexity. In: Proc. of the UAI, pp. 16–23 (1998)
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)
Dechter, R.: Bucket elimination: A unifying framework for probabilistic inference. Artificial Intelligence 113(1-2), 41–85 (1999)
Jensen, F.V.: HUGIN API Reference Manual. HUGIN EXPERT A/S, Reference Manual for the HUGIN version 7.7 (2012), http://www.hugin.com
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., Madsen, A.L.: Bayesian Networks and Influence Diagrams: A Guide to Construction and Analysis, 2nd edn. Springer (2012)
Lauritzen, S.L., Spiegelhalter, D.J.: Local computations with probabilities on graphical structures and their application to expert systems. Journal of the Royal Statistical Society, B 50(2), 157–224 (1988)
Li, Z., D’Ambrosio, B.: Efficient Inference in Bayes Networks as a Combina torial Optimization Problem. Int. J. of Approximate Reasoning 11(1), 55–81 (1994)
Madsen, A.L.: An empirical evaluation of possible variations of lazy propagation. In: Proc. of the UAI, pp. 366–373 (2004)
Madsen, A.L.: Variations Over the Message Computation Algorithm of Lazy Propagation. IEEE TSMC Part B 36(3), 636–648 (2006)
Madsen, A.L.: Improvements to Message Computation in Lazy Propagation. Int. J. of Approximate Reasoning 51(5), 499–514 (2010)
Madsen, A.L., Butz, C.J.: On the Importance of Elimination Heuristics in Lazy Propagation. In: Sixth European Workshop on Probabilistic Graphical Models, pp. 227–234 (2012)
Madsen, A.L., Jensen, F.V., 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 Evaluation of Symmetric Bayesian Decision Problems. In: Proc. of the UAI, pp. 382–390 (1999)
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)
Olesen, K.G., Madsen, A.L.: Maximal Prime Subgraph Decomposition of Bayesian Networks. IEEE TSMC Part B 32(1), 21–31 (2002)
Olmsted, S.M.: On representing and solving decision problems. PhD thesis, Department of Engineering-Economic Systems, Stanford University, CA (1983)
Ottosen, T.J., Vomlel, J.: All roads lead to Rome - New search methods for the optimal triangulation problem. Int. J. of Approximate Reasoning 53(9), 1350–1366 (2012)
Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Series in Representation and Reasoning. Morgan Kaufmann Publishers, San Mateo (1988)
Rose, D.J., Tarjan, R.E., Lueker, G.S.: Algorithmic aspects of vertex elimination on graphs. SIAM Journal of Computing 5(2), 266–283 (1976)
Shachter, R., D’Ambrosio, B., DelFavero, B.: Symbolic probabilistic inference in belief networks. In: Proc. Eighth National Conference on AI, pp. 126–131 (1990)
Shachter, R.D.: Evaluating influence diagrams. Operations Research 34(6), 871–882 (1986)
Shafer, G.R.: Probabilistic Expert Systems. SIAM (1996)
Shenoy, P.P.: Binary join trees for computing marginals in the Shenoy-Shafer architecture. Int. J. of Approximate Reasoning 17(2-3), 239–263 (1997)
Shenoy, P.P., Shafer, G.: Axioms for probability and belief-function propagation. In: Proc. of the UAI, pp. 169–198 (1990)
Zhang, N.L., Poole, D.: A simple approach to bayesian network computations. In: Proc. of the Canadian Conference on AI, pp. 171–178 (1994)
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Madsen, A.L., Butz, C. (2013). On the Tree Structure Used by Lazy Propagation for Inference in Bayesian Networks. In: van der Gaag, L.C. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2013. Lecture Notes in Computer Science(), vol 7958. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39091-3_34
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