Abstract
Two important tasks in probabilistic reasoning are the computation of the maximum posterior probability of a given subset of the variables in a Bayesian network (MAP), and the computation of the maximum expected utility of a strategy in an influence diagram (MEU). Despite their similarities, research on both problems have largely been conducted independently, with algorithmic solutions and insights designed for one problem not (trivially) transferable to the other one. In this work, we show constructively that these two problems are equivalent in the sense that any algorithm designed for one problem can be used to solve the other with small overhead. These equivalences extend the toolbox of either problem, and shall foster new insights into their solution.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
References
Antonucci, A., Piatti, A.: Modeling unreliable observations in Bayesian networks by credal networks. In: Godo, L., Pugliese, A. (eds.) SUM 2009. LNCS, vol. 5785, pp. 28–39. Springer, Heidelberg (2009)
Bodlaender, H., Koster, A., van den Eijkhof, F., van der Gaag, L.: Pre-processing for triangulation of probabilistic networks. In: Proceedings of the 17th Conference on Uncertainty in Artificial Intelligence (UAI), pp. 32–39 (2001)
de Campos, C.P.: New complexity results for MAP in Bayesian networks. In: Proceedings of the 22nd International Joint Conference on Artificial Intelligence (IJCAI), pp. 2100–2106 (2011)
de Campos, L.M., Gámez, J.A., Moral, S.: Partial abductive inference in Bayesian networks by using probability trees. In: 5th International Conference on Enterprise Information Systems (ICEIS), pp. 83–91 (2003)
de Campos, C.P., Ji, Q.: Strategy selection in influence diagrams using imprecise probabilities. In: Proceedings of the 24th Conference in Uncertainty in Artificial Intelligence (UAI), pp. 121–128 (2008)
de Paz, R.C., Gómez-Olmedo, M., Cano, A.: Approximate inference in influence diagrams using binary trees. In: Proceedings of the 6th European Workshop on Probabilistic Graphical Models (PGM), pp. 43–50 (2012)
Dechter, R.: An anytime approximation for optimizing policies under uncertainty. In: Workshop of Decision Theoretic Planning, AIPS (2000)
Dechter, R., Rish, I.: Mini-buckets: A general scheme for bounded inference. Journal of the ACM 50(2), 107–153 (2003)
Detwarasiti, A., Shachter, R.D.: Influence diagrams for team decision analysis. Decision Analysis 2(4), 207–228 (2005)
Howard, R.A., Matheson, J.E.: Influence diagrams. In: Readings on the Principles and Applications of Decision Analysis, pp. 721–762. Strategic Decisions Group (1984)
Huang, J., Chavira, M., Darwiche, A.: Solving MAP exactly by searching on compiled arithmetic circuits. In: Proceedings of the 21st National Conference on Artificial Intelligence (NCAI), pp. 1143–1148 (2006)
Jensen, F.V., Nielsen, T.D.: Bayesian Networks and Decision Graphs, 2nd edn. Information Science and Statistics. Springer (2007)
Jiang, J., Rai, P., Daume III, H.: Message-passing for approximate MAP inference with latent variables. In: Advances in Neural Information Processing Systems 24 (NIPS), pp. 1197–1205 (2011)
Khaled, A., Yuan, C., Hansen, E.: Solving limited memory influence diagrams using branch-and-bound search. In: Proceedings of the 29th Conference on Uncertainty in Artificial Intelligence, UAI (2013)
Koller, D., Friedman, N.: Probabilistic Graphical Models. MIT Press (2009)
Lauritzen, S.L., Nilsson, D.: Representing and solving decision problems with limited information. Management Science 47, 1235–1251 (2001)
Lim, H., Yuan, C., Hansen, E.: Scaling up MAP search in Bayesian networks using external memory. In: Proceedings of the 5th European Workshop on Probabilistic Graphical Models (PGM), pp. 177–184 (2010)
Liu, Q., Ihler, A.: Variational algorithms for marginal MAP. In: Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence (UAI), pp. 453–462 (2011)
Liu, Q., Ihler, A.: Belief propagation for structured decision making. In: Proceedings of the 28th Conference on Uncertainty in Artificial Intelligence (UAI), pp. 523–532 (2012)
Madsen, A.L., Nilsson, D.: Solving influence diagrams using HUGIN, Shafer-Shenoy and lazy propagation. In: Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence (UAI), pp. 337–345 (2001)
Mauá, D.D., de Campos, C.P.: Anytime marginal MAP inference. In: Proceedings of the 28th International Conference on Machine Learning (ICML), pp. 1471–1478 (2012)
Mauá, D.D., de Campos, C.P., Zaffalon, M.: The complexity of approximately solving influence diagrams. In: Proceedings of the 28th Conference on Uncertainty in Artificial Intelligence (UAI), pp. 604–613 (2012)
Mauá, D.D., de Campos, C.P., Zaffalon, M.: On the complexity of solving polytree-shaped limited memory influence diagrams with binary variables. Artificial Intelligence 205, 30–38 (2013)
Mauá, D.D., de Campos, C.P.: Solving decision problems with limited information. In: Advances in Neural Information Processing Systems 24 (NIPS), pp. 603–611 (2011)
Mauá, D.D., de Campos, C.P., Zaffalon, M.: Solving limited memory influence diagrams. Journal of Artificial Intelligence Research 44, 97–140 (2012)
Meek, C., Wexler, Y.: Approximating max-sum-product problems using multiplicative error bounds. Bayesian Statistics 9, 439–472 (2011)
Nilsson, D., Höhle, M.: Computing bounds on expected utilities for optimal policies based on limited information. Research Report 94, Dina (2001)
Nilsson, D., Lauritzen, S.L.: Evaluating influence diagrams using LIMIDs. In: Proceedings of the 16th Conference in Uncertainty in Artificial Intelligence (UAI), pp. 436–445 (2000)
Park, J.D., Darwiche, A.: Solving MAP exactly using systematic search. In: Proceedings of the 19th Conference on Uncertainty in Artificial Intelligence (UAI), pp. 459–468 (2003)
Park, J.D., Darwiche, A.: Complexity results and approximation strategies for MAP explanations. Journal of Artificial Intelligence Research 21, 101–133 (2004)
Shenoy, P.P.: Binary join trees for computing marginals in the Shenoy-Shafer architecture. International Journal of Approximate Reasoning 17(2-3), 239–263 (1997)
Yuan, C., Wu, X., Hansen, E.A.: Solving multistage influence diagrams using branch-and-bound search. In: Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence (UAI), pp. 691–700 (2010)
Zhang, N.L., Qi, R., Poole, D.: A computational theory of decision networks. International Journal of Approximate Reasoning 11(2), 83–158 (1994)
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
Mauá, D.D. (2014). Equivalences between Maximum a Posteriori Inference in Bayesian Networks and Maximum Expected Utility Computation in Influence Diagrams. In: van der Gaag, L.C., Feelders, A.J. (eds) Probabilistic Graphical Models. PGM 2014. Lecture Notes in Computer Science(), vol 8754. Springer, Cham. https://doi.org/10.1007/978-3-319-11433-0_21
Download citation
DOI: https://doi.org/10.1007/978-3-319-11433-0_21
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-11432-3
Online ISBN: 978-3-319-11433-0
eBook Packages: Computer ScienceComputer Science (R0)