Abstract
Testing independencies is a fundamental task in reasoning with Bayesian networks (BNs). In practice, d-separation is often utilized for this task, since it has linear-time complexity. However, many have had difficulties in understanding d-separation in BNs. An equivalent method that is easier to understand, called m-separation, transforms the problem from directed separation in BNs into classical separation in undirected graphs. Two main steps of this transformation are pruning the BN and adding undirected edges.
In this paper, we propose u-separation as an even simpler method for testing independencies in a BN. Our approach also converts the problem into classical separation in an undirected graph. However, our method is based upon the novel concepts of inaugural variables and rationalization. Thereby, the primary advantage of u-separation over m-separation is that m-separation can prune unnecessarily and add superfluous edges. Hence, u-separation is a simpler method in this respect.
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References
Butz, C.J., dos Santos, A.E., Oliveira, J.S., Gonzales, C.: Testing independencies in Bayesian networks with i-Separation. In: Proceedings of the Twenty-Ninth International FLAIRS Conference (2016)
Geiger, D., Verma, T.S., Pearl, J.: d-separation: from theorems to algorithms. In: Fifth Conference on Uncertainty in Artificial Intelligence, pp. 139–148 (1989)
Kjærulff, U.B., Madsen, A.L.: Bayesian Networks and Influence Diagrams: A Guide to Construction and Analysis, 2nd edn. Springer, New York (2013)
Koller, D., Friedman, N.: Probabilistic Graphical Models: Principles and Techniques. MIT Press, Cambridge (2009)
Lauritzen, S.L., Dawid, A.P., Larsen, B.N., Leimer, H.G.: Independence properties of directed Markov fields. Networks 20, 491–505 (1990)
Lauritzen, S.L., Spiegelhalter, D.J.: Local computation with probabilities on graphical structures and their application to expert systems. J. Roy. Stat. Soc. 50, 157–244 (1988)
Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, Burlington (1988)
Pearl, J.: Fusion, propagation and structuring in belief networks. Artif. Intell. 29, 241–288 (1986)
Pearl, J.: Belief networks revisited. Artif. Intell. 59, 49–56 (1993)
Pearl, J.: Causality. Cambridge University Press, Cambridge (2009)
Verma, T., Pearl, J.: Equivalence and synthesis of causal models. In: Sixth Conference on Uncertainty in Artificial Intelligence, pp. 220–227. GE Corporate Research and Development (1990)
Wong, S.K.M., Butz, C.J., Wu, D.: On the implication problem for probabilistic conditional independency. IEEE Trans. Syst. Man Cybern. Part A: Syst. Humans 30(6), 785–805 (2000)
Zhang, N.L., Poole, D.: A simple approach to Bayesian network computations. In: Proceedings of the Tenth Canadian Artificial Intelligence Conference, pp. 171–178 (1994)
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Butz, C.J., dos Santos, A.E., Oliveira, J.S., Gonzales, C. (2016). A Simple Method for Testing Independencies in Bayesian Networks. In: Khoury, R., Drummond, C. (eds) Advances in Artificial Intelligence. Canadian AI 2016. Lecture Notes in Computer Science(), vol 9673. Springer, Cham. https://doi.org/10.1007/978-3-319-34111-8_27
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DOI: https://doi.org/10.1007/978-3-319-34111-8_27
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