Abstract
It is known that d-separation can determine the minimum amount of information needed to process a query during exact inference in discrete Bayesian networks. Unfortunately, no practical method is known for determining the semantics of the intermediate factors constructed during inference. Instead, all inference algorithms are relegated to denoting the inference process in terms of potentials. In this theoretical paper, we give an algorithm, called Semantics in Inference (SI), that uses d-separation to denote the semantics of every potential constructed during inference. We show that SI possesses four salient features: polynomial time complexity, soundness, completeness, and strong completeness. SI provides a better understanding of the theoretical foundation of Bayesian networks and can be used for improved clarity, as shown via an examination of Bayesian network literature.
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
Butz, C.J., Hua, S., Konkel, K., Yao, H.: Join Tree Propagation with Prioritized Messages. Networks 55(4), 350–359 (2010)
Butz, C.J., Konkel, K., Lingras, P.: Join Tree Propagation Utilizing both Arc Reversal and Variable Elimination. Int. J. Approx. Reasoning 52(7), 948–959 (2011)
Butz, C.J., Yan, W., Lingras, P., Yao, Y.Y.: The CPT Structure of Variable Elimination in Discrete Bayesian Networks. In: Ras, Z.W., Tsay, L.S. (eds.) Advances in Intelligent Information Systems. SCI, vol. 265, pp. 245–257. Springer, Heidelberg (2010)
Castillo, E., Gutiérrez, J., Hadi, A.: Expert Systems and Probabilistic Network Models. Springer, New York (1997)
Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms. MIT Press, Cambridge (2009)
Darwiche, A.: Modeling and Reasoning with Bayesian Networks. Cambridge University Press, New York (2009)
Kjaerulff, U.B., Madsen, A.L.: Bayesian Networks and Influence Diagrams. Springer, New York (2008)
Koller, D., Friedman, N.: Probabilistic Graphical Models: Principles and Techniques. MIT Press, Cambridge (2009)
Madsen, A.L.: A Differential Semantics of Lazy AR Propagation. In: 21st Conference on Uncertainty in Artificial Intelligence, pp. 364–371. Morgan Kaufmann, San Mateo (2005)
Madsen, A.L.: Improvements to Message Computation in Lazy Propagation. Int. J. Approximate Reasoning 51(5), 499–514 (2010)
Meek, C.: Strong Completeness and Faithfulness in Bayesian Networks. In: 11th Conference on Uncertainty in Artificial Intelligence, pp. 411–418. Morgan Kaufmann, San Mateo (1995)
Pearl, J.: Fusion, Propagation and Structuring in Belief Networks. Artif. Intell. 29, 241–288 (1986)
Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, San Francisco (1988)
Pearl, J.: Belief Networks Revisited. Artif. Intell. 59, 49–56 (1993)
Shafer, G.: Probabilistic Expert Systems. SIAM, Philadelphia (1996)
Wong, S.K.M., Butz, C.J., Wu, D.: On the Implication Problem for Probabilistic Conditional Independency. IEEE Trans. Syst. Man Cybern. A 30(6), 785–805 (2000)
Zhang, N.L., Poole, D.: A Simple Approach to Bayesian Network Computations. In: 7th Canadian Conference on Artificial Intelligence, pp. 171–178. Springer, New York (1994)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Butz, C.J., Yan, W., Madsen, A.L. (2013). d-Separation: Strong Completeness of Semantics in Bayesian Network Inference. In: Zaïane, O.R., Zilles, S. (eds) Advances in Artificial Intelligence. Canadian AI 2013. Lecture Notes in Computer Science(), vol 7884. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38457-8_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-38457-8_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-38456-1
Online ISBN: 978-3-642-38457-8
eBook Packages: Computer ScienceComputer Science (R0)