Abstract
Causal independence models offer a high level starting point for the design of Bayesian networks but are not maximally exploited as their behaviour is often unclear. One approach is to employ qualitative probabilistic network theory in order to derive a qualitative characterisation of causal independence models. In this paper we exploit polynomial forms of Boolean functions to systematically analyse causal independence models, giving rise to the notion of a polynomial causal independence model. The advantage of the approach is that it allows understanding qualitative probabilistic behaviour in terms of algebraic structure.
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References
DÃez, F.J.: Parameter adjustment in Bayes networks. the generalized noisy or-gate. In: Proceedings of the Ninth Conference on Uncertainty in Artificial Intelligence. Morgan Kaufmann Publishers, San Francisco (1993)
Druzdzel, M.J., Henrion, M.: Intercausal reasoning with uninstantiated ancestor nodes. In: Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence, pp. 317–325. Morgan Kaufmann Publishers, San Mateo (1993)
Enderton, H.B.: A Mathematical Introduction to Logic. Academic Press, Inc, London (1972)
Heckerman, D., Breese, J.: Causal independence for probability assessment and inference using Bayesian networks. IEEE, Systems, Man, and Cybernetics 26, 826–831 (1996)
Henrion, M.: Some practical issues in constructing belief networks. In: Proceedings of the Third Conference on Uncertainty in Artificial Intelligence, pp. 161–173. Elsevier, Amsterdam (1989)
Henrion, M., Druzdzel, M.J.: Qualitative propagation and scenario-based approaches to explanation in probabilistic reasoning. In: Proceedings of the Sixth Conference on Uncertainty in Artificial Intelligence, pp. 17–32 (1991)
Lucas, P.J.F.: Bayesian network modelling by qualitative patterns. Artificial Intelligence 163, 233–263 (2005)
Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann Publishers, San Francisco (1988)
Wegener, I.: The Complexity of Boolean Functions. John Wiley & Sons, New York (1987)
Wellman, M.P.: Fundamental concepts of qualitative probabilistic networks. Artificial Intelligence 44, 257–303 (1990)
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van Gerven, M., Lucas, P., van der Weide, T. (2005). A Qualitative Characterisation of Causal Independence Models Using Boolean Polynomials. In: Godo, L. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2005. Lecture Notes in Computer Science(), vol 3571. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11518655_22
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DOI: https://doi.org/10.1007/11518655_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-27326-4
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