Uncertainty in Artificial Intelligence
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Monotonicity in Bayesian Networks
Linda van der Gaag, Hans Bodlaender, Ad Feelders
Abstract:
For many real-life Bayesian networks, common knowledge dictates that the output established for the main variable of interest increases with higher values for the observable variables. We define two concepts of monotonicity to capture this type of knowledge. We say that a network is isotone in distribution if the probability distribution computed for the output variable given specific observations is stochastically dominated by any such distribution given higher-ordered observations; a network is isotone in mode if a probability distribution given higher observations has a higher mode. We show that establishing whether a network exhibits any of these properties of monotonicity is coNPPP-complete in general, and remains coNP-complete for polytrees. We present an approximate algorithm for deciding whether a network is monotone in distribution and illustrate its application to a real-life network in oncology.
Keywords: null
Pages: 569-576
PS Link:
PDF Link: /papers/04/p569-van_der_gaag.pdf
BibTex:
@INPROCEEDINGS{van der Gaag04,
AUTHOR = "Linda van der Gaag and Hans Bodlaender and Ad Feelders",
TITLE = "Monotonicity in Bayesian Networks",
BOOKTITLE = "Proceedings of the Twentieth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-04)",
PUBLISHER = "AUAI Press",
ADDRESS = "Arlington, Virginia",
YEAR = "2004",
PAGES = "569--576"
}


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