2012/07/11 by Linda C. van der Gaag, van der Gaag, Linda C., Hans L. Bodlaender +3
Computer Science · #Artificial Intelligence (cs.AI) #Bayesian Modeling and Causal Inference #FOS: Computer and information sciences #cs.AI
paper · pdf · doi:10.48550/arxiv.1207.4160
Appears in Proceedings of the Twentieth Conference on Uncertainty in Artificial Intelligence (UAI2004)
arxiv created 2012/07/11 · openalex publication_date 2012/07/11 · arxiv updated 2012/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.