Monotonicity in Bayesian networks
Linda C. van der Gaag, Hans L. Bodlaender, Ad Feelders · 2004
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 dis-tribution 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 observa-tions has a higher mode. We show that estab-lishing whether a network exhibits any of these properties of monotonicity is coNPPP-complete in general, and remains coNP-complete for poly-trees. We present an approximate algorithm for deciding whether a network is monotone in dis-tribution and illustrate its application to a real-life network in oncology. 1