Fundamental concepts of qualitative probabilistic networks
Artificial Intelligence
Bayesian Networks and Decision Graphs
Bayesian Networks and Decision Graphs
Classification trees for problems with monotonicity constraints
ACM SIGKDD Explorations Newsletter
Dualization, decision lists and identification of monotone discrete functions
Annals of Mathematics and Artificial Intelligence
MAP complexity results and approximation methods
UAI'02 Proceedings of the Eighteenth conference on Uncertainty in artificial intelligence
Incremental tradeoff resolution in qualitative probabilistic networks
UAI'98 Proceedings of the Fourteenth conference on Uncertainty in artificial intelligence
Probabilities for a probabilistic network: a case study in oesophageal cancer
Artificial Intelligence in Medicine
Enhanced qualitative probabilistic networks for resolving trade-offs
Artificial Intelligence
Local Monotonicity in Probabilistic Networks
ECSQARU '07 Proceedings of the 9th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Verifying monotonicity of Bayesian networks with domain experts
International Journal of Approximate Reasoning
ACM Transactions on Internet Technology (TOIT)
Attaining monotonicity for Bayesian networks
ECSQARU'11 Proceedings of the 11th European conference on Symbolic and quantitative approaches to reasoning with uncertainty
Most probable explanations in Bayesian networks: Complexity and tractability
International Journal of Approximate Reasoning
The computational complexity of monotonicity in probabilistic networks
FCT'07 Proceedings of the 16th international conference on Fundamentals of Computation Theory
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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 poly-trees. 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.