Monotonicity in Bayesian Networks
This addresses the need for formal verification of monotonicity assumptions in Bayesian networks, particularly in domains like oncology, but is incremental as it builds on existing complexity theory and algorithmic approaches.
The paper tackles the problem of verifying monotonicity in Bayesian networks, showing that determining if a network is monotone in distribution or mode is coNPPP-complete in general and coNP-complete for polytrees, and presents an approximate algorithm for distribution monotonicity applied to an oncology network.
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.