Model Similarity and Rank-Order Based Classification of Bayesian Networks

Suppose that we rank-order the conditional probabilities for a group of subjects that are provided from a Bayesian network (BN) model of binary variables. The conditional probability is the probability that a subject has a certain attribute given an outcome of some other variables and the classification is based on the rank-order. Under the condition that the class sizes are equal across the class levels and that all the variables in the model are positively associated with each other, we compared the classification results between models of binary variables which share the same model structure. In the comparison, we used a BN model, called a similar BN model, which was constructed under some rule based on a set of BN models satisfying certain conditions. Simulation results indicate that the agreement level of the classification between a set of BN models and their corresponding similar BN model is considerably high with the exact agreement for about half of the subjects or more and the agreement up to one-class-level difference for about 90% or more.