(A) study on rank-order based classification and class numbers

Abstract

Consider a rank-ordering problem, ranking a group of subjects by the conditional probability from a Bayesian network (BN) model of binary variables. The conditional probability is the probability that a subject has a certain value given an outcome of some other variables. The classification is based on the rank order and the class levels are assigned in an equal proportion manner. Under the assumption that the random variables are positive associated, we compared the classification results between two BN models of binary variables which share a model structure. We constructed a similar BN model, which was the best in the sense of the Kullback-Leibler divergence measure. Results from numerical experiments indicate that the agreement level of the classification between the actual and similar BN models is considerably high for the class number L = 5,7,9. It is also found that the agreement level decreases in an exponential mode as L increases. We developed an R code for checking similarity between BN models and it is available upon request.