A Short Note on Improvement of Agreement Rate

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 is in a certain state given an outcome of some other variables. The classification is based on the rank order and the class levels are assigned with equal proportions. Two BN models are said to be similar to each other if they are of the same model structure but with different probability distributions each of which satisfies the positive association condition. Let \({\mathcal M}\) be a set of BN models which are similar to each other. We constructed a BN model M^∗, which is similar to all the models in \({\mathcal M}\) and the best with regard to \({\mathcal M}\) in the sense of the Kullback-Leibler divergence measure. It is found by numerical experiments that, on average, the agreement rate of classifications between a model in \({\mathcal M}\) and the similar model M^∗ is far larger than that by a random classification and the difference in agreement rate becomes more apparent as the class number increases.