Learning the Structure of Bayesian Networks from Incomplete Data Using a Mixture Model

Abstract

In this paper, we provide an approach to learning optimal Bayesian network (BN) structures from incomplete data based on the BIC score function using a mixture model to handle miss- ing values. We have compared the proposed approach with other methods. Our experiments have been conducted on different models, some of them Belief Noisy-Or (BNO) ones. We have performed experiments using datasets with values missing completely at random having differ- ent missingness rates and data sizes. We have analyzed the significance of differences between the algorithm performance levels using the Wilcoxon test. The new approach typically learns additional edges in the case of Belief Noisy-or models. We have analyzed this issue using the Chi-square test of independence between the variables in the true models; this approach reveals that additional edges can be explained by strong dependence in generated data. An important property of our new method for learning BNs from incomplete data is that it can learn not only optimal general BNs but also specific Belief Noisy-Or models which is using in many applica- tions such as medical application.