Learning Bayesian networks from incomplete data based on EMI method

Currently, there are few efficient methods in practice for learning Bayesian networks from incomplete data, which affects their use in real world data mining applications. This paper presents a general-duty method that estimates the (Conditional) Mutual Information directly from incomplete datasets, EMI. EMI starts by computing the interval estimates of a joint probability of a variable set, which are obtained from the possible completions of the incomplete dataset. And then computes a point estimate via a convex combination of the extreme points, with weights depending on the assumed pattern of missing data. Finally, based on these point estimates, EMI gets the estimated (conditional) Mutual Information. This paper also applies EMI to the dependency analysis based learning algorithm by J. Cheng so as to efficiently learn BNs with incomplete data. The experimental results on Asia and Alarm networks show that EMI based algorithm is much more efficient than two search & scoring based algorithms, SEM and EM-EA algorithms. In terms of accuracy, EMI based algorithm is more accurate than SEM algorithm, and comparable with EM-EA algorithm.