Bayesian Network Parameter Learning from Data Contains Missing Values

Learning Bayesian network structure from data has attracted a great deal of research in recent years. It is shown that finding the optimal network is an NP-hard problem when data is complete. This problem gets worse when data is incomplete i.e. contains missing values and/or hidden variables. Generally, there are two cases of learning Bayesian networks from incomplete data: in a known structure, and unknown structure. In this paper, we try to find the best parameters for a known structure by introducing the “effective parameter”, in a way that the likelihood of the network structure given the completed data being maximized. This approach can be attached to any algorithm such as SEM (structural expectation maximization) that needs the best parameters to be known to reach the optimal Bayesian network structure. We prove that the proposed method gains the optimal parameters with respect to the likelihood function. Results of applying the proposed method to some known Bayesian networks show the speed of the proposed method compared to the well-known methods.