Bayesian network parameter learning using constraint-based data extension method

Bayesian networks (BNs) are one of the most compelling theoretical models in uncertain knowledge representation and inference. However, many domains are encountering the dilemma of insufficient data. Learning BN parameters using raw data may lead to low learning accuracy. Therefore, this paper seeks to solve the problem via two novel data extension methods. First, a constraint-based nonparametric bootstrap (CNB) method is proposed, which extends the raw data and guides the parameter distribution of the extended data through a constraint-based sample scoring function. The experimental results on 12 BNs show that the extended data can improve the parameter learning accuracy and enhance the existing parameter learning approaches. The CNB is still valid for medium and large networks with relatively large data. When the original data are of inferior quality, the CNB is unattainable to extend it. Then, a constraint-based parametric bootstrap (CPB) method is proposed, creating a new parameter distribution by constraints and the original samples. The experimental results for the missing data demonstrate that the extended data perform better. The CPB is insensitive to the proportion of missing data and remains superior in relatively large data.