Learning Bayesian network parameters from small data set: an adaptive method

For parameter learning of Bayesian networks from small data set, constrained maximum likelihood (CML) method and qualitative maximum a posterior (QMAP) method are two approaches, which suit all types of existing parameter constraints. However, those two approaches dominate each other when samples size, constraint number or true-parameter location varies. That makes it tough to choose between those two methods. For that reason, a novel adaptive parameter learning method is proposed in this paper. First, CML method and QMAP method are employed to learn BN parameters. Then, sample weight, constraint weight, and parameter-location weight are defined and calculated based on rejectionacceptance sampling and spatial maximum a posterior analysis. Finally, a new set of parameters are calculated as the weighted values of CML and QMAP solutions. Furthermore, simulation results reveal that precision of parameters learnt by the proposed method, in any cases, approaches and even outperforms those of CML method and QMAP method.