A Novel Algorithm for Bayesian Network Parameter Learning with Informative Range Constraints and Sorting Model

Learning the parameters of Bayesian networks (BNs) is a key challenge in real-world decision support applications, especially when there are small data available. Maximum A Posteriori (MAP) estimation is alternate way to compute the parameter. But the hyper parameters in MAP are difficult to determine when the samples are small. A conventional way to address this challenge is to introduce domain knowledge/expert judgments that are encoded as qualitative parameter constraints. This paper proposed a Sorting Constraint Auxiliary Model (SCAM) algorithm for learning BN parameter. We firstly translate informative range constraints into mathematics inequality formulation with regards to the relationships among BN parameters by sorting. Then we recruit conjugate distribution fitting using equivalence uniform distribution to generate virtual samplings in parameter space. The sampling counts, combined with small data statistics, help to reconstruct the BN parameter in MAP estimation. The experimental results show that the SCAM algorithm can obtain more accurate parameters than the existing parameter learning algorithms. Moreover, we demonstrate successful application to real threat assessment case studies in case of scarce data.