Bayesian approach to learn Bayesian networks using data and constraints

One of the essential problems on Bayesian networks (BNs) is parameter learning. When purely data-driven methods fail to work, incorporating supplemental information, like expert judgments, can improve the learning of BN parameters. In practice, expert judgments are provided and transformed into qualitative parameter constraints. Moreover, prior distributions of BN parameters are also useful information. In this paper we propose a Bayesian approach to learn parameters from small datasets by integrating both parameter constraints and prior distributions. First, the feasible parameter region is derived from constraints. Then, using the prior distribution, a posterior distribution over the feasible region is developed based on the Bayes theorem. Finally, the parameter estimations are taken as the mean values of the posterior distribution. Learning experiments on standard BNs reveal that the proposed method outperforms most of the existing methods.