A Novel Algorithm for Bayesian Network Parameter Learning with Informative Prior Constraints and Maximum Entropy Model

Abstract

A key challenge in many real-world decision support applications is the parameters learning of Bayesian networks (BNs) is, particularly when the available data is small. An effective way to address this challenge is to introduce related domain expert knowledge which is encoded as prior qualitative parameter constraints. The BN parameter learning method-informative prior constraints and maximum entropy (IPCME) algorithm is proposed for the modeling of BN parameters under the small data sets. The informative qualitative prior knowledge is transformed into inequality constraints which can generate a class of candidate parameter sets by Bootstrap algorithm. Then the BN parameters are estimated according to the maximum entropy principle. Experimental results indicate that learning effects of IPCME algorithm are similar to the classical MLE algorithm when the modeling data size is sufficient. However, when the available data size is small, the parameters of BN can be modeled by IPCME as well, and the learned accuracy is superior to MLE or QMAP algorithm which is the state-of-art. IPCME is also applied to a real fault diagnosis while the data set is relatively small. The results of the diagnosis reasoning show that the proposed parameter learning approach is effective. The IPCME BN parameter learning algorithm shows its potential to benefit many real-world problems when the data sets are small.