An Extended MPL-C Model for Bayesian Network Parameter Learning with Exterior Constraints

Lack of relevant data is a major challenge for learning Bayesi-an networks (BNs) in real-world applications. Knowledge engineering techniques attempt to address this by incorporating domain knowledge from experts. The paper focuses on learning node probability tables using both expert judgment and limited data. To reduce the massive burden of eliciting individual probability table entries (parameters) it is often easier to elicit

constraints

on the parameters from experts. Constraints can be interior (between entries of the same probability table column) or exterior (between entries of different columns). In this paper we introduce the first auxiliary BN method (called MPL-EC) to tackle parameter learning with exterior constraints. The MPL-EC itself is a BN, whose nodes encode the data observations, exterior constraints and parameters in the original BN. Also, MPL-EC addresses (i) how to estimate target parameters with both data and constraints, and (ii) how to fuse the weights from different causal relationships in a robust way. Experimental results demonstrate the superiority of MPL-EC at various sparsity levels compared to conventional parameter learning algorithms and other state-of-the-art parameter learning algorithms with constraints. Moreover, we demonstrate the successful application to learn a real-world software defects BN with sparse data.