A Novel Qualitative Maximum a Posteriori Estimation for Bayesian Network Parameters Based on Computing the Center Point of Constrained Parameter Regions

Abstract

Introducing parameter constraints has become a mainstream approach for learning Bayesian network parameters with small datasets. The QMAP (Qualitative Maximum a Posteriori) estimation has produced the best learning accuracy among existing learning approaches. However, the rejection-acceptance sampling employed in the QMAP algorithm for determining average BN(Bayesian Network) parameter values is time-consuming, particularly when the number of parameter constraints is large. This paper proposes a new analytical approach that enhances the learning efficiency of the QMAP algorithm without reducing its learning accuracy by treating the average value of the parameters as the center point of the constrained parameter region, which is a much more efficient method than the rejection-acceptance sampling method employed in the traditional QMAP algorithm. First, a novel objective function is designed and a constrained objective optimization model is constructed based on parameter constraints. Second, the constructed model is employed to obtain the center point of the constrained parameter region based on its boundary points, and the average parameter value is the average of all boundary points. The results obtained from a large number of simulation experiments with four benchmark Bayesian networks demonstrate that of the parameter learning accuracy of the proposed algorithm is slightly better than that the original QMAP algorithm under specific conditions, and the computational efficiency is substantially increased under all conditions.