Self-Adapted and Filtered Qualitative Maximum a Posterior Algorithm for Small Data Sets

This paper studies Bayesian network parameter learning from small data sets. Among existing techniques for parameter estimation in Bayesian network, qualitative maximum a posterior (QMAP) is state-of-the-art for small data sets. However, the uncertainty of pseudo prior statistic counts and the interference information in the broad prior constraints given by domain experts limit its performance. To further improve the learning accuracy and to eliminate interference information from given constraints, a self-adapted and filtered QMAP (SFQMAP) algorithm is proposed in this paper. The algorithm improves the learning performance by exploiting proper quantities of pseudo prior statistic count and applying the filtration model in QMAP. Via experiments on a series of examples we demonstrate that our approach is significantly more accurate than existing techniques for parameter learning from small data sets.