Bayesian network parameter learning algorithm based on improved QMAP

Abstract

Small data sets make the statistical information in Bayesian network parameter learning inaccurate, which makes it difficult to get accurate Bayesian network parameters based on data. Qualitative maximum a posteriori estimation (QMAP) is the most accurate algorithm for Bayesian network parameter learning under the condition of small data sets. However, when the number of parameter constraints is large or the parameter feasible region is small, the rejection-acceptance sampling process in QMAP algorithm will become extremely time-consuming. In order to improve the learning efficiency of QMAP algorithm and not affect its learning accuracy as much as possible, a new analytical calculation method of the center point of constrained region is designed to replace the original rejection-acceptance sampling calculation method. Firstly, a new objective function is designed, and a constrained objective optimization problem for solving the boundary points of the constrained region is constructed. Secondly, a new optimization engine is used to solve the objective optimization problem, and the boundary points and center points of the constrained region are obtained. Finally, the existing QMAP algorithm is improved by the obtained center points. The simulation results show that the CMAP algorithm proposed in this paper has a slightly worse parameter learning accuracy than the QMAP algorithm, but its computational efficiency is 2-5 times higher than that of the QMAP algorithm.

Keywords

• bayesian network
• parameter learning
• qualitative maximum a posteriori estimation
• parameter constraints
• objective optimization