Bayesian network parameter learning algorithm based on improved QMAP

基于改进QMAP的贝叶斯网络参数学习算法

¹ School of Electronic and Information Engineering, Xi'an Technological University, Xi'an 710021, China
² School of Electronic and Information, Northwestern Polytechnical University, Xi'an 710072, China

Received: 14 April 2021

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.

摘要

小数据集使得贝叶斯网络参数学习中的统计信息不准确，导致只依靠数据难以得到准确的贝叶斯网络参数。定性最大后验估计（QMAP）方法是目前小数据集条件下贝叶斯网络参数学习精度最高的算法。然而，当参数约束数量较多或参数可行域较小时，QMAP算法中的拒绝-接受采样过程会变得极为耗时甚至难以完成。为了提高QMAP算法的学习效率同时又尽量不影响其学习精度，设计了一种约束区域中心点的解析计算方法来替代原有的拒绝-接受采样计算方法。结合参数约束构建一个求解约束区域边界点的目标优化模型；利用凸优化引擎来求解该目标优化模型，获得约束区域的边界点和中心点；通过获得的约束区域中心点改进现有的QMAP算法。仿真实验证明，所提出的CMAP算法的参数学习精度稍差于QMAP算法，但计算效率比QMAP算法提高了2~5倍。