小数据集条件下基于双重约束的BN参数学习

针对小数据集条件下的贝叶斯网络（Bayesian network，BN）参数学习问题，提出了一种基于双重约束的贝叶斯网络参数学习方法. 首先，对网络中的参数进行分析并将网络中的参数划分为: 父节点组合状态相同而子节点状态不同的参数和父节点组合状态不同而子节点状态相同的参数；然后，针对第一类参数提出了一种新的基于Beta分布拟合的贝叶斯估计方法，而针对第二类参数利用已有的保序回归估计方法进行学习，进而实现了对网络中参数的双重约束学习；最后，通过仿真实例说明了基于双重约束的参数学习方法对小数据集条件下贝叶斯网络参数学习精度提高的有效性.

Learning Bayesian Network Parameters under Dual Constraints from Small Data Set

In this paper, a novel dual constraints based parameter learning algorithm is presented to overcome the problem of Bayesian network (BN) parameter learning from small data sets. First, the parameters in the network are analyzed and classified into classes as follows: parameters referring to different child states sharing the same parent configuration state and parameters referring to different parent configuration states sharing the same child state. Then, a novel beta distribution approximation based Bayesian estimation method is proposed, which is suitable for the learning of the first category parameters. Meanwhile, previously proposed isotonic regression estimation method is employed to compute the second category parameters. Finally, simulations demonstrate the effectiveness of the proposed algorithm on improving the precision of Bayesian network parameter learning from small data set.