Abstract: Structure learning algorithms for a Bayesian network mainly include hill-climbing algorithm, K2 algorithm and so on. However, these algorithms require large sample data sets. For the small sample sets in practical problems, this paper introduces the probability density kernel estimation method to achieve the expansion of the original sample set, and then uses the K2 algorithm for a Bayesian network structure learning. By optimizing the kernel function and window width, it achieves the effective expansion of the original sample set based on probability density kernel estimation; it confirms the variable order based on mutual information, and then establishes a Bayesian structure learning algorithm based on a small sample set. Simulation results show that the algorithm is effective and practical.

Key words: Bayesian network, structure learning based on small sample set, K2

摘要： 贝叶斯网络结构学习算法主要包括爬山法和K2算法等，但这些方法均要求面向大样本数据集。针对实际问题中样本集规模小的特点，通过引入概率密度核估计方法以实现对原始样本集的拓展，利用K2算法进行贝叶斯网络结构学习。通过优化选择核函数和窗宽，基于密度核估计方法实现了样本集的有效扩展；同时基于互信息度进行变量顺序的确认，进而建立了小规模样本集的贝叶斯结构学习算法。仿真结果验证了新学习算法的有效性和实用性。

关键词: 贝叶斯网络, 小样本结构学习, K2算法