Abstract: Structure learning is one of the most important branches in Bayesian network, while learning Bayesian network structures from data is NP-complete. An improved algorithm is provided for learning Bayesian network structures from data. It constructs the initial undirected graph based on mutual information, and then orients undirected edges by using conditional independence tests, additionally a local optimal method for four-node and five-node loops is proposed to construct the initial draft about the structure, finally greedy search is performed to explore the optimal structure. Numerical experiments show that both the BIC score and structure error have some improvements, and the number of iterations and running time are greatly reduced. Therefore the structure with highest degree of data matching can be relatively faster determined by the improved algorithm.

Key words: Bayesian network, structure learning, mutual information, conditional independence test, greedy search

摘要： 结构学习是贝叶斯网络的重要分支之一，而由数据学习贝叶斯网络是NP-完全问题，提出了一个由数据学习贝叶斯网络的改进算法。该算法基于互信息知识构造初始无向图，并通过条件独立测试对无向边添加方向；同时提出了一个针对4节点环和5节点环的局部优化方法来构造初始框架，最后利用贪婪搜索算法得到最优网络结构。数值实验结果表明，改进的算法无论是在BIC评分值，还是在结构的误差上都有一定的改善，并且在迭代次数、运行时间上均有明显降低，能较快地确定出与数据匹配程度最高的网络结构。

关键词: 贝叶斯网络, 结构学习, 互信息, 条件独立性测试, 贪婪搜索