Node order is one of the most important factors in learning the structure of a Bayesian network (BN) for probabilistic reasoning. To improve the BN structure learning, we propose a node order learning algorithm based on the frequently used Bayesian information criterion (BIC) score function. The algorithm dramatically reduces the space of node order and makes the results of BN learning more stable and effective. Specifically, we first find the most dependent node for each individual node, prove analytically that the dependencies are undirected, and then construct undirected subgraphs U_G. Secondly, the U_G is examined and connected into a single undirected graph U_GC. The relation between the subgraph number and the node number is analyzed. Thirdly, we provide the rules of orienting directions for all edges in U_GC, which converts it into a directed acyclic graph (DAG). Further, we rank the DAG’s topology order and describe the BIC-based node order learning algorithm. Its complexity analysis shows that the algorithm can be conducted in linear time with respect to the number of samples, and in polynomial time with respect to the number of variables. Finally, experimental results demonstrate significant performance improvement by comparing with other methods.

节点顺序是学习用于概率推理的贝叶斯网络 (BN) 结构的最重要因素之一。为了改进BN结构学习，我们提出了一种基于常用贝叶斯信息准则（BIC）评分函数的节点顺序学习算法。该算法极大地减少了节点顺序空间，使BN学习的结果更加稳定有效。具体来说，我们首先为每个单独的节点找到最依赖的节点，分析证明这些依赖是无向的，然后构造无向子图 U _G。其次，检查U _G并连接成单个无向图 U _GC. 分析子图编号与节点编号的关系。第三，我们提供了 U _{GC 中}所有边的定向规则，将其转换为有向无环图（DAG）。此外，我们对 DAG 的拓扑顺序进行排序并描述基于 BIC 的节点顺序学习算法。其复杂度分析表明，该算法对于样本数可以在线性时间内进行，对于变量数可以在多项式时间内进行。最后，通过与其他方法的比较，实验结果证明了显着的性能提升。