Bayesian Network Structure Learning Algorithm Based on Node Order Constraint

The K2 algorithm is one of the classical algorithms for Bayesian Network structure learning. However, the learning effect of K2 algorithm strongly depends on the maximum node in-degree $\mu$ and the node order $\rho$. In order to solve this problem, this paper proposes a new Bayesian Network structure learning algorithm: MI-Kruskal-K2 algorithm. Firstly, the algorithm calculates the mutual information MI between variables, and uses the Kruskal algorithm in Graph Theory to construct the maximum spanning tree to obtain the maximum node in-degree $\mu$; then, the maximum spanning tree was searched by Depth First Search to obtain the node order $\rho$; finally, the K2 algorithm calls the node in-degree $\mu$ and the node order $\rho$ to learn and obtain the optimal Bayesian Network structure. Experiments are carried out in a small Asia Network. Compared with the Greedy Search (GS) algorithm and Hill-Climbing (HC) algorithm, the MI-Kruskal-K2 algorithm performs better.