It is important for Bayesian network (BN) structure learning, a NP-problem, to improve the accuracy and hybrid algorithms are a kind of effective structure learning algorithms at present. Most hybrid algorithms adopt the strategy of one heuristic search and can be divided into two groups: one heuristic search based on initial BN skeleton and one heuristic search based on initial solutions. The former often fails to guarantee globality of the optimal structure and the latter fails to get the optimal solution because of large search space. In this paper, an efficient hybrid algorithm is proposed with the strategy of two-stage searches. For first-stage search, it firstly determines the local search space based on Maximal Information Coefficient by introducing penalty factors p1, p2, then searches the local space by Binary Particle Swarm Optimization. For second-stage search, an efficient ADR (the abbreviation of Add, Delete, Reverse) algorithm based on three basic operators is designed to extend the local space to the whole space. Experiment results show that the proposed algorithm can obtain better performance of BN structure learning.

中文翻译：

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基于两阶段搜索策略的高效贝叶斯网络结构学习算法

对于NP问题的贝叶斯网络（BN）结构学习而言，提高精度非常重要，而混合算法是目前一种有效的结构学习算法。大多数混合算法都采用一种启发式搜索的策略，可以分为两类：一种基于初始BN骨架的启发式搜索和一种基于初始解的启发式搜索。前者通常不能保证最优结构的整体性，而后者由于搜索空间大而无法获得最优解。本文提出了一种高效的混合算法，并采用了两阶段搜索策略。对于第一阶段搜索，它首先通过引入惩罚因子p1，p2根据最大信息系数来确定局部搜索空间，然后通过二进制粒子群优化算法搜索局部空间。对于第二阶段搜索，设计了一种基于三个基本运算符的有效ADR（添加，删除，反向的缩写）算法，以将局部空间扩展到整个空间。实验结果表明，该算法能获得较好的BN结构学习性能。