Bayesian networks are probabilistic graphical models with a wide range of application areas including gene regulatory networks inference, risk analysis and image processing. Learning the structure of a Bayesian network (BNSL) from discrete data is known to be an NP-hard task with a superexponential search space of directed acyclic graphs. In this work, we propose a new polynomial time algorithm for discovering a subset of all possible cluster cuts, a greedy algorithm for approximately solving the resulting linear program, and a generalised arc consistency algorithm for the acyclicity constraint. We embed these in the constraint programmingbased branch-and-bound solver CPBayes and show that, despite being suboptimal, they improve performance by orders of magnitude. The resulting solver also compares favourably with GOBNILP, a state-of-the-art solver for the BNSL problem which solves an NP-hard problem to discover each cut and solves the linear program exactly.
翻译:Bayesian 网络是概率化的图形模型,应用领域广泛,包括基因监管网络的推断、风险分析和图像处理。从离散数据中学习Bayesian 网络(BNSL)的结构,已知是一项难以完成的任务,其搜索空间超能,有定向环形图。在这项工作中,我们提出一种新的多米时间算法,以发现所有可能的集束切除子集,一种贪婪算法,以大致解决由此产生的线性程序,以及一种通用的周期性制约弧一致性算法。我们将这些算法嵌入基于约束性编程的分支和约束求解器 CPBayes 中,并表明尽管它们不是最理想的,但它们的性能按数量级提高。由此产生的求解器也优于GOBNILP, GONILP是解决BNSL问题的最先进的解算器,它解决了NP-硬的问题,以便发现每一个切断并精确解决线性程序。