In Bayesian Networks (BNs), the direction of edges is crucial for causal reasoning and inference. However, Markov equivalence class considerations mean it is not always possible to establish edge orientations, which is why many BN structure learning algorithms cannot orientate all edges from purely observational data. Moreover, latent confounders can lead to false positive edges. Relatively few methods have been proposed to address these issues. In this work, we present the hybrid mFGS-BS (majority rule and Fast Greedy equivalence Search with Bayesian Scoring) algorithm for structure learning from discrete data that involves an observational data set and one or more interventional data sets. The algorithm assumes causal insufficiency in the presence of latent variables and produces a Partial Ancestral Graph (PAG). Structure learning relies on a hybrid approach and a novel Bayesian scoring paradigm that calculates the posterior probability of each directed edge being added to the learnt graph. Experimental results based on well-known networks of up to 109 variables and 10k sample size show that mFGS-BS improves structure learning accuracy relative to the state-of-the-art and it is computationally efficient.

翻译：在Bayesian Networks(BNs)中,边缘方向对于因果关系推理和推论至关重要。然而,Markov等值类考虑意味着并不总是有可能建立边缘方向,这就是为什么许多BN结构学习算法无法将纯观测数据的所有边缘都定向。此外,潜伏混凝土可能导致假正面边缘。相对而言,为解决这些问题而提出的方法很少。在这项工作中,我们介绍了混合 mFGS-BS(多数规则以及快速与Bayesian Scoring的贪婪等同搜索)算法,用于从离散数据中学习结构的算法,这些数据涉及观察数据集和一个或多个干预数据集。算法假定在存在潜在变量的情况下因果不全,并产生部分的脑力图(PAG)。结构学习依靠混合法和新颖的Bayesian评分模型,该模型计算出每个直接边缘添加到的远端的外缘概率。根据已知的109个变量和10k样本大小的网络得出的实验结果显示,MFGS-BS改进了相对于州-Art-al-al-Arcal-al-al-action-al-action-action-action-action-acal-al-al-al-acal-acal-acc-acc-acc-action-action-action-action-acal-s and