Bayesian causal structure learning aims to learn a posterior distribution over directed acyclic graphs (DAGs), and the mechanisms that define the relationship between parent and child variables. By taking a Bayesian approach, it is possible to reason about the uncertainty of the causal model. The notion of modelling the uncertainty over models is particularly crucial for causal structure learning since the model could be unidentifiable when given only a finite amount of observational data. In this paper, we introduce a novel method to jointly learn the structure and mechanisms of the causal model using Variational Bayes, which we call Variational Bayes-DAG-GFlowNet (VBG). We extend the method of Bayesian causal structure learning using GFlowNets to learn not only the posterior distribution over the structure, but also the parameters of a linear-Gaussian model. Our results on simulated data suggest that VBG is competitive against several baselines in modelling the posterior over DAGs and mechanisms, while offering several advantages over existing methods, including the guarantee to sample acyclic graphs, and the flexibility to generalize to non-linear causal mechanisms.
翻译:贝叶斯因果结构学习旨在学习定向环流图(DAGs)和界定父母与子女关系关系的机制的事后分布。通过采用巴伊西亚方法,可以解释因果模型的不确定性。模型的不确定性概念对于因果结构学习尤为重要,因为如果只给出有限数量的观测数据,该模型就可能无法识别。在本文中,我们采用了一种新颖的方法,用变数贝耶斯-DAG-GFlowNet(VBG)联合学习因果模型的结构和机制,我们称之为变数贝伊斯-DAG-GFlowNet(VBG)。我们推广了巴伊西亚因果结构学习方法,使用GFlowNet(G)不仅学习结构上的外表分布,而且还学习线性-Gausian模型的参数。我们在模拟数据中得出的结果表明,VBG公司在模拟远比DAGs和机制的后数个基线上具有竞争力,同时为现有方法提供了若干优势,包括抽样循环图的保证,以及将灵活性推广到非线性因果机制。