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有向无环图（DAG）的后验分布，以及定义父变量与子变量之间关系的机制。通过采用贝叶斯方法，可以推理因果模型的不确定性。对模型不确定性的建模概念对于因果结构学习尤为重要，因为在仅给定有限观测数据的情况下，模型可能无法识别。本文提出了一种新方法，即利用变分贝叶斯联合学习因果模型的结构与机制，我们将其称为变分贝叶斯-DAG-GFlowNet（VBG）。我们扩展了使用GFlowNet进行贝叶斯因果结构学习的方法，不仅学习结构上的后验分布，还学习线性高斯模型的参数。我们在模拟数据上的结果表明，VBG在对DAG和机制的后验建模方面与多个基线方法竞争，同时相比现有方法具有若干优势，包括保证采样无环图以及泛化到非线性因果机制的灵活性。