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（DAGs）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，可以对因果模型的不确定性进行推断。由于在仅给定有限观测数据时模型可能无法被唯一识别，因此对模型不确定性进行建模的概念对于因果结构学习尤为重要。本文提出一种利用变分贝叶斯联合学习因果模型结构与机制的新方法，称为变分贝叶斯-DAG-GFlowNet（VBG）。我们扩展了基于GFlowNets的贝叶斯因果结构学习方法，使其不仅能学习结构的后验分布，还能学习线性高斯模型的参数。在模拟数据上的实验结果表明，VBG在对DAGs与机制的后验建模方面与多种基线方法具有竞争力，同时相比现有方法具有若干优势，包括保证采样得到无环图，以及能够灵活推广至非线性因果机制。