Bayesian learning of Causal Structure and Mechanisms with GFlowNets and Variational Bayes

TMLR Paper2170 Authors

Abstract: 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 and real-world data suggest that VBG is competitive against several baselines in modelling the posterior over DAGs and mechanisms, while offering several advantages over existing methods which include guaranteed acyclicity of graphs and unlimited sampling from the posterior once the model is trained.

Submission Length: Regular submission (no more than 12 pages of main content)

Changes Since Last Submission:

Minor changes were made to the main text to include suggestions from the reviewers. These include; additional references, clarifications, and corrections.
In the supplementary material, we added experiments for 5 node and 20 node scale-free graphs.
We repeated experiments for 50 node graphs but found that VBG is not able to infer the edges of 50 node graphs even when the sparsity of the graph was increased.

Assigned Action Editor: ~Trevor_Campbell1

Submission Number: 2170