  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.
