  Bayesian causal discovery offers the power to quantify epistemic
uncertainties among a broad range of structurally diverse causal theories
potentially explaining the data, represented in forms of directed acyclic
graphs (DAGs). However, existing methods struggle with efficient DAG sampling
due to the complex acyclicity constraint. In this study, we propose a scalable
Bayesian approach to effectively learn the posterior distribution over causal
graphs given observational data thanks to the ability to generate DAGs without
explicitly enforcing acyclicity. Specifically, we introduce a novel
differentiable DAG sampling method that can generate a valid acyclic causal
graph by mapping an unconstrained distribution of implicit topological orders
to a distribution over DAGs. Given this efficient DAG sampling scheme, we are
able to model the posterior distribution over causal graphs using a simple
variational distribution over a continuous domain, which can be learned via the
variational inference framework. Extensive empirical experiments on both
simulated and real datasets demonstrate the superior performance of the
proposed model compared to several state-of-the-art baselines.
