Specifying Prior Beliefs over DAGs in Deep Bayesian Causal Structure Learning

We consider the principled incorporation of prior knowledge in deep learning based Bayesian approaches to causal structure learning via the prior belief. In particular, we investigate how to include knowledge about individual edges and causal dependencies in the prior over the underlying directed acyclic graph (DAG). While conceptually simple, substantial challenges arise because the acyclicity of a DAG limits the modeling choices of the marginal distributions over its edges. Specifying the marginals iteratively unveils their dependencies and ensures a sound formulation of the probability distribution over DAGs. We provide recipes for formulating valid priors over DAGs for two recent deep learning based Bayesian approaches to causal structure learning and demonstrate empirically that using this prior knowledge can enable significantly more sample-efficient causal structure search.