  Learning the causal structure that underlies data is a crucial step towards
robust real-world decision making. The majority of existing work in causal
inference focuses on determining a single directed acyclic graph (DAG) or a
Markov equivalence class thereof. However, a crucial aspect to acting
intelligently upon the knowledge about causal structure which has been inferred
from finite data demands reasoning about its uncertainty. For instance,
planning interventions to find out more about the causal mechanisms that govern
our data requires quantifying epistemic uncertainty over DAGs. While Bayesian
causal inference allows to do so, the posterior over DAGs becomes intractable
even for a small number of variables. Aiming to overcome this issue, we propose
a form of variational inference over the graphs of Structural Causal Models
(SCMs). To this end, we introduce a parametric variational family modelled by
an autoregressive distribution over the space of discrete DAGs. Its number of
parameters does not grow exponentially with the number of variables and can be
tractably learned by maximising an Evidence Lower Bound (ELBO). In our
experiments, we demonstrate that the proposed variational posterior is able to
provide a good approximation of the true posterior.
