  In this paper, we introduce a novel MCMC sampler, PARNI-DAG, for a
fully-Bayesian approach to the problem of structure learning under
observational data. Under the assumption of causal sufficiency, the algorithm
allows for approximate sampling directly from the posterior distribution on
Directed Acyclic Graphs (DAGs). PARNI-DAG performs efficient sampling of DAGs
via locally informed, adaptive random neighborhood proposal that results in
better mixing properties. In addition, to ensure better scalability with the
number of nodes, we couple PARNI-DAG with a pre-tuning procedure of the
sampler's parameters that exploits a skeleton graph derived through some
constraint-based or scoring-based algorithms. Thanks to these novel features,
PARNI-DAG quickly converges to high-probability regions and is less likely to
get stuck in local modes in the presence of high correlation between nodes in
high-dimensional settings. After introducing the technical novelties in
PARNI-DAG, we empirically demonstrate its mixing efficiency and accuracy in
learning DAG structures on a variety of experiments.
