In this paper, we introduce a novel MCMC sampler, P ARNI-DAG, for a fully-Bayesian approach to the problem of structure learning under observational data.
We establish the first mathematically rigorous link between Bayesian, variational Bayesian, and ensemble methods. A key step towards this is to reformulate the non-convex optimisation problem typically encountered in deep learning as a convex optimisation in the space of probability measures.
However, SBC has drawbacks: The test statistic is somewhat ad-hoc, interactions are difficult to examine, multiple testing is a challenge, and the resulting p-value is not a divergence metric.