  In Bayesian Networks (BNs), the direction of edges is crucial for causal
reasoning and inference. However, Markov equivalence class considerations mean
it is not always possible to establish edge orientations, which is why many BN
structure learning algorithms cannot orientate all edges from purely
observational data. Moreover, latent confounders can lead to false positive
edges. Relatively few methods have been proposed to address these issues. In
this work, we present the hybrid mFGS-BS (majority rule and Fast Greedy
equivalence Search with Bayesian Scoring) algorithm for structure learning from
discrete data that involves an observational data set and one or more
interventional data sets. The algorithm assumes causal insufficiency in the
presence of latent variables and produces a Partial Ancestral Graph (PAG).
Structure learning relies on a hybrid approach and a novel Bayesian scoring
paradigm that calculates the posterior probability of each directed edge being
added to the learnt graph. Experimental results based on well-known networks of
up to 109 variables and 10k sample size show that mFGS-BS improves structure
learning accuracy relative to the state-of-the-art and it is computationally
efficient.
