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In Bayesian Networks (BNs), the direction of edges is crucial for causalreasoning and inference. However, Markov equivalence class considerations meanit is not always possible to establish edge orientations, which is why many BNstructure learning algorithms cannot orientate all edges from purelyobservational data. Moreover, latent confounders can lead to false positiveedges. Relatively few methods have been proposed to address these issues. Inthis work, we present the hybrid mFGS-BS (majority rule and Fast Greedyequivalence Search with Bayesian Scoring) algorithm for structure learning fromdiscrete data that involves an observational data set and one or moreinterventional data sets. The algorithm assumes causal insufficiency in thepresence of latent variables and produces a Partial Ancestral Graph (PAG).Structure learning relies on a hybrid approach and a novel Bayesian scoringparadigm that calculates the posterior probability of each directed edge beingadded to the learnt graph. Experimental results based on well-known networks ofup to 109 variables and 10k sample size show that mFGS-BS improves structurelearning accuracy relative to the state-of-the-art and it is computationallyefficient.

Hybrid Bayesian network discovery with latent variables by scoring multiple interventions