  Latent variables may lead to spurious relationships that can be
misinterpreted as causal relationships. In Bayesian Networks (BNs), this
challenge is known as learning under causal insufficiency. Structure learning
algorithms that assume causal insufficiency tend to reconstruct the ancestral
graph of a BN, where bi-directed edges represent confounding and directed edges
represent direct or ancestral relationships. This paper describes a hybrid
structure learning algorithm, called CCHM, which combines the constraint-based
part of cFCI with hill-climbing score-based learning. The score-based process
incorporates Pearl s do-calculus to measure causal effects and orientate edges
that would otherwise remain undirected, under the assumption the BN is a linear
Structure Equation Model where data follow a multivariate Gaussian
distribution. Experiments based on both randomised and well-known networks show
that CCHM improves the state-of-the-art in terms of reconstructing the true
ancestral graph.
