On scoring Maximal Ancestral Graphs with the Max-Min Hill Climbing algorithm

We consider the problem of causal structure learning in presence of latent confounders. We propose a hybrid method, MAG Max-Min Hill-Climbing (M3HC) that takes as input a data set of continuous variables, assumed to follow a multivariate Gaussian distribution, and outputs the best fitting maximal ancestral graph. M3HC builds upon a previously proposed method, namely GSMAG, by introducing a constraint-based first phase that greatly reduces the space of structures to investigate. On a large scale experimentation we show that the proposed algorithm greatly improves on GSMAG in all comparisons, and over a set of known networks from the literature it compares positively against FCI and cFCI as well as competitively against GFCI, three well known constraint-based approaches for causal-network reconstruction in presence of latent confounders.