A Hybrid Causal Search Algorithm for Latent Variable Models

Existing score-based causal model search algorithms such as \textitGES (and a speeded up version, \textitFGS) are asymptotically correct, fast, and reliable, but make the unrealistic assumption that the true causal graph does not contain any unmeasured confounders. There are several constraint-based causal search algorithms (e.g \textitRFCI, \emphFCI, or \emphFCI+) that are asymptotically correct without assuming that there are no unmeasured confounders, but often perform poorly on small samples. We describe a combined score and constraint-based algorithm, \emphGFCI, that we prove is asymptotically correct. On synthetic data, \textitGFCI is only slightly slower than \emphRFCI but more accurate than \textitFCI, \textitRFCI and \textitFCI+.