Reviews: Constraint-based Causal Structure Learning with Consistent Separating Sets

Summary ------- The authors address a major drawback of constraint-based causal structure learning algorithms (PC algorithm and derivatives), namely, that for finite sample sizes the outputted graphs may be inconsistent regarding separating sets: The final graph may imply different separating sets than those identified in the algorithm. This implies in particular that outputted graphs are not guarenteed to belong to their presumed class of graphical models, for example CPDAGs or PAGs. The main reason is that PC-based methods remove too many true links in the skeleton phase. The authors' solution is based on an iterative application of a modified version of PC until the final graph is consistent with the separating sets. They prove that their solution fixes the problem and demonstrate these improvements with numerical experiments.