Constraint-based Causal Structure Learning with Consistent Separating Sets

Honghao Li, Vincent Cabeli, Nadir Sella, Herve Isambert

Abstract: We consider constraint-based methods for causal structure learning, such as the PC algorithm or any PC-derived algorithms whose first step consists in pruning a complete graph to obtain an undirected graph skeleton, which is subsequently oriented. All constraint-based methods perform this first step of removing dispensable edges, iteratively, whenever a separating set and corresponding conditional independence can be found. Yet, constraint-based methods lack robustness over sampling noise and are prone to uncover spurious conditional independences in finite datasets. In particular, there is no guarantee that the separating sets identified during the iterative pruning step remain consistent with the final graph. In this paper, we propose simple modifications of PC and PC-derived algorithms so as to ensure that all separating sets identified to remove dispensable edges are consistent with the final graph. The additional algorithmic complexity to enforce consistency can be limited by using block-cut tree decomposition of graph skeletons. Ensuring the consistency of separating sets is found to increase their validity in terms of actual d-separation. It also significantly improves the sensitivity of constraint-based methods while retaining good overall structure learning performance. Finally and foremost, ensuring sepset consistency improves the interpretability of constraint-based models for real-life applications.

CMT Num: 8026

Code Link: https://github.com/honghaoli42/consistent_pcalg