Global Directional Priors with Local Statistical Validation for Scalable Causal Discovery

Constraint-based causal discovery relies on conditional independence (CI) tests whose reliability degrades as conditioning sets grow, particularly in hub-dominated graphs. Existing methods constrain adjacency or global structure, but leave conditioning-set dimensionality uncontrolled. In this paper, we propose Ordering-Constrained Markov Blanket discovery (OCMB), a paradigm that treats conditioning-set dimensionality as a first-class constraint. OCMB decouples discovery into two stages: lightweight global ordering estimation providing directional priors, followed by local Markov blanket validation within small, ordering-constrained candidate sets. By enforcing directional constraints before any CI test, OCMB ensures bounded conditioning sets even with hub nodes. We show that OCMB recovers correct parent sets provided a high-recall ordering assumption holds, without requiring the ordering to be globally correct. Experiments demonstrate that OCMB significantly improves precision and robustness over constraint-based and hybrid methods in high-dimensional regimes where conventional CI-based approaches fail.

Many scientific and real-world questions require us to infer which variables cause which others from data, such as genes regulating other genes or proteins influencing a signaling pathway. A common approach tests whether two variables are still related after accounting for other variables, but these tests become unreliable when too many variables must be considered at once, especially in networks where a few “hub” variables connect to many others. We propose OCMB, a causal discovery method that first estimates a rough global ordering of variables and then uses this ordering to limit which variables can be considered as possible causes. Instead of trusting this ordering completely, OCMB uses it only to create small candidate sets, and then performs local statistical checks within those sets. This keeps the difficult tests small and more reliable, even in large or hub-heavy networks. Our results show that OCMB can recover causal structures more accurately and robustly than conventional constraint-based methods in high-dimensional settings, while using far fewer statistical tests. The method is especially useful when the ordering is informative but imperfect, which is common in practice.