A Recursive Markov Blanket-Based Approach to Causal Structure Learning

Constraint-based methods are one of the main approaches for causal structure learning. These methods are particularly valued as they are guaranteed to asymptotically find a structure that is statistically equivalent to the ground truth. On the other hand, they may require an exponentially large number of conditional independence (CI) tests in the number of variables of the system. We propose a novel non-parametric recursive constraint-based method for causal structure learning that significantly reduces the required number of CI tests compared to the existing literature. The key idea of the proposed approach is to recursively use Markov blanket information in order to identify a variable that can be removed from the set of variables without changing the statistical dependencies among the remaining variables. We further provide a lower bound on the number of CI tests required by any constraint-based method. Comparing this lower bound to our achievable bound demonstrates the efficiency of the proposed approach. Our experimental results show that the proposed algorithm outperforms the state of the art both on synthetic and real-world structures.