  Constraint-based methods are one of the main approaches for causal structure
learning that are particularly valued as they are asymptotically guaranteed to
find a structure that is Markov equivalent to the causal graph of the system.
On the other hand, they may require an exponentially large number of
conditional independence (CI) tests in the number of variables of the system.
In this paper, we propose a novel recursive constraint-based method for causal
structure learning that significantly reduces the required number of CI tests
compared to the existing literature. The idea of the proposed approach is to
use Markov boundary information to identify a specific variable that can be
removed from the set of variables without affecting the statistical
dependencies among the other variables. Having identified such a variable, we
discover its neighborhood, remove that variable from the set of variables, and
recursively learn the causal structure over 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 state-of-the-art both on synthetic
and real-world structures.
