Causal Structure Learning by Using Intersection of Markov Blankets

In this paper, we introduce a novel causal structure learning algorithm called Endogenous and Exogenous Markov Blankets Intersection (EEMBI), which combines the properties of Bayesian networks and Structural Causal Models (SCM). Exogenous variables are special variables that are applied in SCM. We find that exogenous variables have some special characteristics and these characteristics are still useful under the property of the Bayesian network. EEMBI intersects the Markov blankets of exogenous variables and Markov blankets of endogenous variables, i.e. the original variables, to remove the irrelevant connections and find the true causal structure theoretically. Furthermore, we propose an extended version of EEMBI, namely EEMBI-PC, which integrates the last step of the PC algorithm into EEMBI. This modification enhances the algorithm's performance by leveraging the strengths of both approaches. Plenty of experiments are provided to prove that EEMBI and EEMBI-PC have state-of-the-art performance on both discrete and continuous datasets.