Intersecting the Markov Blankets of Endogenous and Exogenous Variables for Causal Discovery

Exogenous variables are specially used in Structural Causal Models (SCM), which, however, have some characteristics that are still useful under the property of the Bayesian network. In this paper, we propose a novel causal discovery learning algorithm called Endogenous and Exogenous Markov Blankets Intersection (EEMBI), which combines the properties of Bayesian networks and SCM. Through intersecting the Markov blankets of exogenous variables and endogenous variables (the original variables), EEMBI can remove the irrelevant connections and find the true causal structure theoretically. Furthermore, we propose an extended version of EEMBI, named EEMBI-PC, which integrates the last step of the PC algorithm into EEMBI. This extension enhances the algorithm's performance by leveraging the strengths of both approaches. Plenty of experiments are provided to prove that EEMBI have state-of-the-art performance on continuous datasets, and EEMBI-PC outperforms other algorithms on discrete datasets.