Mining Markov Blankets Without Causal Sufficiency

Abstract

Markov blankets (MBs) in Bayesian networks (BNs) play an important role in both local causal discovery and large-scale BN structure learning. Almost all existing MB discovery algorithms are designed under the assumption of causal sufficiency, which states that there are no latent common causes for two or more of the observed variables in data. However, latent common causes are ubiquitous in many applications, and hence, this assumption is often violated in practice. Thus, developing algorithms for discovering MBs without assuming causal sufficiency is of practical significance, and it is crucial for causal structure learning in real-world data. In this paper, we focus on addressing this problem. Specifically, we adopt a maximal ancestral graph (MAG) model to represent latent common causes and the concept of MBs without assuming causal sufficiency. Then, we propose an effective and efficient algorithm to discover the MB of a target variable in an MAG. Using benchmark and real-world data sets, the experiments validate the algorithm proposed in this paper.