Finding the Minimal Sufficient Set in Causal Graph Under Interventions: A Dimension Reduction Method for Data Analysis

One of the ultimate goals of data analysis is to uncover the inherent causality in data. Pearl’s causal graph model provides the fundamental framework for measuring changes caused by external interventions that are commonly used to reveal the causality. Although the criteria and algorithms of atomic intervention for evaluating causal effects have been proposed in previous studies, the research of causal effects under conditional intervention remains inadequate. In this paper, we propose a criterion to combine the back-door criterion of atomic intervention with conditional intervention when the treatment variable is unique. Under the criterion, the derived minimal sufficient sets under atomic intervention (a-MSSs) can be converted into the one under conditional intervention (c-MSSs). The calculation of c-MSSs can remarkably decrease the complexity of target data analysis regarding data dimension reduction. Based on those steps, we also develop an algorithm to implement the conversion. Case studies demonstrate that our algorithm can enumerate both a-MSSs and c-MSSs effectively when a causal graph is given, which validates the effectiveness of our proposed scheme.