Feature Selection for Discovering Distributional Treatment Effect Modifiers

Finding the features relevant to the difference in treatment effects is essential to unveil the underlying causal mechanisms. Existing methods seek such features by measuring how greatly the feature attributes affect the degree of the {\it conditional average treatment effect} (CATE). However, these methods may overlook important features because CATE, a measure of the average treatment effect, cannot detect differences in distribution parameters other than the mean (e.g., variance). To resolve this weakness of existing methods, we propose a feature selection framework for discovering {\it distributional treatment effect modifiers}. We first formulate a feature importance measure that quantifies how strongly the feature attributes influence the discrepancy between potential outcome distributions. Then we derive its computationally efficient estimator and develop a feature selection algorithm that can control the type I error rate to the desired level. Experimental results show that our framework successfully discovers important features and outperforms the existing mean-based method.