Quantification and cross-fitting inference of asymmetric relations under generative exposure mapping models

In many practical studies, learning directionality between a pair of variables is of great interest while notoriously hard, especially for mechanistic relationships. This paper presents a method that examines directionality in exposure-outcome pairs when a priori assumptions about their relative ordering are unavailable. We propose a coefficient of asymmetry to quantify directional asymmetry using Shannon's entropy and propose a statistical estimation and inference framework for said estimand. Large-sample theoretical guarantees are established through data-splitting and cross-fitting techniques. The proposed methodology is extended to allow both measured confounders and contamination in outcome measurements. The methodology is extensively evaluated through extensive simulation studies, a benchmark dataset, and a real data application.