In many practical studies, learning directionality between a pair of variables is of great interest while notoriously hard when their underlying relation is nonlinear. This paper presents a method that examines asymmetry in exposure-outcome pairs when a priori assumptions about their relative ordering are unavailable. Our approach utilizes a framework of generative exposure mapping (GEM) to study asymmetric relations in continuous exposure-outcome pairs, through which we can capture distributional asymmetries with no prefixed variable ordering. We propose a coefficient of asymmetry to quantify relational asymmetry using Shannon's entropy analytics as well as statistical estimation and inference for such an estimand of directionality. Large-sample theoretical guarantees are established for cross-fitting inference techniques. The proposed methodology is extended to allow both measured confounders and contamination in outcome measurements, which is extensively evaluated through extensive simulation studies and real data applications.

翻译：暂无翻译