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In many practical studies, learning directionality between a pair ofvariables is of great interest while notoriously hard, especially formechanistic relationships. This paper presents a method that examinesdirectionality in exposure-outcome pairs when a priori assumptions about theirrelative ordering are unavailable. We propose a coefficient of asymmetry toquantify directional asymmetry using Shannon's entropy and propose astatistical estimation and inference framework for said estimand. Large-sampletheoretical guarantees are established through data-splitting and cross-fittingtechniques. The proposed methodology is extended to allow both measuredconfounders and contamination in outcome measurements. The methodology isextensively evaluated through extensive simulation studies, a benchmarkdataset, and a real data application.

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