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：在许多实际研究中，探究变量对之间的方向性具有重要价值，但当其潜在关系呈非线性时则极具挑战性。本文提出一种方法，可在缺乏变量相对顺序先验假设的情况下，检验暴露-结果对之间的非对称性。我们的方法利用生成式暴露映射框架研究连续型暴露-结果对中的非对称关系，从而无需预设变量顺序即可捕捉分布层面的非对称性。我们提出一个非对称系数，通过香农熵分析量化关系非对称性，并建立该方向性参数的统计估计与推断方法。针对交叉拟合推断技术，我们建立了大样本理论保证。所提方法可扩展至同时处理可观测混杂因素与结果测量中的污染问题，并通过大量模拟研究与实际数据应用进行了全面评估。