It has been frequently observed that Neyman orthogonality, the central device underlying double/debiased machine learning (Chernozhukov et al., 2018), and pathwise differentiability, a cornerstone concept from semiparametric theory, often lead to the same debiased estimators in practice. Despite the widespread adoption of both ideas, the precise nature of this equivalence has remained elusive, with the two concepts having been developed in largely separate traditions. In this work, we revisit the semiparametric framework of van der Laan and Robins (2003) and identify an implicit regularity assumption on the relationship between target and nuisance parameters -- a local product structure -- that allows us to establish a formal equivalence between Neyman orthogonality and pathwise differentiability. We also show that the two directions of this equivalence impose fundamentally different structural requirements. Finally, we illustrate the theory through three detailed examples of estimating the average treatment effect and expected density in a nonparametric model, as well as the slope in a partially linear model. This helps clarify the relationship between these two foundational frameworks and provides a useful reference for practitioners working at their intersection.

翻译：摘要：实践已反复表明，尼曼正交性（作为双重/去偏机器学习核心工具的概念，由Chernozhukov等学者于2018年提出）与半参数理论基石之一的路径可微性，通常能导出相同的去偏估计量。尽管这两种思想已被广泛应用，但由于两者源于迥异的理论传统，其等价关系的精确性质始终悬而未决。本研究重新审视van der Laan与Robins（2003）提出的半参数框架，揭示了目标参数与干扰参数关系中的一个隐含正则性假设——局部积结构——该假设使我们能够建立尼曼正交性与路径可微性的形式等价关系。我们进一步证明，这种等价关系的两个方向施加了根本不同的结构性要求。最后，通过非参数模型中平均处理效应与期望密度的估计、以及部分线性模型中斜率的估计三个详实案例，对理论进行阐释。这一工作厘清了两种基础框架间的关联，为从事交叉领域研究的实践者提供了实用参考。