The identification theory for causal effects in directed acyclic graphs (DAGs) with hidden variables is well-developed, but methods for estimating and inferring functionals beyond the g-formula remain limited. Previous studies have proposed semiparametric estimators for identifiable functionals in a broad class of DAGs with hidden variables. While demonstrating double robustness in some models, existing estimators face challenges, particularly with density estimation and numerical integration for continuous variables, and their estimates may fall outside the parameter space of the target estimand. Their asymptotic properties are also underexplored, especially when using flexible statistical and machine learning models for nuisance estimation. This study addresses these challenges by introducing novel one-step corrected plug-in and targeted minimum loss-based estimators of causal effects for a class of DAGs that extend classical back-door and front-door criteria (known as the treatment primal fixability criterion in prior literature). These estimators leverage machine learning to minimize modeling assumptions while ensuring key statistical properties such as asymptotic linearity, double robustness, efficiency, and staying within the bounds of the target parameter space. We establish conditions for nuisance functional estimates in terms of L2(P)-norms to achieve root-n consistent causal effect estimates. To facilitate practical application, we have developed the flexCausal package in R.

本研究解决了在具有隐藏变量的有向无环图中，因果效应估计的有效性不足的问题。提出了一种新颖的一步校正插件和目标最小损失估计器，扩展了经典的顺背门和前门标准，结合了机器学习以最小化建模假设，同时保证了渐近线性、双重稳健性和效率。结果显示，所提估计器在实际应用中具备更好的根n一致性，为因果效应的精确估计提供了有力支持。

具有隐藏变量的有向无环图中的平均因果效应估计：顺背门和前门标准的扩展