Many practical problems involve estimating low dimensional statistical quantities with high-dimensional models and datasets. Several approaches address these estimation tasks based on the theory of influence functions, such as debiased/double ML or targeted minimum loss estimation. This paper introduces \textit{Monte Carlo Efficient Influence Functions} (MC-EIF), a fully automated technique for approximating efficient influence functions that integrates seamlessly with existing differentiable probabilistic programming systems. MC-EIF automates efficient statistical estimation for a broad class of models and target functionals that would previously require rigorous custom analysis. We prove that MC-EIF is consistent, and that estimators using MC-EIF achieve optimal $\sqrt{N}$ convergence rates. We show empirically that estimators using MC-EIF are at parity with estimators using analytic EIFs. Finally, we demonstrate a novel capstone example using MC-EIF for optimal portfolio selection.

翻译：许多实际问题涉及使用高维模型和数据集估计低维统计量。基于影响函数理论，已有多种方法应对此类估计任务，例如去偏/双机器学习或定向最小损失估计。本文提出\textit{蒙特卡洛高效影响函数}（MC-EIF），这是一种全自动近似高效影响函数的技术，能够无缝集成到现有可微概率编程系统中。MC-EIF 可对先前需要严格定制分析的大类模型和目标泛函实现自动化高效统计估计。我们证明 MC-EIF 具有一致性，且使用 MC-EIF 的估计量能达到最优的 $\sqrt{N}$ 收敛速率。实验表明，使用 MC-EIF 的估计量与使用解析 EIF 的估计量性能相当。最后，我们展示了一个新颖的顶石案例，即使用 MC-EIF 进行最优投资组合选择。