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：许多实际问题涉及利用高维模型和数据集估计低维统计量。基于影响函数理论，已有多种方法用于解决此类估计任务，例如去偏/双重机器学习或目标最小损失估计。本文提出\textit{蒙特卡洛有效影响函数}（MC-EIF），这是一种全自动逼近有效影响函数的技术，可与现有可微分概率编程系统无缝集成。MC-EIF能够自动实现对广泛模型类别和目标泛函的高效统计估计，而此前这类任务需要严格的定制分析。我们证明了MC-EIF的一致性，且基于MC-EIF的估计量能够实现最优$\sqrt{N}$收敛速度。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，我们以MC-EIF在最优投资组合选择中的应用作为新颖的压轴案例。