Automated Efficient Estimation using Monte Carlo Efficient Influence Functions
This provides an automated solution for efficient statistical estimation in a broad class of models, addressing a bottleneck for researchers and practitioners in statistics and machine learning, though it is incremental as it builds on existing influence function theory.
The paper tackles the problem of estimating low-dimensional statistical quantities with high-dimensional models by introducing Monte Carlo Efficient Influence Functions (MC-EIF), a fully automated technique that approximates efficient influence functions and integrates with differentiable probabilistic programming systems, achieving optimal √N convergence rates and empirical parity with analytic methods.
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.