Automated Efficient Estimation using Monte Carlo Efficient Influence Functions

TL;DR

This paper presents MC-EIF, an automated method for approximating influence functions in high-dimensional models, enabling efficient and consistent statistical estimation without extensive manual analysis.

Contribution

Introduction of MC-EIF, a fully automated, differentiable system for approximating influence functions, simplifying and broadening the application of efficient statistical estimation.

Findings

MC-EIF is consistent and achieves optimal √N convergence rates.

Empirical results show MC-EIF matches analytic EIFs in performance.

Demonstrated application in optimal portfolio selection.

Abstract

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.