Automated Efficient Estimation using Monte Carlo Efficient Influence Functions

• URL: http://arxiv.org/abs/2403.00158v2
• Date: Fri, 8 Mar 2024 16:26:03 GMT
• Title: Automated Efficient Estimation using Monte Carlo Efficient Influence Functions
• Authors: Raj Agrawal, Sam Witty, Andy Zane, Eli Bingham
• Abstract summary: This paper introduces textitMonte Carlo Efficient Influence Functions (MC-EIF) MC-EIF is a fully automated technique for approximating efficient influence functions. We prove that MC-EIF is consistent, and that estimators using MC-EIF achieve optimal $sqrtN$ convergence rates.
• Score: 5.1689445482852765
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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