Automated Efficient Estimation using Monte Carlo Efficient Influence Functions
<|reference_start|>Automated Efficient Estimation using Monte Carlo Efficient Influence Functions: 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.<|reference_end|>
@article{agrawal2024automated,
    title={Automated Efficient Estimation using Monte Carlo Efficient Influence
  Functions},
    author={Raj Agrawal, Sam Witty, Andy Zane, Eli Bingham},
    journal={arXiv preprint arXiv:2403.00158},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.00158},
    primaryClass={stat.CO cs.LG stat.ME}
}