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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.00158 |
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| _version_ | 1866929268449083392 |
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| author | Agrawal, Raj Witty, Sam Zane, Andy Bingham, Eli |
| author_facet | Agrawal, Raj Witty, Sam Zane, Andy Bingham, Eli |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_00158 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Automated Efficient Estimation using Monte Carlo Efficient Influence Functions Agrawal, Raj Witty, Sam Zane, Andy Bingham, Eli Computation Machine Learning Methodology 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. |
| title | Automated Efficient Estimation using Monte Carlo Efficient Influence Functions |
| topic | Computation Machine Learning Methodology |
| url | https://arxiv.org/abs/2403.00158 |