Zihao Li, Hui Lan, Vasilis Syrgkanis, Mengdi Wang, Masatoshi Uehara
arXiv 7 Mar 2024 · Machine Learning
arXiv:2403.04236 · PDF · DOI · OpenAlex · Extracted main text
In this paper, we study nonparametric estimation of instrumental variable (IV) regressions. While recent advancements in machine learning have introduced flexible methods for IV estimation, they often encounter one or more of the following limitations: (1) restricting the IV regression to be uniquely identified; (2) requiring minimax computation oracle, which is highly unstable in practice; (3) absence of model selection procedure. In this paper, we present the first method and analysis that can avoid all three limitations, while still enabling general function approximation. Specifically, we propose a minimax-oracle-free method called Regularized DeepIV (RDIV) regression that can converge to the least-norm IV solution. Our method consists of two stages: first, we learn the conditional distribution of covariates, and by utilizing the learned distribution, we learn the estimator by minimizing a Tikhonov-regularized loss function. We further show that our method allows model selection procedures that can achieve the oracle rates in the misspecified regime. When extended to an iterative estimator, our method matches the current state-of-the-art convergence rate. Our method is a Tikhonov regularized variant of the popular DeepIV method with a non-parametric MLE first-stage estimator, and our results provide the first rigorous guarantees for this empirically used method, showcasing the importance of regularization which was absent from the original work.
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| Reference | Intensity | Mentions | Sections | Main text | |
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| 1 | Andrew Bennett, Nathan Kallus, Xiaojie Mao, Whitney Newey, Vasilis S… (2023) Minimax instrumental variable regression and $l_2$ convergence guarantees without identification or closedness, 2023a self | 0.950 | 7 | 5 | 86% |
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| 7 | Nishanth Dikkala, Greg Lewis, Lester Mackey, and Vasilis Syrgkanis (2020) Minimax estimation of conditional moment models self | 0.874 | 6 | 3 | 67% |
| 8 | Nathan Kallus, Xiaojie Mao, and Masatoshi Uehara (2021) Causal inference under unmeasured confounding with negative controls: A minimax learning approach self | 0.874 | 6 | 3 | 67% |
| 9 | Martin J Wainwright (2019) High-dimensional statistics: A non-asymptotic viewpoint, volume 48 | 0.737 | 10 | 4 | 40% |
| 10 | Luofeng Liao, You-Lin Chen, Zhuoran Yang, Bo Dai, Mladen Kolar, and… (2020) Provably efficient neural estimation of structural equation models: An adversarial approach | 0.737 | 5 | 2 | 60% |
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| 1 | Debiased Ill-Posed Regression | 0.693 | 5 | 1 |
| 2 | Penalized GMM Framework for Inference on Functionals of Nonparametric Instrumental Variable Estimators | 0.644 | 2 | 2 |