Regularized DeepIV with Model Selection
This work addresses challenges in flexible IV estimation for causal inference, providing rigorous guarantees for an empirically used method, though it is incremental as a regularized variant of DeepIV.
The paper tackles limitations in nonparametric instrumental variable (IV) estimation by proposing Regularized DeepIV (RDIV), a method that avoids unique identification restrictions, unstable minimax oracles, and lack of model selection, converging to the least-norm IV solution and achieving oracle rates in misspecified regimes.
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.