Causal Inference Under Unmeasured Confounding With Negative Controls: A Minimax Learning Approach
This work addresses a key problem in causal inference for researchers and practitioners dealing with unobserved confounders, offering a more flexible and robust approach compared to previous methods that relied on restrictive assumptions.
The paper tackles the challenge of identifying and estimating bridge functions for causal inference with unmeasured confounding and negative controls, by introducing a new identification strategy that avoids completeness conditions and providing minimax learning estimators that accommodate general function classes like RKHS and neural networks, with finite-sample convergence results for both bridge functions and causal parameters.
We study the estimation of causal parameters when not all confounders are observed and instead negative controls are available. Recent work has shown how these can enable identification and efficient estimation via two so-called bridge functions. In this paper, we tackle the primary challenge to causal inference using negative controls: the identification and estimation of these bridge functions. Previous work has relied on completeness conditions on these functions to identify the causal parameters and required uniqueness assumptions in estimation, and they also focused on parametric estimation of bridge functions. Instead, we provide a new identification strategy that avoids the completeness condition. And, we provide new estimators for these functions based on minimax learning formulations. These estimators accommodate general function classes such as Reproducing Kernel Hilbert Spaces and neural networks. We study finite-sample convergence results both for estimating bridge functions themselves and for the final estimation of the causal parameter under a variety of combinations of assumptions. We avoid uniqueness conditions on the bridge functions as much as possible.