Causal Inference Under Unmeasured Confounding With Negative Controls: A Minimax Learning Approach

Abstract

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 challenges in causal inference with negative controls: identifying and estimating these bridge functions. Previous work has typically relied on completeness conditions for identification, imposed uniqueness assumptions for estimation, and focused on parametric models for the bridge functions. Instead, we provide an alternative identification strategy that assumes the existence of two bridge functions rather than completeness conditions. We also 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.

arXiv commentAccepted by Journal of Machine Learning Research 2026

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Cited by in corpus (4)

• Kernel Methods for Unobserved Confounding: Negative Controls, Proxies, and Instruments
• Proximal Causal Inference without Uniqueness Assumptions
• Proximal Causal Inference for Complex Longitudinal Studies
• Controlling for Unmeasured Confounding in Panel Data Using Minimal Bridge Functions: From Two-Way Fixed Effects to Factor Models