Proximal Balancing for Causal Effect Estimation under Unmeasured Confounding

2026-09-30

AI Summary

This study addresses the challenge of biased causal effect estimation under unmeasured confounding, where existing proxy methods suffer from ill-posed inverse problems or overly strong assumptions. To overcome these limitations, this work proposes the Proximal Balancing method (PROBE algorithm), which extends classical covariate balancing to confounders observed solely through proxies. By learning low-dimensional summaries of covariates and proxies, PROBE achieves treatment group comparability without specifying proxy roles or solving inverse problems, thereby supporting complex data modalities such as high-dimensional images. The proposed approach effectively corrects estimation bias while maintaining broad applicability. Extensive evaluations on multi-dimensional scenarios and real-world datasets validate its effectiveness. Furthermore, this project establishes rigorous statistical identification theory alongside finite-sample guarantees, significantly enhancing the robustness of causal inference in the presence of unmeasured confounding.

Abstract

Estimating causal effects from observational data is central to science and policy, but the effects are not identified when confounders are unmeasured. Proximal causal inference addresses this problem with proxies of the unmeasured confounders. However, existing proxy-based approaches either designate proxy roles and solve an inverse problem, which is ill-posed and hard to estimate with high-dimensional proxies, or use a latent-variable model, which assumes that the learned latent variable matches the hidden confounder and leaves bias when it does not. To address these challenges, we introduce proximal balancing. It carries the classical idea of covariate balancing to confounders that are observed only through proxies: it learns a low-dimensional summary of the covariates and proxies that makes the treatment groups comparable, and then adjusts for this summary. It needs no designated proxy roles, inverse problem, or latent model. We give identification theory, finite-sample guarantees, and a practical algorithm, PROBE. We demonstrate the method on low-dimensional, high-dimensional, and image proxies and on real-world data.

Problem

• causal effect estimation
• unmeasured confounding
• proximal causal inference
• proxy variables
• observational data

Innovation

• Proximal Balancing
• Causal Effect Estimation
• Unmeasured Confounding
• Proxy Variables
• Covariate Balancing