Proximal Balancing for Causal Effect Estimation under 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.
Related
- Spatial causal inference in the presence of unmeasured confounding and interference
- ProximalFM: Amortized Proximal Causal Inference under Hidden Confounding
- Proximal causal inference through cross-proxy balancing
- confoundvis for Visualizing and Reporting Sensitivity to Unmeasured Confounding in R
- Causal Inference with Unobserved Confounding: A Mixture Learning Perspective
BibTeX
@misc{jung2026proximal,
title = {{Proximal Balancing for Causal Effect Estimation under Unmeasured Confounding}},
author = {Yonghan Jung},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.40051},
eprint = {2609.40051},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.40051},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Proximal Balancing for Causal Effect Estimation under Unmeasured Confounding
AU - Yonghan Jung
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2609.40051
UR - https://arxiv.org/abs/2609.40051
AB - 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.
ER -