# Proximal Balancing for Causal Effect Estimation under Unmeasured Confounding

arXiv: https://arxiv.org/abs/2609.40051 · HTML: https://mlsanity.com/paper/2609.40051/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 57 references that are in the map.
- First posted on arXiv 30 Sep 2026.

## Builds on (most cited first, 22 of 22)

- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [Identifying Causal Effects With Proxy Variables of an Unmeasured Confounder](https://mlsanity.com/paper/1609.08816/) (2016)
- [Semiparametric doubly robust targeted double machine learning: a review](https://mlsanity.com/paper/2203.06469/) (2022)
- [Automated versus do-it-yourself methods for causal inference: Lessons learned from a data analysis competition](https://mlsanity.com/paper/1707.02641/) (2017)
- [Semiparametric proximal causal inference](https://mlsanity.com/paper/2011.08411/) (2020)
- [Proximal Causal Learning with Kernels: Two-Stage Estimation and Moment Restriction](https://mlsanity.com/paper/2105.04544/) (2021)
- [Causal Inference Under Unmeasured Confounding With Negative Controls: A Minimax Learning Approach](https://mlsanity.com/paper/2103.14029/) (2021)
- [Double/Debiased Machine Learning for Treatment and Causal Parameters](https://mlsanity.com/paper/1608.00060/) (2016)
- [Deep Proxy Causal Learning and its Application to Confounded Bandit Policy Evaluation](https://mlsanity.com/paper/2106.03907/) (2021)
- [A Critical Look at the Consistency of Causal Estimation With Deep Latent Variable Models](https://mlsanity.com/paper/2102.06648/) (2021)
- [Semiparametric Inference For Causal Effects In Graphical Models With Hidden Variables](https://mlsanity.com/paper/2003.12659/) (2020)
- [Instrumental Variables Estimation with Some Invalid Instruments and its Application to Mendelian Randomization](https://mlsanity.com/paper/1401.5755/) (2014)
- [Proximal Causal Inference With Text Data](https://mlsanity.com/paper/2401.06687/) (2024)
- [Kernel Single Proxy Control for Deterministic Confounding](https://mlsanity.com/paper/2308.04585/) (2023)
- [Single Proxy Control](https://mlsanity.com/paper/2302.06054/) (2023)
- [Adaptive Proximal Causal Inference with Some Invalid Proxies](https://mlsanity.com/paper/2507.19623/) (2025)
- [Data-driven Automated Negative Control Estimation (DANCE): Search for, Validation of, and Causal Inference with Negative Controls](https://mlsanity.com/paper/2210.00528/) (2022)
- [Automating the Selection of Proxy Variables of Unmeasured Confounders](https://mlsanity.com/paper/2405.16130/) (2024)
- [Fortified Proximal Causal Inference with Many Invalid Proxies](https://mlsanity.com/paper/2506.13152/) (2025)
- [Debiased Front-Door Learners for Heterogeneous Effects](https://mlsanity.com/paper/2509.22531/) (2025)
- [Information-Theoretic Causal Bounds under Unmeasured Confounding](https://mlsanity.com/paper/2601.17160/) (2026)
- [Causal Inference with Categorical Unobserved Confounder via Mixture Learning](https://mlsanity.com/paper/2605.19006/) (2026)

## Abstract (arXiv)

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.