# Proximal Causal Learning under Unmeasured Confounding

arXiv: https://arxiv.org/abs/2610.04519 · HTML: https://mlsanity.com/paper/2610.04519/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 32 references that are in the map.
- First posted on arXiv 3 Oct 2026.

## Builds on (most cited first, 14 of 14)

- [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)
- [An Introduction to Proximal Causal Learning](https://mlsanity.com/paper/2009.10982/) (2020)
- [Machine Learning Methods Economists Should Know About](https://mlsanity.com/paper/1903.10075/) (2019)
- [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)
- [Deep Proxy Causal Learning and its Application to Confounded Bandit Policy Evaluation](https://mlsanity.com/paper/2106.03907/) (2021)
- [Adversarial Balancing-based Representation Learning for Causal Effect Inference with Observational Data](https://mlsanity.com/paper/1904.13335/) (2019)
- [Auto IV: Counterfactual Prediction via Automatic Instrumental Variable Decomposition](https://mlsanity.com/paper/2107.05884/) (2021)
- [Learning Disentangled Representations for Counterfactual Regression via Mutual Information Minimization](https://mlsanity.com/paper/2206.01022/) (2022)
- [Deep Learning Methods for Proximal Inference via Maximum Moment Restriction](https://mlsanity.com/paper/2205.09824/) (2022)
- [Cycle-Balanced Representation Learning For Counterfactual Inference](https://mlsanity.com/paper/2110.15484/) (2021)
- [Double Robust Representation Learning for Counterfactual Prediction](https://mlsanity.com/paper/2010.07866/) (2020)
- [Double Machine Learning for Conditional Moment Restrictions: IV Regression, Proximal Causal Learning and Beyond](https://mlsanity.com/paper/2506.14950/) (2025)

## Abstract (arXiv)

Estimating treatment effects from observational data typically relies on the No Unmeasured Confounding Assumption (NUCA), which rarely holds in practice. Proximal causal learning (PCL) addresses unmeasured confounding via proxy variables, yet existing methods require the proxy variables to be pre-specified. Thus, we propose PCL-U, a framework that learns proxy variables directly from observed covariates. PCL-U uses neural encoders to decompose covariates into treatment-inducing, outcome-inducing, and shared proxies, guided by minimax mutual information objectives, and obtains causal estimates through a practical moment-based risk function. Experiments on benchmarks show that PCL-U matches or outperforms existing baselines. Besides, there are two types of synthetic datasets with varying dimensions and confounding strengths that illustrate that our method maintains stable estimation accuracy.