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Proximal Causal Learning under Unmeasured Confounding

arXiv 2610.04519 ↗First posted 3 Oct 2026cs.LGcited by 0

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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.

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.

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References · 14

  1. 2017Causal Effect Inference with Deep Latent-Variable Modelscited by 410
  2. 2016Identifying Causal Effects With Proxy Variables of an Unmeasured Confoundercited by 139
  3. 2020An Introduction to Proximal Causal Learningcited by 95
  4. 2019Machine Learning Methods Economists Should Know Aboutcited by 64
  5. 2020Semiparametric proximal causal inferencecited by 59
  6. 2021Proximal Causal Learning with Kernels: Two-Stage Estimation and Moment Restrictioncited by 55
  7. 2021Deep Proxy Causal Learning and its Application to Confounded Bandit Policy Evaluationcited by 40
  8. 2019Adversarial Balancing-based Representation Learning for Causal Effect Inference with Observational Datacited by 30
  9. 2021Auto IV: Counterfactual Prediction via Automatic Instrumental Variable Decompositioncited by 19
  10. 2022Learning Disentangled Representations for Counterfactual Regression via Mutual Information Minimizationcited by 19
  11. 2022Deep Learning Methods for Proximal Inference via Maximum Moment Restrictioncited by 14
  12. 2021Cycle-Balanced Representation Learning For Counterfactual Inferencecited by 7
2 more
  1. 2020Double Robust Representation Learning for Counterfactual Predictioncited by 5
  2. 2025Double Machine Learning for Conditional Moment Restrictions: IV Regression, Proximal Causal Learning and Beyondcited by 1

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