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Proximal Balancing for Causal Effect Estimation under Unmeasured Confounding

arXiv 2609.40051 ↗First posted 30 Sep 2026stat.ML cs.LG stat.MEcited by 0

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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.

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References · 22

  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. 2022Semiparametric doubly robust targeted double machine learning: a reviewcited by 133
  4. 2017Automated versus do-it-yourself methods for causal inference: Lessons learned from a data analysis competitioncited by 106
  5. 2020Semiparametric proximal causal inferencecited by 59
  6. 2021Proximal Causal Learning with Kernels: Two-Stage Estimation and Moment Restrictioncited by 55
  7. 2021Causal Inference Under Unmeasured Confounding With Negative Controls: A Minimax Learning Approachcited by 44
  8. 2016Double/Debiased Machine Learning for Treatment and Causal Parameterscited by 43
  9. 2021Deep Proxy Causal Learning and its Application to Confounded Bandit Policy Evaluationcited by 40
  10. 2021A Critical Look at the Consistency of Causal Estimation With Deep Latent Variable Modelscited by 29
  11. 2020Semiparametric Inference For Causal Effects In Graphical Models With Hidden Variablescited by 23
  12. 2014Instrumental Variables Estimation with Some Invalid Instruments and its Application to Mendelian Randomizationcited by 22
10 more
  1. 2024Proximal Causal Inference With Text Datacited by 7
  2. 2023Kernel Single Proxy Control for Deterministic Confoundingcited by 5
  3. 2023Single Proxy Controlcited by 4
  4. 2025Adaptive Proximal Causal Inference with Some Invalid Proxiescited by 3
  5. 2022Data-driven Automated Negative Control Estimation (DANCE): Search for, Validation of, and Causal Inference with Negative Controlscited by 2
  6. 2024Automating the Selection of Proxy Variables of Unmeasured Confounderscited by 2
  7. 2025Fortified Proximal Causal Inference with Many Invalid Proxiescited by 2
  8. 2025Debiased Front-Door Learners for Heterogeneous Effectscited by 2
  9. 2026Information-Theoretic Causal Bounds under Unmeasured Confoundingcited by 2
  10. 2026Causal Inference with Categorical Unobserved Confounder via Mixture Learningcited by 2

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