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An Introduction to Proximal Causal Learning

arXiv 2009.10982 ↗First posted 23 Sep 2020stat.MEcited by 91

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Abstract (arXiv)

A standard assumption for causal inference from observational data is that one has measured a sufficiently rich set of covariates to ensure that within covariate strata, subjects are exchangeable across observed treatment values. Skepticism about the exchangeability assumption in observational studies is often warranted because it hinges on investigators' ability to accurately measure covariates capturing all potential sources of confounding. Realistically, confounding mechanisms can rarely if ever, be learned with certainty from measured covariates. One can therefore only ever hope that covariate measurements are at best proxies of true underlying confounding mechanisms operating in an observational study, thus invalidating causal claims made on basis of standard exchangeability conditions. Causal learning from proxies is a challenging inverse problem which has to date remained unresolved. In this paper, we introduce a formal potential outcome framework for proximal causal learning, which while explicitly acknowledging covariate measurements as imperfect proxies of confounding mechanisms, offers an opportunity to learn about causal effects in settings where exchangeability on the basis of measured covariates fails. Sufficient conditions for nonparametric identification are given, leading to the proximal g-formula and corresponding proximal g-computation algorithm for estimation. These may be viewed as generalizations of Robins' foundational g-formula and g-computation algorithm, which account explicitly for bias due to unmeasured confounding. Both point treatment and time-varying treatment settings are considered, and an application of proximal g-computation of causal effects is given for illustration.

Key facts. Cited by 91 papers in the map (data through 7 Oct 2026). First posted on arXiv 23 Sep 2020.

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Citing papers per year: 2021: 14; 2022: 18; 2023: 19; 2024: 17; 2025: 10; 2026: 13.

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  1. 2021Causal Inference in Natural Language Processing: Estimation, Prediction, Interpretation and Beyondcited by 177
  2. 2021Proximal Causal Learning with Kernels: Two-Stage Estimation and Moment Restrictioncited by 54
  3. 2021Causal Inference Under Unmeasured Confounding With Negative Controls: A Minimax Learning Approachcited by 43
  4. 2021Proximal Reinforcement Learning: Efficient Off-Policy Evaluation in Partially Observed Markov Decision Processescited by 40
  5. 2021Deep Proxy Causal Learning and its Application to Confounded Bandit Policy Evaluationcited by 39
  6. 2021Causal Effect Inference for Structured Treatmentscited by 38
  7. 2022Off-Policy Confidence Interval Estimation with Confounded Markov Decision Processcited by 31
  8. 2022Long-term Causal Inference Under Persistent Confounding via Data Combinationcited by 27
  9. 2022Pessimism in the Face of Confounders: Provably Efficient Offline Reinforcement Learning in Partially Observable Markov Decision Processescited by 26
  10. 2022Stochastic Causal Programming for Bounding Treatment Effectscited by 25
  11. 2021Proximal Learning for Individualized Treatment Regimes Under Unmeasured Confoundingcited by 21
  12. 2023Augmented balancing weights as linear regressioncited by 21
38 more
  1. 2021Regularizing towards Causal Invariance: Linear Models with Proxiescited by 20
  2. 2021Minimax Kernel Machine Learning for a Class of Doubly Robust Functionals with Application to Proximal Causal Inferencecited by 20
  3. 2022An Instrumental Variable Approach to Confounded Off-Policy Evaluationcited by 20
  4. 2022Offline Reinforcement Learning with Instrumental Variables in Confounded Markov Decision Processescited by 19
  5. 2022Off-Policy Evaluation for Episodic Partially Observable Markov Decision Processes under Non-Parametric Modelscited by 18
  6. 2023Estimating Treatment Effects from Irregular Time Series Observations with Hidden Confounderscited by 17
  7. 2023Causal isotonic calibration for heterogeneous treatment effectscited by 16
  8. 2022Deep Learning Methods for Proximal Inference via Maximum Moment Restrictioncited by 13
  9. 2025Black Box Causal Inference: Effect Estimation via Meta Predictioncited by 13
  10. 2022Inference on Strongly Identified Functionals of Weakly Identified Functionscited by 12
  11. 2022Spectral Representation Learning for Conditional Moment Modelscited by 12
  12. 2022Adapting to Latent Subgroup Shifts via Concepts and Proxiescited by 12
  13. 2021The Proximal ID Algorithmcited by 11
  14. 2023Estimating long-term causal effects from short-term experiments and long-term observational data with unobserved confoundingcited by 11
  15. 2022Partial Identification with Noisy Covariates: A Robust Optimization Approachcited by 10
  16. 2024Conformal Counterfactual Inference under Hidden Confoundingcited by 10
  17. 2024Quantifying Aleatoric Uncertainty of the Treatment Effect: A Novel Orthogonal Learnercited by 10
  18. 2022Strategic Decision-Making in the Presence of Information Asymmetry: Provably Efficient RL with Algorithmic Instrumentscited by 9
  19. 2021β-Intact-VAE: Identifying and Estimating Causal Effects under Limited Overlapcited by 8
  20. 2023Integrating Earth Observation Data into Causal Inference: Challenges and Opportunitiescited by 8
  21. 2025DeCaFlow: A deconfounding causal generative modelcited by 8
  22. 2022Partial Identification of Dose Responses with Hidden Confounderscited by 7
  23. 2023Proximal Causal Learning of Conditional Average Treatment Effectscited by 7
  24. 2023Debiasing Recommendation by Learning Identifiable Latent Confounderscited by 7
  25. 2023Partial Identification of Causal Effects Using Proxy Variablescited by 7
  26. 2024Proximal Causal Inference With Text Datacited by 7
  27. 2024Causal Effect Identification in LiNGAM Models with Latent Confounderscited by 7
  28. 2021Causal Inference with Hidden Mediatorscited by 6
  29. 2023A Policy Gradient Method for Confounded POMDPscited by 6
  30. 2024Proxy Methods for Domain Adaptationcited by 6
  31. 2024Disentangled Representation Learning for Causal Inference with Instrumentscited by 6
  32. 2025Confounding Robust Deep Reinforcement Learning: A Causal Approachcited by 6
  33. 2022Optimal Treatment Regimes for Proximal Causal Learningcited by 5
  34. 2023Non-parametric identifiability and sensitivity analysis of synthetic control modelscited by 5
  35. 2024Scalable Out-of-distribution Robustness in the Presence of Unobserved Confounderscited by 5
  36. 2024Two-way Deconfounder for Off-policy Evaluation in Causal Reinforcement Learningcited by 5
  37. 2021Towards Principled Causal Effect Estimation by Deep Identifiable Modelscited by 4
  38. 2021Many Proxy Controlscited by 4

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