# An Introduction to Proximal Causal Learning

arXiv: https://arxiv.org/abs/2009.10982 · HTML: https://mlsanity.com/paper/2009.10982/

## Key facts

- Cited by 95 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Sep 2020.

## Built on by (most cited first, 30 of 95)

- [Causal Inference in Natural Language Processing: Estimation, Prediction, Interpretation and Beyond](https://mlsanity.com/paper/2109.00725/) (2021)
- [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)
- [Proximal Reinforcement Learning: Efficient Off-Policy Evaluation in Partially Observed Markov Decision Processes](https://mlsanity.com/paper/2110.15332/) (2021)
- [Deep Proxy Causal Learning and its Application to Confounded Bandit Policy Evaluation](https://mlsanity.com/paper/2106.03907/) (2021)
- [Causal Effect Inference for Structured Treatments](https://mlsanity.com/paper/2106.01939/) (2021)
- [Off-Policy Confidence Interval Estimation with Confounded Markov Decision Process](https://mlsanity.com/paper/2202.10589/) (2022)
- [Long-term Causal Inference Under Persistent Confounding via Data Combination](https://mlsanity.com/paper/2202.07234/) (2022)
- [Pessimism in the Face of Confounders: Provably Efficient Offline Reinforcement Learning in Partially Observable Markov Decision Processes](https://mlsanity.com/paper/2205.13589/) (2022)
- [Stochastic Causal Programming for Bounding Treatment Effects](https://mlsanity.com/paper/2202.10806/) (2022)
- [Proximal Learning for Individualized Treatment Regimes Under Unmeasured Confounding](https://mlsanity.com/paper/2105.01187/) (2021)
- [Augmented balancing weights as linear regression](https://mlsanity.com/paper/2304.14545/) (2023)
- [Regularizing towards Causal Invariance: Linear Models with Proxies](https://mlsanity.com/paper/2103.02477/) (2021)
- [Minimax Kernel Machine Learning for a Class of Doubly Robust Functionals with Application to Proximal Causal Inference](https://mlsanity.com/paper/2104.02929/) (2021)
- [An Instrumental Variable Approach to Confounded Off-Policy Evaluation](https://mlsanity.com/paper/2212.14468/) (2022)
- [Offline Reinforcement Learning with Instrumental Variables in Confounded Markov Decision Processes](https://mlsanity.com/paper/2209.08666/) (2022)
- [Off-Policy Evaluation for Episodic Partially Observable Markov Decision Processes under Non-Parametric Models](https://mlsanity.com/paper/2209.10064/) (2022)
- [Estimating Treatment Effects from Irregular Time Series Observations with Hidden Confounders](https://mlsanity.com/paper/2303.02320/) (2023)
- [Causal isotonic calibration for heterogeneous treatment effects](https://mlsanity.com/paper/2302.14011/) (2023)
- [Deep Learning Methods for Proximal Inference via Maximum Moment Restriction](https://mlsanity.com/paper/2205.09824/) (2022)
- [Black Box Causal Inference: Effect Estimation via Meta Prediction](https://mlsanity.com/paper/2503.05985/) (2025)
- [Inference on Strongly Identified Functionals of Weakly Identified Functions](https://mlsanity.com/paper/2208.08291/) (2022)
- [Spectral Representation Learning for Conditional Moment Models](https://mlsanity.com/paper/2210.16525/) (2022)
- [Adapting to Latent Subgroup Shifts via Concepts and Proxies](https://mlsanity.com/paper/2212.11254/) (2022)
- [Estimating long-term causal effects from short-term experiments and long-term observational data with unobserved confounding](https://mlsanity.com/paper/2302.10625/) (2023)
- [The Proximal ID Algorithm](https://mlsanity.com/paper/2108.06818/) (2021)
- [Partial Identification with Noisy Covariates: A Robust Optimization Approach](https://mlsanity.com/paper/2202.10665/) (2022)
- [Conformal Counterfactual Inference under Hidden Confounding](https://mlsanity.com/paper/2405.12387/) (2024)
- [Quantifying Aleatoric Uncertainty of the Treatment Effect: A Novel Orthogonal Learner](https://mlsanity.com/paper/2411.03387/) (2024)
- [Strategic Decision-Making in the Presence of Information Asymmetry: Provably Efficient RL with Algorithmic Instruments](https://mlsanity.com/paper/2208.11040/) (2022)

## 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.