mlsanityData to 7 Oct 2026

Causal Inference Under Unmeasured Confounding With Negative Controls: A Minimax Learning Approach

arXiv 2103.14029 ↗First posted 25 Mar 2021stat.ML cs.LG stat.MEcited by 43

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Abstract (arXiv)

We study the estimation of causal parameters when not all confounders are observed and instead negative controls are available. Recent work has shown how these can enable identification and efficient estimation via two so-called bridge functions. In this paper, we tackle the primary challenge to causal inference using negative controls: the identification and estimation of these bridge functions. Previous work has relied on completeness conditions on these functions to identify the causal parameters and required uniqueness assumptions in estimation, and they also focused on parametric estimation of bridge functions. Instead, we provide a new identification strategy that avoids the completeness condition. And, we provide new estimators for these functions based on minimax learning formulations. These estimators accommodate general function classes such as Reproducing Kernel Hilbert Spaces and neural networks. We study finite-sample convergence results both for estimating bridge functions themselves and for the final estimation of the causal parameter under a variety of combinations of assumptions. We avoid uniqueness conditions on the bridge functions as much as possible.

Key facts. Cited by 43 papers in the map (data through 7 Oct 2026). Builds on 22 of its 65 references that are in the map. First posted on arXiv 25 Mar 2021.

Builds on

22 of 65 references.

References · 22

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2017Training GANs with Optimismcited by 217
  3. 2015Doubly Robust Policy Evaluation and Optimizationcited by 158
  4. 2019Orthogonal Statistical Learningcited by 150
  5. 2019Minimax Weight and Q-Function Learning for Off-Policy Evaluationcited by 150
  6. 2016Identifying Causal Effects With Proxy Variables of an Unmeasured Confoundercited by 138
  7. 2017Non-convex Optimization for Machine Learningcited by 132
  8. 2019Kernel Instrumental Variable Regressioncited by 118
  9. 2020An Introduction to Proximal Causal Learningcited by 91
  10. 2019Deep Generalized Method of Moments for Instrumental Variable Analysiscited by 88
  11. 2020Off-Policy Evaluation via the Regularized Lagrangiancited by 86
  12. 2020Minimax Estimation of Conditional Moment Modelscited by 83
10 more
  1. 2019Off-Policy Evaluation in Partially Observable Environmentscited by 65
  2. 2020Semiparametric proximal causal inferencecited by 58
  3. 2019A Kernel Loss for Solving the Bellman Equationcited by 37
  4. 2018Adversarial Generalized Method of Momentscited by 34
  5. 2020Adversarial Estimation of Riesz Representerscited by 34
  6. 2017Augmented Minimax Linear Estimationcited by 33
  7. 2020Provably Efficient Neural Estimation of Structural Equation Model: An Adversarial Approachcited by 31
  8. 2017Nonparametric causal effects based on incremental propensity score interventionscited by 28
  9. 2020Kernel Methods for Unobserved Confounding: Negative Controls, Proxies, and Instrumentscited by 27
  10. 2020The Variational Method of Momentscited by 23

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Citing papers per year: 2021: 8; 2022: 12; 2023: 12; 2024: 4; 2025: 1; 2026: 6.

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  1. 2021Proximal Reinforcement Learning: Efficient Off-Policy Evaluation in Partially Observed Markov Decision Processescited by 40
  2. 2022Provably Efficient Reinforcement Learning in Partially Observable Dynamical Systemscited by 35
  3. 2021A Minimax Learning Approach to Off-Policy Evaluation in Confounded Partially Observable Markov Decision Processescited by 34
  4. 2022Off-Policy Confidence Interval Estimation with Confounded Markov Decision Processcited by 31
  5. 2024Applied Causal Inference Powered by ML and AIcited by 30
  6. 2022Long-term Causal Inference Under Persistent Confounding via Data Combinationcited by 27
  7. 2022Pessimism in the Face of Confounders: Provably Efficient Offline Reinforcement Learning in Partially Observable Markov Decision Processescited by 26
  8. 2021Proximal Learning for Individualized Treatment Regimes Under Unmeasured Confoundingcited by 21
  9. 2023Augmented balancing weights as linear regressioncited by 21
  10. 2021Minimax Kernel Machine Learning for a Class of Doubly Robust Functionals with Application to Proximal Causal Inferencecited by 20
  11. 2022Future-Dependent Value-Based Off-Policy Evaluation in POMDPscited by 20
  12. 2022An Instrumental Variable Approach to Confounded Off-Policy Evaluationcited by 20
31 more
  1. 2022Reinforcement Learning from Partial Observation: Linear Function Approximation with Provable Sample Efficiencycited by 15
  2. 2022Deep Learning Methods for Proximal Inference via Maximum Moment Restrictioncited by 13
  3. 2023Minimax Instrumental Variable Regression and L2 Convergence Guarantees without Identification or Closednesscited by 13
  4. 2022Inference on Strongly Identified Functionals of Weakly Identified Functionscited by 12
  5. 2022Spectral Representation Learning for Conditional Moment Modelscited by 12
  6. 2022Adapting to Latent Subgroup Shifts via Concepts and Proxiescited by 12
  7. 2021The Proximal ID Algorithmcited by 11
  8. 2023Falsification of Internal and External Validity in Observational Studies via Conditional Moment Restrictionscited by 10
  9. 2021A Simple and General Debiased Machine Learning Theorem with Finite Sample Guaranteescited by 9
  10. 2023Source Condition Double Robust Inference on Functionals of Inverse Problemscited by 8
  11. 2023Proximal Causal Learning of Conditional Average Treatment Effectscited by 7
  12. 2024Proximal Causal Inference With Text Datacited by 7
  13. 2021Causal Inference with Hidden Mediatorscited by 6
  14. 2024Regularized DeepIV with Model Selectioncited by 6
  15. 2022Optimal Treatment Regimes for Proximal Causal Learningcited by 5
  16. 2023Kernel Single Proxy Control for Deterministic Confoundingcited by 5
  17. 2023Policy Learning with Distributional Welfarecited by 5
  18. 2021Many Proxy Controlscited by 4
  19. 2023Doubly Robust Proximal Causal Learning for Continuous Treatmentscited by 4
  20. 2023Counterfactual Co-occurring Learning for Bias Mitigation in Weakly-supervised Object Localizationcited by 3
  21. 2024Causal Inference with Complex Treatments: A Surveycited by 3
  22. 2023Kernel Conditional Moment Constraints for Confounding Robust Inferencecited by 2
  23. 2023Assumption-lean falsification tests of rate double-robustness of double-machine-learning estimatorscited by 2
  24. 2025Density Ratio-Free Doubly Robust Proxy Causal Learningcited by 1
  25. 2026Proximal Path-Specific Inferencecited by 1
  26. 2023A Convex Framework for Confounding Robust Inferencecited by 0
  27. 2026PAC Guarantees for Reinforcement Learning: Sample Complexity, Coverage, and Structurecited by 0
  28. 2026Adaptive Estimation and Inference in Conditional Moment Models via the Discrepancy Principlecited by 0
  29. 2026Nonparametric Instrumental Variable Analysis Without Structural Equations: Debiased Inference on Functionals of Inverse Problems with No Solutionscited by 0
  30. 2026Decision-Aware Proximal Bridge Learning for Optimal Treatment Selectioncited by 0
  31. 2026Proximal Balancing for Causal Effect Estimation under Unmeasured Confoundingcited by 0