mlsanityData to 7 Oct 2026

Proximal Causal Learning with Kernels: Two-Stage Estimation and Moment Restriction

arXiv 2105.04544 ↗First posted 10 May 2021cs.LGcited by 54

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Abstract (arXiv)

We address the problem of causal effect estimation in the presence of unobserved confounding, but where proxies for the latent confounder(s) are observed. We propose two kernel-based methods for nonlinear causal effect estimation in this setting: (a) a two-stage regression approach, and (b) a maximum moment restriction approach. We focus on the proximal causal learning setting, but our methods can be used to solve a wider class of inverse problems characterised by a Fredholm integral equation. In particular, we provide a unifying view of two-stage and moment restriction approaches for solving this problem in a nonlinear setting. We provide consistency guarantees for each algorithm, and we demonstrate these approaches achieve competitive results on synthetic data and data simulating a real-world task. In particular, our approach outperforms earlier methods that are not suited to leveraging proxy variables.

Key facts. Cited by 54 papers in the map (data through 7 Oct 2026). Builds on 14 of its 80 references that are in the map. First posted on arXiv 10 May 2021.

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14 of 80 references.

References · 14

  1. 2016Kernel Mean Embedding of Distributions: A Review and Beyondcited by 360
  2. 2016Identifying Causal Effects With Proxy Variables of an Unmeasured Confoundercited by 138
  3. 2019Kernel Instrumental Variable Regressioncited by 118
  4. 2020An Introduction to Proximal Causal Learningcited by 91
  5. 2019Deep Generalized Method of Moments for Instrumental Variable Analysiscited by 88
  6. 2020Minimax Estimation of Conditional Moment Modelscited by 83
  7. 2014Learning Theory for Distribution Regressioncited by 48
  8. 2020Provably Efficient Neural Estimation of Structural Equation Model: An Adversarial Approachcited by 31
  9. 2020Kernel Methods for Unobserved Confounding: Negative Controls, Proxies, and Instrumentscited by 27
  10. 2020Kernel Conditional Moment Test via Maximum Moment Restrictioncited by 18
  11. 2020Ivy: Instrumental Variable Synthesis for Causal Inferencecited by 17
  12. 2013Typing linear algebra: A biproduct-oriented approachcited by 4
2 more
  1. 2017Fixing an error in Caponnetto and de Vito (2007)cited by 2
  2. 2015A New Method for Partial Correction of Residual Confounding in Time-Series and other Observational Studiescited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 7; 2022: 11; 2023: 8; 2024: 12; 2025: 9; 2026: 7.

54 papers.

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  1. 2021Deep Proxy Causal Learning and its Application to Confounded Bandit Policy Evaluationcited by 39
  2. 2021Causal Effect Inference for Structured Treatmentscited by 38
  3. 2022Provably Efficient Reinforcement Learning in Partially Observable Dynamical Systemscited by 35
  4. 2021A Minimax Learning Approach to Off-Policy Evaluation in Confounded Partially Observable Markov Decision Processescited by 34
  5. 2022Long-term Causal Inference Under Persistent Confounding via Data Combinationcited by 27
  6. 2022Pessimism in the Face of Confounders: Provably Efficient Offline Reinforcement Learning in Partially Observable Markov Decision Processescited by 26
  7. 2023Towards Optimal Sobolev Norm Rates for the Vector-Valued Regularized Least-Squares Algorithmcited by 22
  8. 2022Deep Learning Methods for Proximal Inference via Maximum Moment Restrictioncited by 13
  9. 2024Practical Kernel Tests of Conditional Independencecited 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. 2024Optimal Rates for Vector-Valued Spectral Regularization Learning Algorithmscited by 12
38 more
  1. 2024Spectral Representation for Causal Estimation with Hidden Confounderscited by 12
  2. 2022Causal Inference with Treatment Measurement Error: A Nonparametric Instrumental Variable Approachcited by 9
  3. 2025DeCaFlow: A deconfounding causal generative modelcited by 8
  4. 2022Partial Identification of Dose Responses with Hidden Confounderscited by 7
  5. 2023Proximal Causal Learning of Conditional Average Treatment Effectscited by 7
  6. 2024Proximal Causal Inference With Text Datacited by 7
  7. 2024Nonparametric Instrumental Regression via Kernel Methods is Minimax Optimalcited by 7
  8. 2024Proxy Methods for Domain Adaptationcited by 6
  9. 2025On the Hardness of Conditional Independence Testing In Practicecited by 6
  10. 2022Optimal Treatment Regimes for Proximal Causal Learningcited by 5
  11. 2023Kernel Single Proxy Control for Deterministic Confoundingcited by 5
  12. 2024An Overview of Causal Inference using Kernel Embeddingscited by 5
  13. 2021Towards Principled Causal Effect Estimation by Deep Identifiable Modelscited by 4
  14. 2023Doubly Robust Proximal Causal Learning for Continuous Treatmentscited by 4
  15. 2024Stochastic Optimization Algorithms for Instrumental Variable Regression with Streaming Datacited by 4
  16. 2021Quasi-Bayesian Dual Instrumental Variable Regressioncited by 3
  17. 2022Causal Inference from Small High-dimensional Datasetscited by 3
  18. 2023Causal Discovery via Conditional Independence Testing with Proxy Variablescited by 3
  19. 2024Synthetic Potential Outcomes and Causal Mixture Identifiabilitycited by 3
  20. 2024Causal Inference with Complex Treatments: A Surveycited by 3
  21. 2025Adjustment for Confounding using Pre-Trained Representationscited by 3
  22. 2021Instrument Space Selection for Kernel Maximum Moment Restrictioncited by 2
  23. 2023Kernel Conditional Moment Constraints for Confounding Robust Inferencecited by 2
  24. 2024Automating the Selection of Proxy Variables of Unmeasured Confounderscited by 2
  25. 2025An Analysis of Causal Effect Estimation using Outcome Invariant Data Augmentationcited by 2
  26. 2026The Generalised Kernel Covariance Measurecited by 2
  27. 2023The Blessings of Multiple Treatments and Outcomes in Treatment Effect Estimationcited by 1
  28. 2025Density Ratio-Free Doubly Robust Proxy Causal Learningcited by 1
  29. 2025A Kernel-based Stochastic Approximation Framework for Nonlinear Operator Learningcited by 1
  30. 2025ActiveCQ: Active Estimation of Causal Quantitiescited by 1
  31. 2026Detecting Unobserved Confounders: A Kernelized Regression Approachcited by 1
  32. 2021Multi-treatment Effect Estimation from Biomedical Datacited by 0
  33. 2022Dual Instrumental Method for Confounded Kernelized Banditscited by 0
  34. 2023A Convex Framework for Confounding Robust Inferencecited by 0
  35. 2024Recovering Latent Confounders from High-dimensional Proxy Variablescited by 0
  36. 2025Transferring Causal Effects using Proxiescited by 0
  37. 2025Estimating Bidirectional Causal Effects with Large Scale Online Kernel Learningcited by 0
  38. 2026Point-Identification of a Robust Predictor Under Latent Shift with Imperfect Proxiescited by 0

50 most cited of 54 All 54 (JSON)