mlsanityData to 7 Oct 2026

Deep Proxy Causal Learning and its Application to Confounded Bandit Policy Evaluation

arXiv 2106.03907 ↗First posted 7 Jun 2021cs.LG stat.MLcited by 39

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Abstract (arXiv)

Proxy causal learning (PCL) is a method for estimating the causal effect of treatments on outcomes in the presence of unobserved confounding, using proxies (structured side information) for the confounder. This is achieved via two-stage regression: in the first stage, we model relations among the treatment and proxies; in the second stage, we use this model to learn the effect of treatment on the outcome, given the context provided by the proxies. PCL guarantees recovery of the true causal effect, subject to identifiability conditions. We propose a novel method for PCL, the deep feature proxy variable method (DFPV), to address the case where the proxies, treatments, and outcomes are high-dimensional and have nonlinear complex relationships, as represented by deep neural network features. We show that DFPV outperforms recent state-of-the-art PCL methods on challenging synthetic benchmarks, including settings involving high dimensional image data. Furthermore, we show that PCL can be applied to off-policy evaluation for the confounded bandit problem, in which DFPV also exhibits competitive performance.

Key facts. Cited by 39 papers in the map (data through 7 Oct 2026). Builds on 19 of its 38 references that are in the map. First posted on arXiv 7 Jun 2021.

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19 of 38 references.

References · 19

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  3. 2013Auto-Encoding Variational Bayescited by 3,980
  4. 2018Spectral Normalization for Generative Adversarial Networkscited by 1,618
  5. 2017Causal Effect Inference with Deep Latent-Variable Modelscited by 408
  6. 2016Learning Representations for Counterfactual Inferencecited by 327
  7. 2019Optimizing Millions of Hyperparameters by Implicit Differentiationcited by 303
  8. 2016Identifying Causal Effects With Proxy Variables of an Unmeasured Confoundercited by 138
  9. 2019Kernel Instrumental Variable Regressioncited by 118
  10. 2020An Introduction to Proximal Causal Learningcited by 91
  11. 2019Deep Generalized Method of Moments for Instrumental Variable Analysiscited by 88
  12. 2019Off-Policy Evaluation in Partially Observable Environmentscited by 65
7 more
  1. 2020Learning Deep Features in Instrumental Variable Regressioncited by 65
  2. 2021Proximal Causal Learning with Kernels: Two-Stage Estimation and Moment Restrictioncited by 54
  3. 2018A confounding bridge approach for double negative control inference on causal effectscited by 36
  4. 2020Provably Efficient Neural Estimation of Structural Equation Model: An Adversarial Approachcited by 31
  5. 2020Kernel Methods for Unobserved Confounding: Negative Controls, Proxies, and Instrumentscited by 27
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  7. 2018Estimation of Individual Treatment Effect in Latent Confounder Models via Adversarial Learningcited by 4

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 3; 2022: 11; 2023: 6; 2024: 8; 2025: 7; 2026: 4.

39 papers.

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  1. 2023A Survey on Causal Reinforcement Learningcited by 43
  2. 2021Proximal Reinforcement Learning: Efficient Off-Policy Evaluation in Partially Observed Markov Decision Processescited by 40
  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. 2022An Instrumental Variable Approach to Confounded Off-Policy Evaluationcited by 20
  7. 2024Functional Bilevel Optimization for Machine Learningcited by 20
  8. 2022Estimating individual treatment effects under unobserved confounding using binary instrumentscited by 17
  9. 2022Deep Learning Methods for Proximal Inference via Maximum Moment Restrictioncited by 13
  10. 2022Spectral Representation Learning for Conditional Moment Modelscited by 12
  11. 2024Spectral Representation for Causal Estimation with Hidden Confounderscited by 12
  12. 2023Causal Fairness under Unobserved Confounding: A Neural Sensitivity Frameworkcited by 10
27 more
  1. 2022A Neural Mean Embedding Approach for Back-door and Front-door Adjustmentcited by 8
  2. 2021Learning Causal Models from Conditional Moment Restrictions by Importance Weightingcited by 7
  3. 2023Stochastic Online Instrumental Variable Regression: Regrets for Endogeneity and Bandit Feedbackcited by 7
  4. 2024Regularized DeepIV with Model Selectioncited by 6
  5. 2023Kernel Single Proxy Control for Deterministic Confoundingcited by 5
  6. 2024An Overview of Causal Inference using Kernel Embeddingscited by 5
  7. 2023Doubly Robust Proximal Causal Learning for Continuous Treatmentscited by 4
  8. 2025Demystifying Spectral Feature Learning for Instrumental Variable Regressioncited by 4
  9. 2024Causal Inference with Complex Treatments: A Surveycited by 3
  10. 2024Learning to Embed Distributions via Maximum Kernel Entropycited by 3
  11. 2025Conformal Prediction with Corrupted Labels: Uncertain Imputation and Robust Re-weightingcited by 3
  12. 2025Closed-Form Last Layer Optimizationcited by 3
  13. 2024Predictive Performance Comparison of Decision Policies Under Confoundingcited by 2
  14. 2024Automating the Selection of Proxy Variables of Unmeasured Confounderscited by 2
  15. 2025Outcome-Aware Spectral Feature Learning for Instrumental Variable Regressioncited by 2
  16. 2022Importance Weighting Approach in Kernel Bayes' Rulecited by 1
  17. 2023The Blessings of Multiple Treatments and Outcomes in Treatment Effect Estimationcited by 1
  18. 2025Density Ratio-Free Doubly Robust Proxy Causal Learningcited by 1
  19. 2022Dual Instrumental Method for Confounded Kernelized Banditscited by 0
  20. 2022Statistical Estimation of Confounded Linear MDPs: An Instrumental Variable Approachcited by 0
  21. 2022Nonlinear Causal Discovery via Kernel Anchor Regressioncited by 0
  22. 2025Coupling Generative Modeling and an Autoencoder with the Causal Bridgecited by 0
  23. 2025Transferring Causal Effects using Proxiescited by 0
  24. 2026Adaptive Estimation and Inference in Conditional Moment Models via the Discrepancy Principlecited by 0
  25. 2026Decision-Aware Proximal Bridge Learning for Optimal Treatment Selectioncited by 0
  26. 2026The Good, the Bad, and the Ugly of Markov Boundary for Tabular Predictioncited by 0
  27. 2026Proximal Balancing for Causal Effect Estimation under Unmeasured Confoundingcited by 0