mlsanityData to 14 Oct 2026

Deep Learning Methods for Proximal Inference via Maximum Moment Restriction

arXiv 2205.09824 ↗First posted 19 May 2022stat.ML cs.LGcited by 14

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Abstract (arXiv)

The No Unmeasured Confounding Assumption is widely used to identify causal effects in observational studies. Recent work on proximal inference has provided alternative identification results that succeed even in the presence of unobserved confounders, provided that one has measured a sufficiently rich set of proxy variables, satisfying specific structural conditions. However, proximal inference requires solving an ill-posed integral equation. Previous approaches have used a variety of machine learning techniques to estimate a solution to this integral equation, commonly referred to as the bridge function. However, prior work has often been limited by relying on pre-specified kernel functions, which are not data adaptive and struggle to scale to large datasets. In this work, we introduce a flexible and scalable method based on a deep neural network to estimate causal effects in the presence of unmeasured confounding using proximal inference. Our method achieves state of the art performance on two well-established proximal inference benchmarks. Finally, we provide theoretical consistency guarantees for our method.

Key facts. Cited by 14 papers in the map (data through 14 Oct 2026). Builds on 16 of its 37 references that are in the map. First posted on arXiv 19 May 2022.

Builds on

16 of 37 references.

References · 16

  1. 2017Causal Effect Inference with Deep Latent-Variable Modelscited by 410
  2. 2016Identifying Causal Effects With Proxy Variables of an Unmeasured Confoundercited by 139
  3. 2019Kernel Instrumental Variable Regressioncited by 118
  4. 2020An Introduction to Proximal Causal Learningcited by 95
  5. 2019Deep Generalized Method of Moments for Instrumental Variable Analysiscited by 88
  6. 2020Minimax Estimation of Conditional Moment Modelscited by 83
  7. 2020Learning Deep Features in Instrumental Variable Regressioncited by 66
  8. 2020Semiparametric proximal causal inferencecited by 59
  9. 2021Proximal Causal Learning with Kernels: Two-Stage Estimation and Moment Restrictioncited by 55
  10. 2021Causal Inference Under Unmeasured Confounding With Negative Controls: A Minimax Learning Approachcited by 44
  11. 2021Deep Proxy Causal Learning and its Application to Confounded Bandit Policy Evaluationcited by 40
  12. 2018Adversarial Generalized Method of Momentscited by 34
4 more
  1. 2020Kernel Methods for Unobserved Confounding: Negative Controls, Proxies, and Instrumentscited by 28
  2. 2021Minimax Kernel Machine Learning for a Class of Doubly Robust Functionals with Application to Proximal Causal Inferencecited by 20
  3. 2020Kernel Conditional Moment Test via Maximum Moment Restrictioncited by 18
  4. 2021Learning Causal Models from Conditional Moment Restrictions by Importance Weightingcited by 7

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 1; 2023: 4; 2024: 3; 2025: 4; 2026: 2.

14 papers.

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  1. 2024Spectral Representation for Causal Estimation with Hidden Confounderscited by 12
  2. 2025DeCaFlow: A deconfounding causal generative modelcited by 8
  3. 2023Proximal Causal Learning of Conditional Average Treatment Effectscited by 7
  4. 2022Optimal Treatment Regimes for Proximal Causal Learningcited by 5
  5. 2023Kernel Single Proxy Control for Deterministic Confoundingcited by 5
  6. 2023Doubly Robust Proximal Causal Learning for Continuous Treatmentscited by 4
  7. 2023Assumption-lean falsification tests of rate double-robustness of double-machine-learning estimatorscited by 2
  8. 2024DAG-aware Transformer for Causal Effect Estimationcited by 2
  9. 2025Density Ratio-Free Doubly Robust Proxy Causal Learningcited by 1
  10. 2024DNA-SE: Towards Deep Neural-Nets Assisted Semiparametric Estimationcited by 0
  11. 2025DISCO: Mitigating Bias in Deep Learning with Conditional Distance Correlationcited by 0
  12. 2025Coupling Generative Modeling and an Autoencoder with the Causal Bridgecited by 0
2 more
  1. 2026Decision-Aware Proximal Bridge Learning for Optimal Treatment Selectioncited by 0
  2. 2026Proximal Causal Learning under Unmeasured Confoundingcited by 0