mlsanityData to 7 Oct 2026

Kernel Single Proxy Control for Deterministic Confounding

arXiv 2308.04585 ↗First posted 8 Aug 2023stat.ML cs.LGcited by 5

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Abstract (arXiv)

We consider the problem of causal effect estimation with an unobserved confounder, where we observe a single proxy variable that is associated with the confounder. Although it has been shown that the recovery of an average causal effect is impossible in general from a single proxy variable, we show that causal recovery is possible if the outcome is generated deterministically. This generalizes existing work on causal methods with a single proxy variable to the continuous treatment setting. We propose two kernel-based methods for this setting: the first based on the two-stage regression approach, and the second based on a maximum moment restriction approach. We prove that both approaches can consistently estimate the causal effect, and we empirically demonstrate that we can successfully recover the causal effect on challenging synthetic benchmarks.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 14 of its 32 references that are in the map. First posted on arXiv 8 Aug 2023.

Builds on

14 of 32 references.

References · 14

  1. 2017Causal Effect Inference with Deep Latent-Variable Modelscited by 408
  2. 2018Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learningcited by 278
  3. 2016Identifying Causal Effects With Proxy Variables of an Unmeasured Confoundercited by 138
  4. 2017Sobolev Norm Learning Rates for Regularized Least-Squares Algorithmcited by 113
  5. 2020A Measure-Theoretic Approach to Kernel Conditional Mean Embeddingscited by 86
  6. 2021Proximal Causal Learning with Kernels: Two-Stage Estimation and Moment Restrictioncited by 54
  7. 2022Optimal Rates for Regularized Conditional Mean Embedding Learningcited by 50
  8. 2021Causal Inference Under Unmeasured Confounding With Negative Controls: A Minimax Learning Approachcited by 43
  9. 2021Deep Proxy Causal Learning and its Application to Confounded Bandit Policy Evaluationcited by 39
  10. 2021A Critical Look at the Consistency of Causal Estimation With Deep Latent Variable Modelscited by 29
  11. 2020Kernel Methods for Unobserved Confounding: Negative Controls, Proxies, and Instrumentscited by 27
  12. 2022Deep Learning Methods for Proximal Inference via Maximum Moment Restrictioncited by 13
2 more
  1. 2023Single Proxy Controlcited by 4
  2. 2023ChemGymRL: An Interactive Framework for Reinforcement Learning for Digital Chemistrycited by 3

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 2; 2025: 1; 2026: 2.

5 papers.

  1. 2024Proxy Methods for Domain Adaptationcited by 6
  2. 2024Scalable Out-of-distribution Robustness in the Presence of Unobserved Confounderscited by 5
  3. 2025Density Ratio-Free Doubly Robust Proxy Causal Learningcited by 1
  4. 2026Identifying Causal Effects Using a Single Proxy Variablecited by 0
  5. 2026Proximal Balancing for Causal Effect Estimation under Unmeasured Confoundingcited by 0