mlsanityData to 14 Oct 2026

Doubly Robust Proximal Causal Learning for Continuous Treatments

arXiv 2309.12819 ↗First posted 22 Sep 2023stat.ME cs.LGcited by 4

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Abstract (arXiv)

Proximal causal learning is a promising framework for identifying the causal effect under the existence of unmeasured confounders. Within this framework, the doubly robust (DR) estimator was derived and has shown its effectiveness in estimation, especially when the model assumption is violated. However, the current form of the DR estimator is restricted to binary treatments, while the treatment can be continuous in many real-world applications. The primary obstacle to continuous treatments resides in the delta function present in the original DR estimator, making it infeasible in causal effect estimation and introducing a heavy computational burden in nuisance function estimation. To address these challenges, we propose a kernel-based DR estimator that can well handle continuous treatments. Equipped with its smoothness, we show that its oracle form is a consistent approximation of the influence function. Further, we propose a new approach to efficiently solve the nuisance functions. We then provide a comprehensive convergence analysis in terms of the mean square error. We demonstrate the utility of our estimator on synthetic datasets and real-world applications.

Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). Builds on 28 of its 64 references that are in the map. First posted on arXiv 22 Sep 2023.

Builds on

28 of 64 references.

References · 28

  1. 2015Variational Inference with Normalizing Flowscited by 2,170
  2. 2016Density estimation using Real NVPcited by 2,042
  3. 2019Neural Spline Flowscited by 596
  4. 2019Orthogonal Statistical Learningcited by 151
  5. 2016Identifying Causal Effects With Proxy Variables of an Unmeasured Confoundercited by 139
  6. 2017A Tutorial on Kernel Density Estimation and Recent Advancescited by 101
  7. 2020An Introduction to Proximal Causal Learningcited by 95
  8. 2020Minimax Estimation of Conditional Moment Modelscited by 83
  9. 2015Nonparametric methods for doubly robust estimation of continuous treatment effectscited by 64
  10. 2020Semiparametric proximal causal inferencecited by 59
  11. 2018Policy Evaluation and Optimization with Continuous Treatmentscited by 58
  12. 2021Proximal Causal Learning with Kernels: Two-Stage Estimation and Moment Restrictioncited by 55
16 more
  1. 2021Causal Inference Under Unmeasured Confounding With Negative Controls: A Minimax Learning Approachcited by 44
  2. 2021Deep Proxy Causal Learning and its Application to Confounded Bandit Policy Evaluationcited by 40
  3. 2015The Influence Function of Semiparametric Estimatorscited by 36
  4. 2018A confounding bridge approach for double negative control inference on causal effectscited by 36
  5. 2020Kernel Methods for Unobserved Confounding: Negative Controls, Proxies, and Instrumentscited by 28
  6. 2021Proximal Learning for Individualized Treatment Regimes Under Unmeasured Confoundingcited by 21
  7. 2021Minimax Kernel Machine Learning for a Class of Doubly Robust Functionals with Application to Proximal Causal Inferencecited by 20
  8. 2020Kernel Conditional Moment Test via Maximum Moment Restrictioncited by 18
  9. 2021Proximal Causal Inference for Complex Longitudinal Studiescited by 16
  10. 2017The Kernel Mixture Network: A Nonparametric Method for Conditional Density Estimation of Continuous Random Variablescited by 15
  11. 2022Deep Learning Methods for Proximal Inference via Maximum Moment Restrictioncited by 14
  12. 2020Entropy Balancing for Continuous Treatmentscited by 12
  13. 2020Doubly Robust Off-Policy Value and Gradient Estimation for Deterministic Policiescited by 10
  14. 2022A New Central Limit Theorem for the Augmented IPW Estimator: Variance Inflation, Cross-Fit Covariance and Beyondcited by 5
  15. 2021Automatic Double Machine Learning for Continuous Treatment Effectscited by 4
  16. 2023A Bayesian Nonparametric Method to Adjust for Unmeasured Confounding with Negative Controlscited by 1

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 1; 2024: 0; 2025: 1; 2026: 2.

4 papers.

  1. 2023The Blessings of Multiple Treatments and Outcomes in Treatment Effect Estimationcited by 1
  2. 2025Density Ratio-Free Doubly Robust Proxy Causal Learningcited by 1
  3. 2026Proximal Path-Specific Inferencecited by 1
  4. 2026Decision-Aware Proximal Bridge Learning for Optimal Treatment Selectioncited by 0