Data to 14 Oct 2026

Minimax Kernel Machine Learning for a Class of Doubly Robust Functionals with Application to Proximal Causal Inference

arXiv 2104.02929 ↗First posted 7 Apr 2021stat.ML cs.LG econ.EMcited by 20

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Abstract (arXiv)

Robins et al. (2008) introduced a class of influence functions (IFs) which could be used to obtain doubly robust moment functions for the corresponding parameters. However, that class does not include the IF of parameters for which the nuisance functions are solutions to integral equations. Such parameters are particularly important in the field of causal inference, specifically in the recently proposed proximal causal inference framework of Tchetgen Tchetgen et al. (2020), which allows for estimating the causal effect in the presence of latent confounders. In this paper, we first extend the class of Robins et al. to include doubly robust IFs in which the nuisance functions are solutions to integral equations. Then we demonstrate that the double robustness property of these IFs can be leveraged to construct estimating equations for the nuisance functions, which enables us to solve the integral equations without resorting to parametric models. We frame the estimation of the nuisance functions as a minimax optimization problem. We provide convergence rates for the nuisance functions and conditions required for asymptotic linearity of the estimator of the parameter of interest. The experiment results demonstrate that our proposed methodology leads to robust and high-performance estimators for average causal effect in the proximal causal inference framework.

Key facts. Cited by 20 papers in the map (data through 14 Oct 2026). Builds on 25 of its 82 references that are in the map. First posted on arXiv 7 Apr 2021.

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25 of 82 references.

References · 25

2015Estimation and Inference of Heterogeneous Treatment Effects using Random Forestscited by 600
2017Quasi-Oracle Estimation of Heterogeneous Treatment Effectscited by 332
2019Orthogonal Statistical Learningcited by 151
2016Identifying Causal Effects With Proxy Variables of an Unmeasured Confoundercited by 139
2019Kernel Instrumental Variable Regressioncited by 118
2020An Introduction to Proximal Causal Learningcited by 95
2019Deep Generalized Method of Moments for Instrumental Variable Analysiscited by 88
2020Minimax Estimation of Conditional Moment Modelscited by 83
2020Semiparametric proximal causal inferencecited by 59
2018Policy Evaluation and Optimization with Continuous Treatmentscited by 58
2018Orthogonal Random Forest for Causal Inferencecited by 51
2016Approximate Residual Balancing: De-Biased Inference of Average Treatment Effects in High Dimensionscited by 50

13 more

2021Causal Inference Under Unmeasured Confounding With Negative Controls: A Minimax Learning Approachcited by 44
2018A confounding bridge approach for double negative control inference on causal effectscited by 36
2020Adversarial Estimation of Riesz Representerscited by 35
2020Provably Efficient Neural Estimation of Structural Equation Model: An Adversarial Approachcited by 31
2015Optimal Sup-norm Rates and Uniform Inference on Nonlinear Functionals of Nonparametric IV Regressioncited by 30
2020Kernel Methods for Unobserved Confounding: Negative Controls, Proxies, and Instrumentscited by 28
2019Semi-Parametric Efficient Policy Learning with Continuous Actionscited by 26
2019Localized Debiased Machine Learning: Efficient Inference on Quantile Treatment Effects and Beyondcited by 23
2020A Selective Review of Negative Control Methods in Epidemiologycited by 16
2019Selective machine learning of doubly robust functionalscited by 9
2021Kernel Ridge Riesz Representers: Generalization, Mis-specification, and the Counterfactual Effective Dimensioncited by 6
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2020On Proximal Causal Learning with Many Hidden Confounderscited by 1

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 4; 2022: 5; 2023: 6; 2024: 1; 2025: 0; 2026: 4.

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2021Proximal Reinforcement Learning: Efficient Off-Policy Evaluation in Partially Observed Markov Decision Processescited by 41
2021A Minimax Learning Approach to Off-Policy Evaluation in Confounded Partially Observable Markov Decision Processescited by 36
2022Long-term Causal Inference Under Persistent Confounding via Data Combinationcited by 27
2021Proximal Learning for Individualized Treatment Regimes Under Unmeasured Confoundingcited by 21
2023Augmented balancing weights as linear regressioncited by 21
2022Deep Learning Methods for Proximal Inference via Maximum Moment Restrictioncited by 14
2022Inference on Strongly Identified Functionals of Weakly Identified Functionscited by 12
2022Causal Inference with Treatment Measurement Error: A Nonparametric Instrumental Variable Approachcited by 9
2023Proximal Causal Learning of Conditional Average Treatment Effectscited by 7
2023Partial Identification of Causal Effects Using Proxy Variablescited by 7
2021Causal Inference with Hidden Mediatorscited by 6
2022Optimal Treatment Regimes for Proximal Causal Learningcited by 5

8 more

2024Anytime-Valid Inference for Double/Debiased Machine Learning of Causal Parameterscited by 5
2023Doubly Robust Proximal Causal Learning for Continuous Treatmentscited by 4
2023Causal Discovery via Conditional Independence Testing with Proxy Variablescited by 3
2023Assumption-lean falsification tests of rate double-robustness of double-machine-learning estimatorscited by 2
2026Proximal Path-Specific Inferencecited by 1
2026Causal Imitation Learning Under Measurement Error and Distribution Shiftcited by 0
2026Decision-Aware Proximal Bridge Learning for Optimal Treatment Selectioncited by 0
2026What You Observe Determines How You Identify Causal Effects: Evaluating Causal Models across Observational Viewscited by 0