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

arXiv: https://arxiv.org/abs/2104.02929 · HTML: https://mlsanity.com/paper/2104.02929/

## 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.

## Builds on (most cited first, 25 of 25)

- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Quasi-Oracle Estimation of Heterogeneous Treatment Effects](https://mlsanity.com/paper/1712.04912/) (2017)
- [Orthogonal Statistical Learning](https://mlsanity.com/paper/1901.09036/) (2019)
- [Identifying Causal Effects With Proxy Variables of an Unmeasured Confounder](https://mlsanity.com/paper/1609.08816/) (2016)
- [Kernel Instrumental Variable Regression](https://mlsanity.com/paper/1906.00232/) (2019)
- [An Introduction to Proximal Causal Learning](https://mlsanity.com/paper/2009.10982/) (2020)
- [Deep Generalized Method of Moments for Instrumental Variable Analysis](https://mlsanity.com/paper/1905.12495/) (2019)
- [Minimax Estimation of Conditional Moment Models](https://mlsanity.com/paper/2006.07201/) (2020)
- [Semiparametric proximal causal inference](https://mlsanity.com/paper/2011.08411/) (2020)
- [Policy Evaluation and Optimization with Continuous Treatments](https://mlsanity.com/paper/1802.06037/) (2018)
- [Orthogonal Random Forest for Causal Inference](https://mlsanity.com/paper/1806.03467/) (2018)
- [Approximate Residual Balancing: De-Biased Inference of Average Treatment Effects in High Dimensions](https://mlsanity.com/paper/1604.07125/) (2016)
- [Causal Inference Under Unmeasured Confounding With Negative Controls: A Minimax Learning Approach](https://mlsanity.com/paper/2103.14029/) (2021)
- [A confounding bridge approach for double negative control inference on causal effects](https://mlsanity.com/paper/1808.04945/) (2018)
- [Adversarial Estimation of Riesz Representers](https://mlsanity.com/paper/2101.00009/) (2020)
- [Provably Efficient Neural Estimation of Structural Equation Model: An Adversarial Approach](https://mlsanity.com/paper/2007.01290/) (2020)
- [Optimal Sup-norm Rates and Uniform Inference on Nonlinear Functionals of Nonparametric IV Regression](https://mlsanity.com/paper/1508.03365/) (2015)
- [Kernel Methods for Unobserved Confounding: Negative Controls, Proxies, and Instruments](https://mlsanity.com/paper/2012.10315/) (2020)
- [Semi-Parametric Efficient Policy Learning with Continuous Actions](https://mlsanity.com/paper/1905.10116/) (2019)
- [Localized Debiased Machine Learning: Efficient Inference on Quantile Treatment Effects and Beyond](https://mlsanity.com/paper/1912.12945/) (2019)
- [A Selective Review of Negative Control Methods in Epidemiology](https://mlsanity.com/paper/2009.05641/) (2020)
- [Selective machine learning of doubly robust functionals](https://mlsanity.com/paper/1911.02029/) (2019)
- [Kernel Ridge Riesz Representers: Generalization, Mis-specification, and the Counterfactual Effective Dimension](https://mlsanity.com/paper/2102.11076/) (2021)
- [Honest data-adaptive inference for the average treatment effect under model misspecification using penalised bias-reduced double-robust estimation](https://mlsanity.com/paper/1708.03787/) (2017)
- [On Proximal Causal Learning with Many Hidden Confounders](https://mlsanity.com/paper/2012.06725/) (2020)

## Built on by (most cited first, 20 of 20)

- [Proximal Reinforcement Learning: Efficient Off-Policy Evaluation in Partially Observed Markov Decision Processes](https://mlsanity.com/paper/2110.15332/) (2021)
- [A Minimax Learning Approach to Off-Policy Evaluation in Confounded Partially Observable Markov Decision Processes](https://mlsanity.com/paper/2111.06784/) (2021)
- [Long-term Causal Inference Under Persistent Confounding via Data Combination](https://mlsanity.com/paper/2202.07234/) (2022)
- [Proximal Learning for Individualized Treatment Regimes Under Unmeasured Confounding](https://mlsanity.com/paper/2105.01187/) (2021)
- [Augmented balancing weights as linear regression](https://mlsanity.com/paper/2304.14545/) (2023)
- [Deep Learning Methods for Proximal Inference via Maximum Moment Restriction](https://mlsanity.com/paper/2205.09824/) (2022)
- [Inference on Strongly Identified Functionals of Weakly Identified Functions](https://mlsanity.com/paper/2208.08291/) (2022)
- [Causal Inference with Treatment Measurement Error: A Nonparametric Instrumental Variable Approach](https://mlsanity.com/paper/2206.09186/) (2022)
- [Proximal Causal Learning of Conditional Average Treatment Effects](https://mlsanity.com/paper/2301.10913/) (2023)
- [Partial Identification of Causal Effects Using Proxy Variables](https://mlsanity.com/paper/2304.04374/) (2023)
- [Causal Inference with Hidden Mediators](https://mlsanity.com/paper/2111.02927/) (2021)
- [Optimal Treatment Regimes for Proximal Causal Learning](https://mlsanity.com/paper/2212.09494/) (2022)
- [Anytime-Valid Inference for Double/Debiased Machine Learning of Causal Parameters](https://mlsanity.com/paper/2408.09598/) (2024)
- [Doubly Robust Proximal Causal Learning for Continuous Treatments](https://mlsanity.com/paper/2309.12819/) (2023)
- [Causal Discovery via Conditional Independence Testing with Proxy Variables](https://mlsanity.com/paper/2305.05281/) (2023)
- [Assumption-lean falsification tests of rate double-robustness of double-machine-learning estimators](https://mlsanity.com/paper/2306.10590/) (2023)
- [Proximal Path-Specific Inference](https://mlsanity.com/paper/2605.09462/) (2026)
- [Causal Imitation Learning Under Measurement Error and Distribution Shift](https://mlsanity.com/paper/2601.22206/) (2026)
- [Decision-Aware Proximal Bridge Learning for Optimal Treatment Selection](https://mlsanity.com/paper/2605.16989/) (2026)
- [What You Observe Determines How You Identify Causal Effects: Evaluating Causal Models across Observational Views](https://mlsanity.com/paper/2609.36881/) (2026)

## 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.