# Density Ratio-Free Doubly Robust Proxy Causal Learning

arXiv: https://arxiv.org/abs/2505.19807 · HTML: https://mlsanity.com/paper/2505.19807/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 57 references that are in the map.
- First posted on arXiv 26 May 2025.

## Builds on (most cited first, 24 of 24)

- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [Identifying Causal Effects With Proxy Variables of an Unmeasured Confounder](https://mlsanity.com/paper/1609.08816/) (2016)
- [Semiparametric doubly robust targeted double machine learning: a review](https://mlsanity.com/paper/2203.06469/) (2022)
- [Sobolev Norm Learning Rates for Regularized Least-Squares Algorithm](https://mlsanity.com/paper/1702.07254/) (2017)
- [A Measure-Theoretic Approach to Kernel Conditional Mean Embeddings](https://mlsanity.com/paper/2002.03689/) (2020)
- [Semiparametric proximal causal inference](https://mlsanity.com/paper/2011.08411/) (2020)
- [Proximal Causal Learning with Kernels: Two-Stage Estimation and Moment Restriction](https://mlsanity.com/paper/2105.04544/) (2021)
- [Optimal Rates for Regularized Conditional Mean Embedding Learning](https://mlsanity.com/paper/2208.01711/) (2022)
- [Causal Inference Under Unmeasured Confounding With Negative Controls: A Minimax Learning Approach](https://mlsanity.com/paper/2103.14029/) (2021)
- [Deep Proxy Causal Learning and its Application to Confounded Bandit Policy Evaluation](https://mlsanity.com/paper/2106.03907/) (2021)
- [The Influence Function of Semiparametric Estimators](https://mlsanity.com/paper/1508.01378/) (2015)
- [Kernel Methods for Causal Functions: Dose, Heterogeneous, and Incremental Response Curves](https://mlsanity.com/paper/2010.04855/) (2020)
- [A Rigorous Theory of Conditional Mean Embeddings](https://mlsanity.com/paper/1912.00671/) (2019)
- [Kernel Methods for Unobserved Confounding: Negative Controls, Proxies, and Instruments](https://mlsanity.com/paper/2012.10315/) (2020)
- [Probabilistic Evaluation of Sequential Plans from Causal Models with Hidden Variables](https://mlsanity.com/paper/1302.4977/) (2013)
- [Towards Optimal Sobolev Norm Rates for the Vector-Valued Regularized Least-Squares Algorithm](https://mlsanity.com/paper/2312.07186/) (2023)
- [Visually Communicating and Teaching Intuition for Influence Functions](https://mlsanity.com/paper/1810.03260/) (2018)
- [Kernel Conditional Moment Test via Maximum Moment Restriction](https://mlsanity.com/paper/2002.09225/) (2020)
- [Deep Learning Methods for Proximal Inference via Maximum Moment Restriction](https://mlsanity.com/paper/2205.09824/) (2022)
- [Nonparametric Instrumental Regression via Kernel Methods is Minimax Optimal](https://mlsanity.com/paper/2411.19653/) (2024)
- [Doubly Robust Proximal Causal Learning for Continuous Treatments](https://mlsanity.com/paper/2309.12819/) (2023)
- [Kernel Single Proxy Control for Deterministic Confounding](https://mlsanity.com/paper/2308.04585/) (2023)
- [Estimation of Individual Treatment Effect in Latent Confounder Models via Adversarial Learning](https://mlsanity.com/paper/1811.08943/) (2018)
- [Density Ratio-based Proxy Causal Learning Without Density Ratios](https://mlsanity.com/paper/2503.08371/) (2025)

## Built on by (most cited first, 2 of 2)

- [Nonparametric Instrumental Variable Regression with Observed Covariates](https://mlsanity.com/paper/2511.19404/) (2025)
- [Decision-Aware Proximal Bridge Learning for Optimal Treatment Selection](https://mlsanity.com/paper/2605.16989/) (2026)

## Abstract (arXiv)

We study the problem of causal function estimation in the Proxy Causal Learning (PCL) framework, where confounders are not observed but proxies for the confounders are available. Two main approaches have been proposed: outcome bridge-based and treatment bridge-based methods. In this work, we propose two kernel-based doubly robust estimators that combine the strengths of both approaches, and naturally handle continuous and high-dimensional variables. Our identification strategy builds on a recent density ratio-free method for treatment bridge-based PCL; furthermore, in contrast to previous approaches, it does not require indicator functions or kernel smoothing over the treatment variable. These properties make it especially well-suited for continuous or high-dimensional treatments. By using kernel mean embeddings, we propose the first density-ratio free doubly robust estimators for proxy causal learning, which have closed form solutions and strong uniform consistency guarantees. Our estimators outperform existing methods on PCL benchmarks, including a prior doubly robust method that requires both kernel smoothing and density ratio estimation.