# Kernel Single Proxy Control for Deterministic Confounding

arXiv: https://arxiv.org/abs/2308.04585 · HTML: https://mlsanity.com/paper/2308.04585/

## Key facts

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

## Builds on (most cited first, 14 of 14)

- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning](https://mlsanity.com/paper/1805.08651/) (2018)
- [Identifying Causal Effects With Proxy Variables of an Unmeasured Confounder](https://mlsanity.com/paper/1609.08816/) (2016)
- [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)
- [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)
- [A Critical Look at the Consistency of Causal Estimation With Deep Latent Variable Models](https://mlsanity.com/paper/2102.06648/) (2021)
- [Kernel Methods for Unobserved Confounding: Negative Controls, Proxies, and Instruments](https://mlsanity.com/paper/2012.10315/) (2020)
- [Deep Learning Methods for Proximal Inference via Maximum Moment Restriction](https://mlsanity.com/paper/2205.09824/) (2022)
- [Single Proxy Control](https://mlsanity.com/paper/2302.06054/) (2023)
- [ChemGymRL: An Interactive Framework for Reinforcement Learning for Digital Chemistry](https://mlsanity.com/paper/2305.14177/) (2023)

## Built on by (most cited first, 5 of 5)

- [Proxy Methods for Domain Adaptation](https://mlsanity.com/paper/2403.07442/) (2024)
- [Scalable Out-of-distribution Robustness in the Presence of Unobserved Confounders](https://mlsanity.com/paper/2411.19923/) (2024)
- [Density Ratio-Free Doubly Robust Proxy Causal Learning](https://mlsanity.com/paper/2505.19807/) (2025)
- [Identifying Causal Effects Using a Single Proxy Variable](https://mlsanity.com/paper/2604.09135/) (2026)
- [Proximal Balancing for Causal Effect Estimation under Unmeasured Confounding](https://mlsanity.com/paper/2609.40051/) (2026)

## 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.