# Causal Inference with Treatment Measurement Error: A Nonparametric Instrumental Variable Approach

arXiv: https://arxiv.org/abs/2206.09186 · HTML: https://mlsanity.com/paper/2206.09186/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 40 references that are in the map.
- First posted on arXiv 18 Jun 2022.

## Builds on (most cited first, 15 of 15)

- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [Identifying Causal Effects With Proxy Variables of an Unmeasured Confounder](https://mlsanity.com/paper/1609.08816/) (2016)
- [On the Equivalence between Kernel Quadrature Rules and Random Feature Expansions](https://mlsanity.com/paper/1502.06800/) (2015)
- [Kernel Instrumental Variable Regression](https://mlsanity.com/paper/1906.00232/) (2019)
- [Deep Generalized Method of Moments for Instrumental Variable Analysis](https://mlsanity.com/paper/1905.12495/) (2019)
- [Counterfactual Probabilities: Computational Methods, Bounds and Applications](https://mlsanity.com/paper/1302.6784/) (2013)
- [Learning Deep Features in Instrumental Variable Regression](https://mlsanity.com/paper/2010.07154/) (2020)
- [Proximal Causal Learning with Kernels: Two-Stage Estimation and Moment Restriction](https://mlsanity.com/paper/2105.04544/) (2021)
- [Optimal Rates for Random Fourier Features](https://mlsanity.com/paper/1506.02155/) (2015)
- [Optimal Sup-norm Rates and Uniform Inference on Nonlinear Functionals of Nonparametric IV Regression](https://mlsanity.com/paper/1508.03365/) (2015)
- [Causal Inference with Noisy and Missing Covariates via Matrix Factorization](https://mlsanity.com/paper/1806.00811/) (2018)
- [Minimax Kernel Machine Learning for a Class of Doubly Robust Functionals with Application to Proximal Causal Inference](https://mlsanity.com/paper/2104.02929/) (2021)
- [Causal Inference with Corrupted Data: Measurement Error, Missing Values, Discretization, and Differential Privacy](https://mlsanity.com/paper/2107.02780/) (2021)
- [Partial Identifiability in Discrete Data With Measurement Error](https://mlsanity.com/paper/2012.12449/) (2020)
- [Operationalizing Complex Causes: A Pragmatic View of Mediation](https://mlsanity.com/paper/2106.05074/) (2021)

## Built on by (most cited first, 9 of 9)

- [An Efficient Doubly-Robust Test for the Kernel Treatment Effect](https://mlsanity.com/paper/2304.13237/) (2023)
- [Stochastic Online Instrumental Variable Regression: Regrets for Endogeneity and Bandit Feedback](https://mlsanity.com/paper/2302.09357/) (2023)
- [Stochastic Optimization Algorithms for Instrumental Variable Regression with Streaming Data](https://mlsanity.com/paper/2405.19463/) (2024)
- [Robust Bayesian Inference for Measurement Error Misspecification: The Berkson and Classical Cases](https://mlsanity.com/paper/2306.01468/) (2023)
- [Causal Effect Regularization: Automated Detection and Removal of Spurious Attributes](https://mlsanity.com/paper/2306.11072/) (2023)
- [ActiveCQ: Active Estimation of Causal Quantities](https://mlsanity.com/paper/2509.24293/) (2025)
- [Nonlinear Causal Discovery via Kernel Anchor Regression](https://mlsanity.com/paper/2210.16775/) (2022)
- [Using uncertainty-aware machine learning models to study aerosol-cloud interactions](https://mlsanity.com/paper/2301.11921/) (2022)
- [Identifiable causal inference with noisy treatment and no side information](https://mlsanity.com/paper/2306.10614/) (2023)

## Abstract (arXiv)

We propose a kernel-based nonparametric estimator for the causal effect when the cause is corrupted by error. We do so by generalizing estimation in the instrumental variable setting. Despite significant work on regression with measurement error, additionally handling unobserved confounding in the continuous setting is non-trivial: we have seen little prior work. As a by-product of our investigation, we clarify a connection between mean embeddings and characteristic functions, and how learning one simultaneously allows one to learn the other. This opens the way for kernel method research to leverage existing results in characteristic function estimation. Finally, we empirically show that our proposed method, MEKIV, improves over baselines and is robust under changes in the strength of measurement error and to the type of error distributions.