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

Yuchen Zhu, Limor Gultchin, Arthur Gretton, Matt Kusner, Ricardo Silva

Keywords: Causal Inference, Kernel Methods

TL;DR: We propose MEKIV, a causal effect estimation algorithm, using instruments to correct for measurement error in treatment records while additionally also handling confounding.

Abstract: 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.