Reproduce “Causal Inference with Treatment Measurement Error: A Nonparametric Instrumental Variable Approach” on OpenResearch

About this paper

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

MEKIV estimates a causal response curve when treatment is confounded and observed only through two noisy measurements. It uses an instrument and measurement-error assumptions to learn a kernel representation of latent treatment, then applies a kernel instrumental-variable outcome stage. In simulations, it beat baselines at the highest tested error level, but weak instruments and restrictive measurement assumptions limit its scope.

Key insights

• For symmetric, characteristic, and translation-invariant kernels, learning the kernel mean embedding of a distribution is equivalent to learning its characteristic function.
• The characteristic function of a latent variable X conditioned on an instrument Z can be identified from observable quantities (two noisy measurements M, N, and Z) by solving a differential equation, which avoids direct integration.
• The proposed three-stage algorithm (observable CME estimation, latent X CME learning, structural function estimation) effectively combines IV regression with measurement error correction in a nonparametric setting.

Summary by alphaXiv.