Canonical correlation regression with noisy data

Isaac Meza; Rahul Singh

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arXiv · 2512.22697

Canonical correlation regression with noisy data

Isaac Meza·Rahul Singh

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Abstract

We study instrumental variable regression in data rich environments. The goal is to estimate a linear model from many noisy covariates and many noisy instruments. Our key assumption is that true covariates and true instruments are repetitive, though possibly different in nature; they each reflect a few underlying factors, however those underlying factors may be misaligned. We analyze a family of estimators based on two stage least squares with spectral regularization: canonical correlations between covariates and instruments are learned in the first stage, which are used as regressors in the second stage. As a theoretical contribution, we derive upper and lower bounds on estimation error, proving optimality of the method with noisy data. As a practical contribution, we provide guidance on which types of spectral regularization to use in different regimes.

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BibTeX RIS

Isaac Meza, Rahul Singh. 2025-12-27. Canonical correlation regression with noisy data. https://arxiv.org/abs/2512.22697

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