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Canonical correlation regression with noisy data

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  • Isaac Meza
  • Rahul Singh

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.

Suggested Citation

  • Isaac Meza & Rahul Singh, 2025. "Canonical correlation regression with noisy data," Papers 2512.22697, arXiv.org.
    • Handle: RePEc:arx:papers:2512.22697
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    References listed on IDEAS

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