Canonical correlation regression with noisy data
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Abstract (arXiv)
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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References · 8
- 2016Rate-Optimal Perturbation Bounds for Singular Subspaces with Applications to High-Dimensional Statisticscited by 45
- 2015Optimal Sup-norm Rates and Uniform Inference on Nonlinear Functionals of Nonparametric IV Regressioncited by 30
- 2021Causal Inference with Corrupted Data: Measurement Error, Missing Values, Discretization, and Differential Privacycited by 18
- 2024Spectral Representation for Causal Estimation with Hidden Confounderscited by 12
- 2025Nonparametric Instrumental Variable Inference with Many Weak Instrumentscited by 5
- 2025Demystifying Spectral Feature Learning for Instrumental Variable Regressioncited by 4
- 2024Canonical Correlation Analysis: reviewcited by 3
- 2025Inference of high-dimensional weak instrumental variable regression models without ridge-regularizationcited by 1
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