On Robustness of Principal Component Regression

Principal component regression (PCR) is a simple, but powerful and ubiquitously utilized method. Its effectiveness well established when the covariates exhibit low-rank structure. However, its ability to handle settings with noisy, missing, mixed-valued, that is, discrete continuous, not understood remains an important open challenge. As main contribution of this work, we establish robustness PCR, without any change, in respect provide meaningful finite-sample analysis. To do so, PCR equivalent performing linear after preprocessing covariate matrix via hard singular value thresholding (HSVT). result, context counterfactual analysis using observational data, show recently proposed robust variant synthetic control method, known as (RSC). immediate consequence, obtain RSC estimator was previously absent. controls literature, (approximate) exists setting generalized factor model, or latent variable model; traditionally existence needs be assumed exist axiom. We further discuss surprising implication property noise, can learn good predictive model even if are tactfully transformed preserve differential privacy. Finally, work advances state-of-the-art for HSVT by establishing stronger guarantees l2,?-norm rather than Frobenius norm commonly done estimation which may interest own right.