A note on the prediction error of principal component regression

11/07/2018

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by   Martin Wahl, et al.

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We analyse the prediction error of principal component regression (PCR) and prove non-asymptotic upper bounds for the corresponding squared risk. Under mild assumptions, we conclude that PCR performs as well as the oracle method obtained by replacing empirical principal components by their population counterparts. Our approach relies on perturbation bounds for the excess risk of principal component analysis.