Open Access
April 2020 Nonasymptotic upper bounds for the reconstruction error of PCA
Markus Reiß, Martin Wahl
Ann. Statist. 48(2): 1098-1123 (April 2020). DOI: 10.1214/19-AOS1839


We analyse the reconstruction error of principal component analysis (PCA) and prove nonasymptotic upper bounds for the corresponding excess risk. These bounds unify and improve existing upper bounds from the literature. In particular, they give oracle inequalities under mild eigenvalue conditions. The bounds reveal that the excess risk differs significantly from usually considered subspace distances based on canonical angles. Our approach relies on the analysis of empirical spectral projectors combined with concentration inequalities for weighted empirical covariance operators and empirical eigenvalues.


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Markus Reiß. Martin Wahl. "Nonasymptotic upper bounds for the reconstruction error of PCA." Ann. Statist. 48 (2) 1098 - 1123, April 2020.


Received: 1 March 2018; Revised: 1 November 2018; Published: April 2020
First available in Project Euclid: 26 May 2020

zbMATH: 07241582
MathSciNet: MR4102689
Digital Object Identifier: 10.1214/19-AOS1839

Primary: 62H25
Secondary: 15A42 , 60F10

Keywords: Concentration inequalities , excess risk , Principal Component Analysis , reconstruction error , Spectral projectors

Rights: Copyright © 2020 Institute of Mathematical Statistics

Vol.48 • No. 2 • April 2020
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