Non-asymptotic upper bounds for the reconstruction error of PCA

Martin Wahl (HU Berlin)
Wednesday, December 2, 2015 - 10:00am
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

Principal component analysis (PCA) is a standard tool for dimension reduction. Classical objects of interest are the principal subspaces and their empirical counterparts. In this talk, we focus on the reconstruction error of PCA, and prove a non-asymptotic upper bound for the corresponding excess risk. This bound unifies and improves several upper bounds which were previously obtained by empirical process theory. Moreover, the bound reveals that the excess risk differs considerably from the usual subspace distance based on canonical angles. Our proof relies on the analysis of empirical spectral projectors and uses recent concentration inequalities for sample covariance operators.