This work obtains novel finite sample guarantees for Principal Component Analysis (PCA). These hold even when the corrupting noise is non-isotropic, and a part (or all of it) is data-dependent. Because of the latter, in general, the noise and the true data are correlated. The results in this work are a significant improvement over those given in our earlier work where this "correlated-PCA" problem was first studied. In the regime analyzed in this work, our results imply that the sample complexity required to achieve subspace recovery error that is a constant fraction of the noise level is near-optimal. We demonstrate the validity of our analysis through numerical experiments.
This is given in the long version of this work REF .
Finite sample guarantees for PCA in non-isotropic and data-dependent noise
2017 55th Annual Allerton Conference on Communication, Control, and Computing (Allerton)
2017 55th Annual Allerton Conference on Communication, Control, and Computing (Allerton)
Computer Science Mathematics