PCA in Data-Dependent Noise (Correlated-PCA): Nearly Optimal Finite Sample Guarantees

We study Principal Component Analysis (PCA) in a setting where a part of the corrupting noise is data-dependent and, hence, the noise and the true data are correlated. Under a bounded-ness assumption on both the true data and noise, and a few assumptions on the data-noise correlation, we obtain a sample complexity bound for the most common PCA solution, singular value decomposition (SVD). This bound, which is within a logarithmic factor of the best achievable, significantly improves upon our bound from recent work (NIPS 2016) where we first studied this "correlated-PCA" problem.