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This work obtains novel finite sample guarantees for Principal ComponentAnalysis (PCA). These hold even when the corrupting noise is non-isotropic, anda part (or all of it) is data-dependent. Because of the latter, in general, thenoise and the true data are correlated. The results in this work are asignificant improvement over those given in our earlier work where this"correlated-PCA" problem was first studied. In fact, in certain regimes, ourresults imply that the sample complexity required to achieve subspace recoveryerror that is a constant fraction of the noise level is near-optimal. Usefulcorollaries of our result include guarantees for PCA in sparse data-dependentnoise and for PCA with missing data. An important application of the former isin proving correctness of the subspace update step of a popular onlinealgorithm for dynamic robust PCA.

Finite Sample Guarantees for PCA in Non-Isotropic and Data-Dependent Noise