  A general framework for principal component analysis (PCA) in the presence of
heteroskedastic noise is introduced. We propose an algorithm called HeteroPCA,
which involves iteratively imputing the diagonal entries of the sample
covariance matrix to remove estimation bias due to heteroskedasticity. This
procedure is computationally efficient and provably optimal under the
generalized spiked covariance model. A key technical step is a deterministic
robust perturbation analysis on singular subspaces, which can be of independent
interest. The effectiveness of the proposed algorithm is demonstrated in a
suite of problems in high-dimensional statistics, including singular value
decomposition (SVD) under heteroskedastic noise, Poisson PCA, and SVD for
heteroskedastic and incomplete data.
