Rate-optimal perturbation bounds for singular subspaces with applications to high-dimensional statistics

Perturbation bounds for singular spaces, in particular Wedin’s \mathop{\mathrm{sin}}\nolimits \Thetatheorem, are a fundamental tool in many fields including high-dimensional statistics, machine learning and applied mathematics. In this paper, we establish separate perturbation bounds, measured in both spectral and Frobenius \mathop{\mathrm{sin}}\nolimits \Thetadistances, for the left and right singular subspaces. Lower bounds, which show...