
Perturbation expansions and error bounds for the truncated singular value decomposition
Truncated singular value decomposition is a reduced version of the singu...
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A Schattenq Matrix Perturbation Theory via Perturbation Projection Error Bound
This paper studies the Schattenq error of lowrank matrix estimation by...
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Feature selection in weakly coherent matrices
A problem of paramount importance in both pure (Restricted Invertibility...
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Spectral Methods for Data Science: A Statistical Perspective
Spectral methods have emerged as a simple yet surprisingly effective app...
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Datadependent Confidence Regions of Singular Subspaces
Matrix singular value decomposition (SVD) is popular in statistical data...
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Edge statistics of large dimensional deformed rectangular matrices
We consider the edge statistics of large dimensional deformed rectangula...
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Smoothed analysis of the least singular value without inverse LittlewoodOfford theory
We study the lower tail behavior of the least singular value of an n× n ...
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An exact sinΘ formula for matrix perturbation analysis and its applications
Singular vector perturbation is an important topic in numerical analysis and statistics. The main goal of this paper is to provide a useful tool to tackle matrix perturbation problems. Explicitly, we establish a useful formula for the sinΘ angles between the perturbed and the original singular subspaces. This formula is expressed in terms of the perturbation matrix and therefore characterizes how the singular vector perturbation is induced by the additive noise. We then use this formula to derive a onesided version of the sinΘ theorem, as well as improve the bound on the ℓ_2,∞ norm of the singular vector perturbation error. Following this, we proceed to show that two other popular stability problems (i.e., the stability of the Principal Component Analysis and the stability of the singular value thresholding operator) can be solved with the help of these new results.
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