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• W3204694634 abstract "This paper considers a large class of problems where we seek to recover a low rank matrix and/or sparse vector from some set of measurements. While methods based on convex relaxations suffer from a (possibly large) estimator bias, and other nonconvex methods require the rank or sparsity to be known a priori, we use nonconvex regularizers to minimize the rank and $l_0$ norm without the estimator bias from the convex relaxation. We present a novel analysis of the alternating proximal gradient descent algorithm applied to such problems, and bound the error between the iterates and the ground truth sparse and low rank matrices. The algorithm and error bound can be applied to sparse optimization, matrix completion, and robust principal component analysis as special cases of our results." @default.
• W3204694634 created "2021-10-11" @default.
• W3204694634 creator A5026582535 @default.
• W3204694634 creator A5074563047 @default.
• W3204694634 date "2021-09-26" @default.
• W3204694634 modified "2023-09-27" @default.
• W3204694634 title "Provable Low Rank Plus Sparse Matrix Separation Via Nonconvex Regularizers" @default.
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• W3204694634 hasPublicationYear "2021" @default.
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