Provable Low Rank Plus Sparse Matrix Separation Via Nonconvex Regularizers

• URL: http://arxiv.org/abs/2109.12713v1
• Date: Sun, 26 Sep 2021 22:09:42 GMT
• Title: Provable Low Rank Plus Sparse Matrix Separation Via Nonconvex Regularizers
• Authors: April Sagan, John E. Mitchell
• Abstract summary: This paper considers a large problem where we seek to recover a low rank matrix/or sparse vector from some set of measurements. While methods based on convex bias estimators suffer from bias the rank or sparsity to be known as a priori, we use non regularizers. We present a novel analysis of the proximal alternating bias descent algorithm applied to such problems.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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