Provable Low Rank Plus Sparse Matrix Separation Via Nonconvex Regularizers

09/26/2021
by   April Sagan, et al.
0

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.

READ FULL TEXT

page 21

page 22

page 23

research
11/13/2019

Factor Group-Sparse Regularization for Efficient Low-Rank Matrix Recovery

This paper develops a new class of nonconvex regularizers for low-rank m...
research
11/14/2018

Matrix rigidity and the ill-posedness of Robust PCA and matrix completion

Robust Principal Component Analysis (PCA) (Candes et al., 2011) and low-...
research
11/26/2018

Sparse spectral estimation with missing and corrupted measurements

Supervised learning methods with missing data have been extensively stud...
research
02/28/2018

Exactly Robust Kernel Principal Component Analysis

We propose a novel method called robust kernel principal component analy...
research
05/21/2018

A Nonconvex Projection Method for Robust PCA

Robust principal component analysis (RPCA) is a well-studied problem wit...
research
07/09/2019

Global Optimality Guarantees for Nonconvex Unsupervised Video Segmentation

In this paper, we consider the problem of unsupervised video object segm...
research
06/06/2019

Nonconvex Approach for Sparse and Low-Rank Constrained Models with Dual Momentum

In this manuscript, we research on the behaviors of surrogates for the r...

Please sign up or login with your details

Forgot password? Click here to reset