Recovering Simultaneously Structured Data via Non-Convex Iteratively Reweighted Least Squares

• URL: http://arxiv.org/abs/2306.04961v2
• Date: Thu, 18 Jan 2024 16:47:33 GMT
• Title: Recovering Simultaneously Structured Data via Non-Convex Iteratively Reweighted Least Squares
• Authors: Christian K\"ummerle and Johannes Maly
• Abstract summary: We propose a new algorithm for recovering data that adheres to multiple, heterogeneous low-dimensional structures from linear observations. We show that the IRLS method favorable in identifying low/comckuele state measurements.
• Score: 0.8702432681310401
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose a new algorithm for the problem of recovering data that adheres to multiple, heterogeneous low-dimensional structures from linear observations. Focusing on data matrices that are simultaneously row-sparse and low-rank, we propose and analyze an iteratively reweighted least squares (IRLS) algorithm that is able to leverage both structures. In particular, it optimizes a combination of non-convex surrogates for row-sparsity and rank, a balancing of which is built into the algorithm. We prove locally quadratic convergence of the iterates to a simultaneously structured data matrix in a regime of minimal sample complexity (up to constants and a logarithmic factor), which is known to be impossible for a combination of convex surrogates. In experiments, we show that the IRLS method exhibits favorable empirical convergence, identifying simultaneously row-sparse and low-rank matrices from fewer measurements than state-of-the-art methods. Code is available at https://github.com/ckuemmerle/simirls.

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