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

MCML Authors

Johannes Maly

Prof. Dr.

Associate

Mathematical Data Science and Artificial Intelligence

Abstract

We propose a new algorithm for the problem of recovering data that adheres to multiple, heterogenous low-dimensional structures from linear observations. Focussing 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.

inproceedings

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NeurIPS 2023

37th Conference on Neural Information Processing Systems. New Orleans, LA, USA, Dec 10-16, 2023.

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Authors

C. Kümmerle • J. Maly

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Links

URL

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Research Area

 A2 | Mathematical Foundations