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Statistics > Machine Learning
Title: A Majorization-Minimization Gauss-Newton Method for 1-Bit Matrix Completion
(Submitted on 27 Apr 2023 (this version), latest version 23 Apr 2024 (v2))
Abstract: In 1-bit matrix completion, the aim is to estimate an underlying low-rank matrix from a partial set of binary observations. We propose a novel method for 1-bit matrix completion called MMGN. Our method is based on the majorization-minimization (MM) principle, which yields a sequence of standard low-rank matrix completion problems in our setting. We solve each of these sub-problems by a factorization approach that explicitly enforces the assumed low-rank structure and then apply a Gauss-Newton method. Our numerical studies and application to a real-data example illustrate that MMGN outputs comparable if not more accurate estimates, is often significantly faster, and is less sensitive to the spikiness of the underlying matrix than existing methods.
Submission history
From: Xiaoqian Liu [view email][v1] Thu, 27 Apr 2023 03:16:52 GMT (2038kb,D)
[v2] Tue, 23 Apr 2024 02:10:25 GMT (199kb,D)
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