{"title":"A Majorization-Minimization Gauss-Newton Method for 1-Bit Matrix Completion.","authors":"Xiaoqian Liu, Xu Han, Eric C Chi, Boaz Nadler","doi":"10.1080/10618600.2024.2428610","DOIUrl":null,"url":null,"abstract":"<p><p>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 Majorization-Minimization Gauss-Newton (MMGN). Our method is based on the majorization-minimization principle, which converts the original optimization problem into a sequence of standard low-rank matrix completion problems. We solve each of these subproblems by a factorization approach that explicitly enforces the assumed low-rank structure and then apply a Gauss-Newton method. Using simulations and a real data example, we illustrate that in comparison to existing 1-bit matrix completion methods, MMGN outputs comparable if not more accurate estimates. In addition, it is often significantly faster, and less sensitive to the spikiness of the underlying matrix. In comparison with three standard generic optimization approaches that directly minimize the original objective, MMGN also exhibits a clear computational advantage, especially when the fraction of observed entries is small.</p>","PeriodicalId":15422,"journal":{"name":"Journal of Computational and Graphical Statistics","volume":" ","pages":""},"PeriodicalIF":1.8000,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12327443/pdf/","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational and Graphical Statistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/10618600.2024.2428610","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
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 Majorization-Minimization Gauss-Newton (MMGN). Our method is based on the majorization-minimization principle, which converts the original optimization problem into a sequence of standard low-rank matrix completion problems. We solve each of these subproblems by a factorization approach that explicitly enforces the assumed low-rank structure and then apply a Gauss-Newton method. Using simulations and a real data example, we illustrate that in comparison to existing 1-bit matrix completion methods, MMGN outputs comparable if not more accurate estimates. In addition, it is often significantly faster, and less sensitive to the spikiness of the underlying matrix. In comparison with three standard generic optimization approaches that directly minimize the original objective, MMGN also exhibits a clear computational advantage, especially when the fraction of observed entries is small.
期刊介绍:
The Journal of Computational and Graphical Statistics (JCGS) presents the very latest techniques on improving and extending the use of computational and graphical methods in statistics and data analysis. Established in 1992, this journal contains cutting-edge research, data, surveys, and more on numerical graphical displays and methods, and perception. Articles are written for readers who have a strong background in statistics but are not necessarily experts in computing. Published in March, June, September, and December.