A Majorization-Minimization Gauss-Newton Method for 1-Bit Matrix Completion.

IF 1.8 2区 数学 Q2 STATISTICS & PROBABILITY
Xiaoqian Liu, Xu Han, Eric C Chi, Boaz Nadler
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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.

1位矩阵补全的最大化-最小化高斯-牛顿方法。
在1位矩阵补全中,目的是从二值观测的部分集合中估计一个潜在的低秩矩阵。我们提出了一种新的1位矩阵补全方法,称为最大化-最小化高斯-牛顿(MMGN)。该方法基于最大-最小原则,将原优化问题转化为一系列标准的低秩矩阵补全问题。我们通过显式执行假设的低秩结构的分解方法来解决这些子问题,然后应用高斯-牛顿方法。通过模拟和实际数据示例,我们说明了与现有的1位矩阵补全方法相比,MMGN输出的估计即使不是更准确,也是相当的。此外,它通常要快得多,而且对底层矩阵的尖刺不那么敏感。与直接最小化原始目标的三种标准通用优化方法相比,MMGN还显示出明显的计算优势,特别是当观察到的条目的比例很小时。
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来源期刊
CiteScore
3.50
自引率
8.30%
发文量
153
审稿时长
>12 weeks
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.
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