Intelligent Initialization and Adaptive Thresholding for Iterative Matrix Completion: Some Statistical and Algorithmic Theory for Adaptive-Impute. Issue 2 (3rd April 2019)

• Record Type: Journal Article
• Authors: Cho, Juhee; Kim, Donggyu; Rohe, Karl
• Is Part Of: Journal of computational and graphical statistics. Volume 28:Issue 2(2019)
• Page Start: 323
• Page End: 333
• Publication Date: 2019-04-03
• Subjects: Generalized-softImpute -- Nonconvex optimization -- Thresholded singular value decomposition -- softImpute; Mathematical statistics -- Data processing -- Periodicals; Mathematical statistics -- Graphic methods -- Periodicals; 519.50285
• DOI: 10.1080/10618600.2018.1518238
• Languages: English
• ISSNs: 1061-8600

Abstract

Abstract: Over the past decade, various matrix completion algorithms have been developed. Thresholded singular value decomposition (SVD) is a popular technique in implementing many of them. A sizable number of studies have shown its theoretical and empirical excellence, but choosing the right threshold level still remains as a key empirical difficulty. This article proposes a novel matrix completion algorithm which iterates thresholded SVD with theoretically justified and data-dependent values of thresholding parameters. The estimate of the proposed algorithm enjoys the minimax error rate and shows outstanding empirical performances. The thresholding scheme that we use can be viewed as a solution to a nonconvex optimization problem, understanding of whose theoretical convergence guarantee is known to be limited. We investigate this problem by introducing a simpler algorithm, generalized- softImpute, analyzing its convergence behavior, and connecting it to the proposed algorithm.