Intelligent Initialization and Adaptive Thresholding for Iterative Matrix Completion: Some Statistical and Algorithmic Theory for Adaptive-Impute

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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.
Publisher
AMER STATISTICAL ASSOC
Issue Date
2019-04
Language
English
Article Type
Article
Citation

JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS, v.28, no.2, pp.323 - 333

ISSN
1061-8600
DOI
10.1080/10618600.2018.1518238
URI
http://hdl.handle.net/10203/263334
Appears in Collection
MT-Journal Papers(저널논문)
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