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Matrix completion from a computational statistics perspective
Author(s) -
Chi Eric C.,
Li Tianxi
Publication year - 2019
Publication title -
wiley interdisciplinary reviews: computational statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.693
H-Index - 38
eISSN - 1939-0068
pISSN - 1939-5108
DOI - 10.1002/wics.1469
Subject(s) - matrix completion , matrix (chemical analysis) , rank (graph theory) , perspective (graphical) , missing data , statistics , low rank approximation , data matrix , computer science , mathematics , algorithm , artificial intelligence , combinatorics , mathematical analysis , clade , biochemistry , materials science , physics , chemistry , quantum mechanics , hankel matrix , gene , composite material , gaussian , phylogenetic tree
In the matrix completion problem, we seek to estimate the missing entries of a matrix from a small sample of the total number of entries in a matrix. While this task is hopeless in general, structured matrices that are appropriately sampled can be completed with surprising accuracy. In this review, we examine the success behind low‐rank matrix completion, one of the most studied and employed versions of matrix completion. Formulating the matrix completion problem as a low‐rank matrix estimation problem admits several strengths: good empirical performance on real data, statistical guarantees, and practical algorithms with convergence guarantees. We also examine how matrix completion relates to the classical study of missing data analysis (MDA) in statistics. By drawing on the MDA perspective, we see opportunities to weaken the commonly enforced assumption of missing completely at random in matrix completion. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Multivariate Analysis