Fast exact matrix completion: A unified optimization framework for matrix completion
Name
19-471.pdf
Description
Published version
Size
418.19 KB
Format
Adobe PDF
Checksum (MD5)
4163aa62e17196d8499b2e54216329f5
Author(s)
Bertsimas, D
Li, ML
Date Issued
November 1, 2020
Journal
Journal of Machine Learning Research
Version
Final published version
Abstract
© 2020 Dimitris Bertsimas and Michael Lingzhi Li. License: CC-BY 4.0, see https://creativecommons.org/licenses/by/4.0/. Attribution requirements are provided at http://jmlr.org/papers/v21/19-471.html. We formulate the problem of matrix completion with and without side information as a non-convex optimization problem. We design fastImpute based on non-convex gradient descent and show it converges to a global minimum that is guaranteed to recover closely the underlying matrix while it scales to matrices of sizes beyond 105 × 105. We report experiments on both synthetic and real-world datasets that show fastImpute is competitive in both the accuracy of the matrix recovered and the time needed across all cases. Furthermore, when a high number of entries are missing, fastImpute is over 75% lower in MAPE and 15 times faster than current state-of-the-art matrix completion methods in both the case with side information and without.
MIT Department
Massachusetts Institute of Technology. Department of Economics
Terms of Use
Creative Commons Attribution 4.0 International license
Persistent DSpace Link
DOI of Published Version
https://jmlr.org/papers/v21/19-471.html
