Fast Exact Matrix Completion: A Unified Optimization Framework for Matrix Completion
Machine Learning
2021-01-05 v2 Optimization and Control
Methodology
Machine Learning
Abstract
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 . 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 lower in MAPE and times faster than current state-of-the-art matrix completion methods in both the case with side information and without.
Cite
@article{arxiv.1910.09092,
title = {Fast Exact Matrix Completion: A Unified Optimization Framework for Matrix Completion},
author = {Dimitris Bertsimas and Michael Lingzhi Li},
journal= {arXiv preprint arXiv:1910.09092},
year = {2021}
}