Towards Faster Rates and Oracle Property for Low-Rank Matrix Estimation
Abstract
We present a unified framework for low-rank matrix estimation with a nonconvex penalty. A proximal gradient homotopy algorithm is proposed to solve the proposed optimization problem. Theoretically, we first prove that the proposed estimator attains a faster statistical rate than the traditional low-rank matrix estimator with nuclear norm penalty. Moreover, we rigorously show that under a certain condition on the magnitude of the nonzero singular values, the proposed estimator enjoys oracle property (i.e., exactly recovers the true rank of the matrix), besides attaining a faster rate. Extensive numerical experiments on both synthetic and real world datasets corroborate our theoretical findings.
Cite
Text
Gui et al. "Towards Faster Rates and Oracle Property for Low-Rank Matrix Estimation." International Conference on Machine Learning, 2016.Markdown
[Gui et al. "Towards Faster Rates and Oracle Property for Low-Rank Matrix Estimation." International Conference on Machine Learning, 2016.](https://mlanthology.org/icml/2016/gui2016icml-faster/)BibTeX
@inproceedings{gui2016icml-faster,
title = {{Towards Faster Rates and Oracle Property for Low-Rank Matrix Estimation}},
author = {Gui, Huan and Han, Jiawei and Gu, Quanquan},
booktitle = {International Conference on Machine Learning},
year = {2016},
pages = {2300-2309},
volume = {48},
url = {https://mlanthology.org/icml/2016/gui2016icml-faster/}
}