Towards Faster Rates and Oracle Property for Low-Rank Matrix Estimation

@InProceedings{pmlr-v48-gui16,
  title = 	 {Towards Faster Rates and Oracle Property for Low-Rank Matrix Estimation},
  author = 	 {Gui, Huan and Han, Jiawei and Gu, Quanquan},
  booktitle = 	 {Proceedings of The 33rd International Conference on Machine Learning},
  pages = 	 {2300--2309},
  year = 	 {2016},
  editor = 	 {Balcan, Maria Florina and Weinberger, Kilian Q.},
  volume = 	 {48},
  series = 	 {Proceedings of Machine Learning Research},
  address = 	 {New York, New York, USA},
  month = 	 {20--22 Jun},
  publisher =    {PMLR},
  pdf = 	 {http://proceedings.mlr.press/v48/gui16.pdf},
  url = 	 {https://proceedings.mlr.press/v48/gui16.html},
  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.}
}