TY - GEN
T1 - Towards faster rates and oracle property for low-rank matrix estimation
AU - Gui, Huan
AU - Han, Jiawei
AU - Gu, Quanquan
PY - 2016/1/1
Y1 - 2016/1/1
N2 - We present a unified framework for low-rank matrix estimation with nonconvex penalty. A proximal gradient homotopy algorithm is developed 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.copyright
AB - We present a unified framework for low-rank matrix estimation with nonconvex penalty. A proximal gradient homotopy algorithm is developed 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.copyright
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M3 - Conference contribution
AN - SCOPUS:84998849966
T3 - 33rd International Conference on Machine Learning, ICML 2016
SP - 3405
EP - 3431
BT - 33rd International Conference on Machine Learning, ICML 2016
A2 - Weinberger, Kilian Q.
A2 - Balcan, Maria Florina
PB - International Machine Learning Society (IMLS)
T2 - 33rd International Conference on Machine Learning, ICML 2016
Y2 - 19 June 2016 through 24 June 2016
ER -