Towards faster rates and oracle property for low-rank matrix estimation

Huan Gui, Jiawei Han, Quanquan Gu

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

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

Original languageEnglish (US)
Title of host publication33rd International Conference on Machine Learning, ICML 2016
EditorsKilian Q. Weinberger, Maria Florina Balcan
PublisherInternational Machine Learning Society (IMLS)
Pages3405-3431
Number of pages27
ISBN (Electronic)9781510829008
StatePublished - Jan 1 2016
Event33rd International Conference on Machine Learning, ICML 2016 - New York City, United States
Duration: Jun 19 2016Jun 24 2016

Publication series

Name33rd International Conference on Machine Learning, ICML 2016
Volume5

Other

Other33rd International Conference on Machine Learning, ICML 2016
CountryUnited States
CityNew York City
Period6/19/166/24/16

ASJC Scopus subject areas

  • Artificial Intelligence
  • Software
  • Computer Networks and Communications

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