Sparse nonlinear regression: Parameter estimation under nonconvexity

Zhuoran Yang, Zhaoran Wang, Han Liu, Yonina C. Eldar, Tong Zhang

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

3 Scopus citations

Abstract

We study parameter estimation for sparse nonlinear regression. More specifically, we assume the data are given by y = f(xTβ) + e, where / is nonlinear. To recover β, we propose an ℓ1- regularized least-squares estimator. Unlike classical linear regression, the corresponding optimization problem is nonconvex because of the nonlin- earityof ℓ. In spite of the nonconvexity, we prove that under mild conditions, every stationary point of the objective enjoys an optimal statistical rate of convergence. Detailed numerical results are provided to back up our theory.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)
Pages3668-3677
Number of pages10
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

All Science Journal Classification (ASJC) codes

  • Artificial Intelligence
  • Software
  • Computer Networks and Communications

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  • Cite this

    Yang, Z., Wang, Z., Liu, H., Eldar, Y. C., & Zhang, T. (2016). Sparse nonlinear regression: Parameter estimation under nonconvexity. In K. Q. Weinberger, & M. F. Balcan (Eds.), 33rd International Conference on Machine Learning, ICML 2016 (pp. 3668-3677). (33rd International Conference on Machine Learning, ICML 2016; Vol. 5). International Machine Learning Society (IMLS).