Sparse Nonlinear Regression: Parameter Estimation under Nonconvexity

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

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 proceeding › Conference contribution

Abstract

We study parameter estimation for sparse nonlinear regression. More specifically, we assume the data are given by y = f(xτβ*) + ε, where f 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 nonlinearity of f. 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.

Original language	English
Title of host publication	Proceedings of the 33rd International Conference on Machine learning (ICML 2016)
Editors	Maria Florina Balcan, Kilian Q. Weinberger
Publisher	Association for Computing Machinery (ACM)
Pages	2472–2481
Number of pages	10
Volume	48
ISBN (Electronic)	9781510829008
State	Published - Jun 2016
Externally published	Yes
Event	33rd International Conference on Machine learning - New York, United States Duration: 19 Jun 2016 → 24 Jun 2016 Conference number: 33rd

Publication series

Name	33rd International Conference on Machine Learning, ICML 2016
Volume	5

Conference

Conference	33rd International Conference on Machine learning
Abbreviated title	ICML 2016
Country/Territory	United States
City	New York
Period	19/06/16 → 24/06/16

All Science Journal Classification (ASJC) codes

Software
Artificial Intelligence
Computer Networks and Communications

Access to Document

http://proceedings.mlr.press/v48/yangc16.htmlLicense: Unspecified

Cite this

Yang, Z., Wang, Z., Liu, H., Eldar, Y. C., & Zhang, T. (2016). Sparse Nonlinear Regression: Parameter Estimation under Nonconvexity. In M. F. Balcan, & K. Q. Weinberger (Eds.), Proceedings of the 33rd International Conference on Machine learning (ICML 2016) (Vol. 48, pp. 2472–2481). (33rd International Conference on Machine Learning, ICML 2016; Vol. 5). Association for Computing Machinery (ACM). http://proceedings.mlr.press/v48/yangc16.html

Yang, Zhuoran ; Wang, Zhaoran ; Liu, Han et al. / Sparse Nonlinear Regression : Parameter Estimation under Nonconvexity. Proceedings of the 33rd International Conference on Machine learning (ICML 2016). editor / Maria Florina Balcan ; Kilian Q. Weinberger. Vol. 48 Association for Computing Machinery (ACM), 2016. pp. 2472–2481 (33rd International Conference on Machine Learning, ICML 2016).

@inproceedings{dee4c073c2ea44998a723799d5904ba4,

title = "Sparse Nonlinear Regression: Parameter Estimation under Nonconvexity",

abstract = "We study parameter estimation for sparse nonlinear regression. More specifically, we assume the data are given by y = f(xτβ*) + ε, where f 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 nonlinearity of f. 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.",

author = "Zhuoran Yang and Zhaoran Wang and Han Liu and Eldar, \{Yonina C.\} and Tong Zhang",

note = "Publisher Copyright: {\textcopyright} 2016 by the author(s).; 33rd International Conference on Machine learning ; Conference date: 19-06-2016 Through 24-06-2016",

year = "2016",

month = jun,

language = "الإنجليزيّة",

volume = "48",

series = "33rd International Conference on Machine Learning, ICML 2016",

publisher = "Association for Computing Machinery (ACM)",

pages = "2472–2481",

editor = "Balcan, \{Maria Florina\} and Weinberger, \{Kilian Q.\}",

booktitle = "Proceedings of the 33rd International Conference on Machine learning (ICML 2016)",

address = "الولايات المتّحدة",

}

Yang, Z, Wang, Z, Liu, H, Eldar, YC & Zhang, T 2016, Sparse Nonlinear Regression: Parameter Estimation under Nonconvexity. in MF Balcan & KQ Weinberger (eds), Proceedings of the 33rd International Conference on Machine learning (ICML 2016). vol. 48, 33rd International Conference on Machine Learning, ICML 2016, vol. 5, Association for Computing Machinery (ACM), pp. 2472–2481, 33rd International Conference on Machine learning, New York, New York, United States, 19/06/16. <http://proceedings.mlr.press/v48/yangc16.html>

Sparse Nonlinear Regression: Parameter Estimation under Nonconvexity. / Yang, Zhuoran; Wang, Zhaoran; Liu, Han et al.
Proceedings of the 33rd International Conference on Machine learning (ICML 2016). ed. / Maria Florina Balcan; Kilian Q. Weinberger. Vol. 48 Association for Computing Machinery (ACM), 2016. p. 2472–2481 (33rd International Conference on Machine Learning, ICML 2016; Vol. 5).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Sparse Nonlinear Regression

T2 - 33rd International Conference on Machine learning

AU - Yang, Zhuoran

AU - Wang, Zhaoran

AU - Liu, Han

AU - Eldar, Yonina C.

AU - Zhang, Tong

N1 - Conference code: 33rd

PY - 2016/6

Y1 - 2016/6

N2 - We study parameter estimation for sparse nonlinear regression. More specifically, we assume the data are given by y = f(xτβ*) + ε, where f 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 nonlinearity of f. 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.

AB - We study parameter estimation for sparse nonlinear regression. More specifically, we assume the data are given by y = f(xτβ*) + ε, where f 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 nonlinearity of f. 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.

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M3 - منشور من مؤتمر

VL - 48

T3 - 33rd International Conference on Machine Learning, ICML 2016

SP - 2472

EP - 2481

BT - Proceedings of the 33rd International Conference on Machine learning (ICML 2016)

A2 - Balcan, Maria Florina

A2 - Weinberger, Kilian Q.

PB - Association for Computing Machinery (ACM)

Y2 - 19 June 2016 through 24 June 2016

ER -

Sparse Nonlinear Regression: Parameter Estimation under Nonconvexity

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