TY - GEN
T1 - Sparse nonlinear regression
T2 - 33rd International Conference on Machine Learning, ICML 2016
AU - Yang, Zhuoran
AU - Wang, Zhaoran
AU - Liu, Han
AU - Eldar, Yonina C.
AU - Zhang, Tong
N1 - Publisher Copyright: © 2016 by the author(s).
PY - 2016
Y1 - 2016
N2 - 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
AB - 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
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M3 - Conference contribution
T3 - 33rd International Conference on Machine Learning, ICML 2016
SP - 3668
EP - 3677
BT - 33rd International Conference on Machine Learning, ICML 2016
A2 - Weinberger, Kilian Q.
A2 - Balcan, Maria Florina
PB - International Machine Learning Society (IMLS)
Y2 - 19 June 2016 through 24 June 2016
ER -