Kernel based approaches to local nonlinear non-parametric variable selection

Er-wei Bai; Kang Li; Wenxiao Zhao; Weiyu Xu

doi:10.1016/j.automatica.2013.10.010

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Kernel based approaches to local nonlinear non-parametric variable selection

Journal article

Peer reviewed

Kernel based approaches to local nonlinear non-parametric variable selection

Er-wei Bai, Kang Li, Wenxiao Zhao and Weiyu Xu

Automatica (Oxford), Vol.50(1), pp.100-113

01/2014

DOI: 10.1016/j.automatica.2013.10.010

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Abstract

In this paper, we consider the variable selection problem for a nonlinear non-parametric system. Two approaches are proposed, one top-down approach and one bottom-up approach. The top-down algorithm selects a variable by detecting if the corresponding partial derivative is zero or not at the point of interest. The algorithm is shown to have not only the parameter but also the set convergence. This is critical because the variable selection problem is binary, a variable is either selected or not selected. The bottom-up approach is based on the forward/backward stepwise selection which is designed to work if the data length is limited. Both approaches determine the most important variables locally and allow the unknown non-parametric nonlinear system to have different local dimensions at different points of interest. Further, two potential applications along with numerical simulations are provided to illustrate the usefulness of the proposed algorithms.

Forward and backward stepwise selections

Kernel

Nonlinear identification

Adaptive LASSO

Variable selection

Details

Title: Subtitle: Kernel based approaches to local nonlinear non-parametric variable selection
Creators: Er-wei Bai - Department of Electrical and Computer Engineering, University of Iowa, Iowa City, IA 52242, United States
Kang Li - School of Electronics, Electrical Engineering and Computer Science, Queen’s University, Belfast, UK
Wenxiao Zhao - Academy of Mathematics and Systems Science, China
Weiyu Xu - Department of Electrical and Computer Engineering, University of Iowa, Iowa City, IA 52242, United States
Resource Type: Journal article
Publication Details: Automatica (Oxford), Vol.50(1), pp.100-113
Publisher: Elsevier Ltd
DOI: 10.1016/j.automatica.2013.10.010
ISSN: 0005-1098
eISSN: 1873-2836
Grant note: CNS-1329657 / NSF DE-FG52-09NA29364 / DoE 61104052; 61273193; 61134013 / NNSF of China
Language: English
Date published: 01/2014
Academic Unit: Electrical and Computer Engineering
Record Identifier: 9984083994202771

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