Consistent Variable Selection for a Nonparametric Nonlinear System by Inverse and Contour Regressions

Changming Cheng; Er-wei Bai; Zhike Peng

doi:10.1109/TAC.2018.2867252

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Consistent Variable Selection for a Nonparametric Nonlinear System by Inverse and Contour Regressions

Journal article

Open access

Peer reviewed

Consistent Variable Selection for a Nonparametric Nonlinear System by Inverse and Contour Regressions

Changming Cheng, Er-wei Bai and Zhike Peng

IEEE transactions on automatic control, Vol.64(7), pp.2653-2664

07/2019

DOI: 10.1109/TAC.2018.2867252

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Abstract

A parsimonious model is always preferred in engineering applications not only because it has a better prediction ability but also because it suffers less from the curse of dimensionality in data-based modeling. One way to achieve a parsimonious model is to identify contributing variables from the candidate variables and then to eliminate noncontributing or redundant variables. However, identifying which variables contribute and which variables do not contribute is not an easy task for a nonparametric nonlinear system. This paper considers variable-selection problems for a nonlinear nonparametric system. Two approaches, inverse and contour variable-selection algorithms, are proposed along with their theoretical analysis and numerical algorithms. Neither approach suffers from the curse of dimensionality, which is usually a problem for traditional variable-selection methods for a nonparametric nonlinear system. Furthermore, no elliptic symmetry nor independent input variables are assumed, so both algorithms enjoy wide applications. Numerical algorithms for both approaches are fairly straightforward and simple.

Data models

Dimensionality reduction

Estimation

Input variables

Kernel

Mutual information

nonlinear identification

Nonlinear systems

nonparametric systems

variable selection

Details

Title: Subtitle: Consistent Variable Selection for a Nonparametric Nonlinear System by Inverse and Contour Regressions
Creators: Changming Cheng - Shanghai Jiao Tong University
Er-wei Bai - University of Iowa
Zhike Peng - Shanghai Jiao Tong University
Resource Type: Journal article
Publication Details: IEEE transactions on automatic control, Vol.64(7), pp.2653-2664
Publisher: IEEE
DOI: 10.1109/TAC.2018.2867252
ISSN: 0018-9286
eISSN: 1558-2523
Grant note: CNS-1239509 / National Science Foundation (10.13039/100000001) 11632011; 11702171; 51121063 / Chinese Natural Science Foundation 15005188 / China Postdoctoral Science Foundation (10.13039/501100002858)
Language: English
Date published: 07/2019
Academic Unit: Electrical and Computer Engineering
Record Identifier: 9984197349202771

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