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

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 ca...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2019-07, Vol.64 (7), p.2653-2664
Main Authors: Cheng, Changming, Bai, Er-wei, Peng, Zhike
Format: Article
Language:English
Subjects:
Algorithms
Contours
Data models
Dimensionality reduction
Estimation
Independent variables
Input variables
Kernel
Mathematical models
Mutual information
nonlinear identification
Nonlinear systems
Nonparametric statistics
nonparametric systems
Regression analysis
Shape
variable selection
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Summary: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.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2018.2867252