Kernel based approaches to local nonlinear non-parametric variable selection

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

Research output: Contribution to journalArticle

22 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)100-113
Number of pages14
JournalAutomatica
Volume50
Issue number1
Early online date31 Oct 2013
DOIs
Publication statusPublished - Jan 2014

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