Sufficient variable selection of high dimensional nonparametric nonlinear systems based on Fourier spectrum of density-weighted derivative

doi:10.1007/s10483-024-3183-6

Applied Mathematics and Mechanics (English Edition) ›› 2024, Vol. 45 ›› Issue (11): 2011-2022.doi: https://doi.org/10.1007/s10483-024-3183-6

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Sufficient variable selection of high dimensional nonparametric nonlinear systems based on Fourier spectrum of density-weighted derivative

Bing SUN¹^,², Changming CHENG¹^,*(), Qiaoyan CAI², Zhike PENG¹^,³

¹ State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, Shanghai 200240, China
² China Academy of Launch Vehicle Technology, Beijing 100076, China
³ School of Mechanical Engineering, Ningxia University, Yinchuan 750021, China

Received:2024-08-08 Online:2024-11-03 Published:2024-10-30
Contact: Changming CHENG E-mail:ccming@sjtu.edu.cn
Supported by:
the National Key Research and Development Program of China(2021YFB3400700);the National Natural Science Foundation of China(12422201);the National Natural Science Foundation of China(12072188);the National Natural Science Foundation of China(12121002);the National Natural Science Foundation of China(12372017);Project supported by the National Key Research and Development Program of China (No. 2021YFB3400700) and the National Natural Science Foundation of China (Nos. 12422201, 12072188, 12121002, and 12372017)

Abstract

Abstract:

The variable selection of high dimensional nonparametric nonlinear systems aims to select the contributing variables or to eliminate the redundant variables. For a high dimensional nonparametric nonlinear system, however, identifying whether a variable contributes or not is not easy. Therefore, based on the Fourier spectrum of density-weighted derivative, one novel variable selection approach is developed, which does not suffer from the dimensionality curse and improves the identification accuracy. Furthermore, a necessary and sufficient condition for testing a variable whether it contributes or not is provided. The proposed approach does not require strong assumptions on the distribution, such as elliptical distribution. The simulation study verifies the effectiveness of the novel variable selection algorithm.

Key words: nonlinear system identification, variable selection, Fourier spectrum, nonparametric nonlinear system

2010 MSC Number:

45Q05

Bing SUN, Changming CHENG, Qiaoyan CAI, Zhike PENG. Sufficient variable selection of high dimensional nonparametric nonlinear systems based on Fourier spectrum of density-weighted derivative. Applied Mathematics and Mechanics (English Edition), 2024, 45(11): 2011-2022.

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Sufficient variable selection of high dimensional nonparametric nonlinear systems based on Fourier spectrum of density-weighted derivative

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