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

作　　者：Bing SUN Changming CHENG Qiaoyan CAI Zhike PENG 

机构地区：[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

出　　处：《Applied Mathematics and Mechanics(English Edition)》2024年第11期2011-2022,共12页应用数学和力学（英文版）

基　　金：Project supported by the National Key Research and Development Program of China(No.2021YFB3400700);the National Natural Science Foundation of China(Nos.12422201,12072188,12121002,and 12372017)。

摘　　要：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 densityweighted 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.

关 键 词：nonlinear system identification variable selection Fourier spectrum non-parametric nonlinear system 

分 类 号：N945.14[自然科学总论—系统科学]