Variable selection of high-dimensional non-parametric nonlinear systems by derivative averaging to avoid the curse of dimensionality

• Autores: Er-wei Bai-, Changping Chen, Wen-Xiao Zhao
• Localización: Automatica: A journal of IFAC the International Federation of Automatic Control, ISSN 0005-1098, Nº. 101, 2019, págs. 138-149
• Idioma: inglés
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• Resumen

  • In identification, variable selection for a nonlinear non-parametric and high-dimensional system is the first and often one of the most difficult problems. The issue is the curse of dimensionality. This paper presents a numerically efficient algorithm of variable selection for high-dimensional nonlinear non-parametric systems. It is based on averaging derivatives and relies on one dimensional estimates of the density function and its derivative. Thus, it avoids the curse of dimensionality usually encountered for high-dimensional systems. Theoretical analysis is provided and the conditions are derived for a variable to contribute or not to contribute for a large class of nonlinear systems. Further, convergence results are established.