Journal article
Variable Selection and Identification of High-Dimensional Nonparametric Additive Nonlinear Systems
IEEE transactions on automatic control, Vol.62(5), pp.2254-2269
05/2017
DOI: 10.1109/TAC.2016.2605741
Abstract
This paper considers variable selection and identification of dynamic additive nonlinear systems via kernel-based nonparametric approaches, where the number of variables and additive functions may be large. Variable selection aims to find which additive functions contribute and which do not. The proposed variable selection consists of two successive steps. At the first step, one estimates each additive function by kernel-based nonparametric identification approaches without suffering from the curse of dimensionality. At the second step, a nonnegative garrote estimator is applied to identify which additive functions are nonzero by utilizing the obtained nonparametric estimates of each function. Under weak conditions, the nonparametric estimates of each additive function can achieve the same asymptotic properties as for 1D nonparametric identification based on kernel functions. It is also established that the nonnegative garrote estimator turns a consistent estimate for each additive function into a consistent variable selection with probability one as the number of samples tends to infinity. Two simulation examples are presented to verify the effectiveness of the variable selection and identification approaches proposed in the paper.
Details
- Title: Subtitle
- Variable Selection and Identification of High-Dimensional Nonparametric Additive Nonlinear Systems
- Creators
- Biqiang Mu - Chinese Academy of SciencesWei Xing Zheng - The University of SydneyEr-Wei Bai
- Resource Type
- Journal article
- Publication Details
- IEEE transactions on automatic control, Vol.62(5), pp.2254-2269
- DOI
- 10.1109/TAC.2016.2605741
- ISSN
- 0018-9286
- eISSN
- 1558-2523
- Grant note
- name: President Fund of Academy of Mathematics and Systems Science, CAS, award: 2015-hwyxqnrcmbq; name: National Key Basic Research Program of China (973 Program), award: 2014CB845301; DOI: 10.13039/501100001809, name: National Natural Science Foundation of China, award: 61603379; DOI: 10.13039/501100000923, name: Australian Research Council, award: DP120104986; DOI: 10.13039/100000001, name: National Science Foundation, award: CNS-1239509
- Language
- English
- Date published
- 05/2017
- Academic Unit
- Electrical and Computer Engineering
- Record Identifier
- 9984197110702771
Metrics
15 Record Views