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Multimodality Prediction of Chaotic Time Series with Sparse Hard-Cut EM Learning of the Gaussian Process Mixture Model |
| Ya-Tong Zhou1**, Yu Fan1,2, Zi-Yi Chen3, Jian-Cheng Sun4 |
1School of Electronics and Information Engineering, Hebei University of Technology, Tianjin 300401
2Weinan Meteorological Bureau, Weinan 714000
3Department of Statistical Science, Cornell University, Ithaca 14853, USA
4School of Software and Communication Engineering, Jiangxi University of Finance and Economics, Nanchang 330013
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| Cite this article: |
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Ya-Tong Zhou, Yu Fan, Zi-Yi Chen et al 2017 Chin. Phys. Lett. 34 050502 |
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Abstract The contribution of this work is twofold: (1) a multimodality prediction method of chaotic time series with the Gaussian process mixture (GPM) model is proposed, which employs a divide and conquer strategy. It automatically divides the chaotic time series into multiple modalities with different extrinsic patterns and intrinsic characteristics, and thus can more precisely fit the chaotic time series. (2) An effective sparse hard-cut expectation maximization (SHC-EM) learning algorithm for the GPM model is proposed to improve the prediction performance. SHC-EM replaces a large learning sample set with fewer pseudo inputs, accelerating model learning based on these pseudo inputs. Experiments on Lorenz and Chua time series demonstrate that the proposed method yields not only accurate multimodality prediction, but also the prediction confidence interval. SHC-EM outperforms the traditional variational learning in terms of both prediction accuracy and speed. In addition, SHC-EM is more robust and insusceptible to noise than variational learning.
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Received: 18 November 2016
Published: 29 April 2017
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| PACS: |
05.45.-a
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(Nonlinear dynamics and chaos)
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05.45.Tp
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(Time series analysis)
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07.05.Mh
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(Neural networks, fuzzy logic, artificial intelligence)
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| Fund: Supported by the National Natural Science Foundation of China under Grant No 60972106, the China Postdoctoral Science Foundation under Grant No 2014M561053, the Humanity and Social Science Foundation of Ministry of Education of China under Grant No 15YJA630108, and the Hebei Province Natural Science Foundation under Grant No E2016202341. |
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