混沌时间序列的高斯过程混合模型预测
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摘要
高斯过程混合(Gaussian Processes Mixture,GPM)模型现有的学习算法如马尔科夫链蒙特卡洛法、变分法或留一法等,计算复杂度偏高,提出一种隐变量后验硬划分迭代学习算法,简化模型的学习过程,基于该算法将GPM模型用于混沌时间序列预测,并讨论嵌入维、时间延迟、学习样本和测试样本数目等参数对预测性能的影响。实验结果表明,GPM模型预测精度高于支持向量机(Support Vector Machine,SVM)、高斯过程(Gaussian Process,GP)和径向基(Radical Basis Function,RBF)网络,学习速度介于RBF网络、GP和SVM之间。
Aiming at the problem that the existing learning algorithms of Gaussian processes mixture(GPM) model, such as Markov Chain Monte Carlo(MCMC), variation or leave one out, have high computational complexity, a hidden variables posterior hard-cut iterative training algorithm is proposed,which simplifies the training process of the model. The GPM model based on the proposed algorithm is applied to chaotic time series prediction. The effects of embedding dimension, time delay, learning sample number, and testing sample numbers on predictive ability are discussed. It is demonstrated by the experimental results that the prediction of the GPM model is more accurate than SVM, GP and RBF network, and the training speed of GPM model falls in between RBF network, GP model, and SVM.
Aiming at the problem that the existing learning algorithms of Gaussian processes mixture(GPM) model, such as Markov Chain Monte Carlo(MCMC), variation or leave one out, have high computational complexity, a hidden variables posterior hard-cut iterative training algorithm is proposed,which simplifies the training process of the model. The GPM model based on the proposed algorithm is applied to chaotic time series prediction. The effects of embedding dimension, time delay, learning sample number, and testing sample numbers on predictive ability are discussed. It is demonstrated by the experimental results that the prediction of the GPM model is more accurate than SVM, GP and RBF network, and the training speed of GPM model falls in between RBF network, GP model, and SVM.
引文
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[18]Zhou Y T,Zhang T Y,Sun J C.Multi-scale Gaussian processes:a novel model for chaotic time series prediction[J].Chinese Physics Letters(S0256-307X),2007,24(1):42-45.
[19]Zhou Y T,Zhang T Y,Li X H.Prediction of chaotic time series based on multi-scale Gaussian processes[J].Lecture Notes in Computer Science(S0302-9743),2006,4224(9):183-190.
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[2]崔万照,朱长纯,保文星,等.混沌时间序列的支持向量机预测[J].物理学报,2004,53(10):3303-3310.Cui Wanzhao,Zhu Changchun,Bao Wenxing,et al.Prediction of the chaotic time series using support vector machines[J].Acta Physica Sinica,2004,53(10):3303-3310.
[3]Sun J C,Zhou Y T,Luo J G.Prediction of chaotic systems with multidimensional recurrent least squares support vector machines[J].Chinese Physics(S1674-1056),2006,15(6):1208-1215.
[4]Sun J,Zheng C,Zhou Y,et al.Nonlinear noise reduction of chaotic time series based on multidimensional recurrent LS-SVM[J].Neurocomputing(S0925-2312),2008,71(16):3675-3679.
[5]唐舟进,任峰,彭涛,等.基于迭代误差补偿的混沌时间序列最小二乘支持向量机预测算法[J].物理学报,2014,63(5):050505.Tang Zhoujin,Ren Feng,Peng Tao,et al.A least square support vector machine prediction algorithm for chaotic time series based on the iterative error correction[J].Acta Physica Sinica,2014,63(5):050505.
[6]田中大,高宪文,石彤.用于混沌时间序列预测的组合核函数最小二乘支持向量机[J].物理学报,2014,63(16):160508.Tian Zhongda,Gao Xianwen,Shi Tong.Combination kernel function least squares supp ort vector machine for chaotic time series prediction[J].Acta Physica Sinica,2014,63(16):160508.
[7]叶美盈,汪晓东,张浩然.基于在线最小二乘支持向量机的混沌时间序列预测[J].物理学报,2005,54(6):2568-2573.Ye Meiying,Wang Xiaodong,Zhang Haoran.Chaotic time series forecasting using online least squares support vector machine regression[J].Acta Physica Sinica,2005,54(6):2568-2573.
[8]Arash M,Majid A.Developing a local least-squares support vector machines-based neuro-fuzzy model for nonlinear and chaotic time series prediction[J].IEEETransactions on Neural Networks and Learning Systems(S2162-237X),2013,24(2):207-218.
[9]Shi Z W,Han M.Support vector echo-state machine for chaotic time-series prediction[J].IEEE Transactions on Neural Networks(S1045-9227),2007,18(2):359-372.
[10]Li S,Luo Y,Zhang M R.Prediction method for chaotic time series of optimized BP neural network based on genetic algorithm[J].Computer Engineering and Applications(S1002-8331),2011,47(29):52-55.
[11]宋彤,李菡.基于小波回声状态网络的混沌时间序列预测[J].物理学报,2012,61(8):080506.Song Tong,Li Han.Chaotic time series prediction based on wavelet echo state network[J].Acta Physica Sinica,2012,61(8):080506.
[12]Zhang J,Chung S H,Lo W L.Chaotic Time Series Prediction Using a Neuro-Fuzzy System with Time-Delay Coordinates[J].IEEE Transactions on Knowledge and Data Engineering(S1041-4347),2008,20(7):956-964.
[13]Yin L S,He Y G,Dong X P,et al.Adaptive chaotic prediction algorithm of RBF neural network filtering model based on phase space reconstruction[J].Journal of Computers(S1796-203X),2013,8(6):1449-1455.
[14]李松,刘力军,刘颖鹏.改进PSO优化BP神经网络的混沌时间序列预测[J].计算机工程与应用,2013,49(6):245-248.Li Song,Liu Lijun,Liu Yingpeng.Prediction for chaotic time series of optimized BP neural network based on modified PSO[J].Computer Engineering and Applications,2013,49(6):245-248.
[15]Li S,Zhao H,Ru Z,et al.Probabilistic back analysis based on Bayesian and multi-output support vector machine for a high cut rock slope[J].Engineering Geology(S0013-7952),2016,203(3):178-190.
[16]Rasmussen C E,Nickisch H.Gaussian Processes for Machine Learning(GPML)Toolbox[J].Journal of Machine Learning Research(S1532-4435),2010,11(6):3011-3015.
[17]李军,张友鹏.基于高斯过程的混沌时间序列单步与多步预测[J].物理学报,2011,60(7):070513.Li Jun,Zhang Youpeng.Single-step and multiple-step prediction of chaotic time series using Gaussian process model[J].Acta Physica Sinica,2011,60(7):070513.
[18]Zhou Y T,Zhang T Y,Sun J C.Multi-scale Gaussian processes:a novel model for chaotic time series prediction[J].Chinese Physics Letters(S0256-307X),2007,24(1):42-45.
[19]Zhou Y T,Zhang T Y,Li X H.Prediction of chaotic time series based on multi-scale Gaussian processes[J].Lecture Notes in Computer Science(S0302-9743),2006,4224(9):183-190.
[20]Chen Z,Ma J,Zhou Y.A Precise Hard-Cut EMAlgorithm for Mixtures of Gaussian Processes[C].International Conference on Intelligent Computing.Cham:Springer,2014:68-75.
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