Abstract This paper presents a novel method for predicting chaotic time series which is based on the support vector machines approach and it uses the mean-field theory for developing an easy and efficient learning procedure for the support vector machine. The proposed method approximates the distribution of the support vector machine parameters to a Gaussian process and uses the mean-field theory to estimate these parameters easily, and select the weights of the mixture of kernels used in the support vector machine estimation more accurately and faster than traditional quadratic programming-based algorithms. Finally, relationships between the embedding dimension and the predicting performance of this method are discussed, and the Mackey-Glass equation is applied to test this method. The stimulations show that the mean-field theory for support vector machine can predict chaotic time series accurately, and even if the embedding dimension is unknown, the predicted results are still satisfactory. This result implies that the mean-field theory for support vector machine is a good tool for studying chaotic time series.
Received: 11 November 2004
Revised: 14 December 2004
Published: 19 May 2005
Fund: 国家自然科学基金资助（60476037 和 60276037）
Cite this article:
Cui Wan-Zhao, Zhu Chang-Chun, Bao Wen-Xing, Liu Jun-Hua Chaotic time series prediction using mean-field theory for support vector machine 2005 Chin. Phys. 14 922