无核相关向量机在时间序列预测中的应用

Relevance Vector Machine with Reservoir for Time Series Prediction

针对采用核函数方法预测多元混沌时间序列时存在的高计算复杂度问题,该文在相关向量机的基础上,提出了一种不受核函数约束的无核相关向量机学习模型.利用储备池代替核函数,构建高维特征空间,将原始时间序列预测问题转化成与储备池参数相关的回归问题.在稀疏贝叶斯学习的框架下,给模型参数施加一个条件概率分布的约束,以得到稀疏的解空间,进而降低模型的复杂度,提高计算速度和预测精度.基于Lorenz混沌时间序列及太阳黑子-黄河径流量序列的仿真结果验证了所提模型的有效性.

Considering that there may exist the problem of high computational complexity when kernel methods are used to predict the multivariate time series. In this paper, on the basis of rele- vance vector machine, we propose a new model without the constraint of kernel functions, named Relevance Vector Echo State Machine （RVESM）. It uses a high-dimension dynamic reservoir to replace the kernel function, and then transforms the nonlinear time series prediction problem into a linear regression problem. The parameters of the proposed model are estimated by sparse Bayesian learning, which imposes an individual hyperparameter on each parameter by defining a probability distrbution over them. By this way, the solution is sparse and the computational complexity is reduced. Meanwhile, RVESM has fast computational speed and high prediction accuracy. Simulation results on Lorenz chaotic time series and Sunspots-Runoff in Yellow River datasets substantiate the effectiveness of the proposed model.