Relevance vector machine with reservoir for time series prediction

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 relevance 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 distribution 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. ©, 2014, Science Press. All right reserved.