Evolving Gaussian process models for predicting chaotic time-series

Abstract

Gaussian process (GP) models are nowadays considered among the state-of-the-art tools in modern dynamic system identification. GP models are probabilistic, non-parametric models based on the principles of Bayesian probability. As a kernel methods they do not try to approximate the modelled system by fitting the parameters of the selected basis functions, but rather by searching for relationships among the measured data. While GP models are Bayesian models they are more robust to overfitting. Moreover, their output is normal distribution, expressed in terms of mean and variance. Due to these features they are used in various fields, e.g. model-based control, time-series prediction, modelling and estimation in engineering applications, etc. But, due to the matrix inversion calculation, whose computationally demand increases with the third power of the number of input data, the amount of training data is limited to at most a few thousand cases. Therefore GP models in principle are not applicable for modelling dynamic systems whose states evolve in time, such as chaotic time-series. In this paper we demonstrate an Evolving GP (EGP) models for predicting chaotic time-series. The EGP is iterative method which adapts model with information obtained from streaming data and concurrently optimizes hyperparameter values. To assess the viability of the EGP an empirical tests were carried out together with a comparative study of various evolving fuzzy methods on a benchmark chaotic time-series MacKey-Glass. The results indicate that the EGP can successfully identify MacKey-Glass chaotic time-series and demonstrate superior performance.