Multi-scale Gaussian process experts for dynamic evolution prediction of complex systems

Predictive analytics has become an important topic in expert and intelligent systems, with broad applications across various engineering and business domains, such as the prediction of exchange rate in finance, weather and demand for energy using mixture of experts. However, selection of the number of experts and assignment of the input to individual experts remain elusive, especially for highly nonlinear and nonstationary systems. This paper presents a novel mixture of experts, namely, nonparametric multi-scale Gaussian process (MGP) experts to predict the dynamic evolution of such complex systems. Concretely, intrinsic time-scale decomposition is first used to iteratively decompose the time series generated from such complex systems into a series of proper rotation components and a baseline trend component. Those components delineate the true time-frequency-energy patterns of the complex systems at different granularity. A Gaussian process (GP) expert is then applied on each component to predict the system evolution at each scale. MGP circumvent the tedious selection and assignment problems via the nonparametric ITD. Summation of those individual forecasts represents the overall evolution of the original time series. Case studies using synthetic and real-world data elucidated that the proposed MGP model significantly outperforms conventional autoregressive models, composite GP model, and support vector regression in terms of prediction accuracy, and it is particularly effective for multi-step forecasting.