Predicting Nonstationary Time Series with Multi-scale Gaussian Processes Model
DOI: 10.1007/11893028_57 Conference: Neural Information Processing, 13th International Conference, ICONIP 2006, Hong Kong, China, October 3-6, 2006, Proceedings, Part I
The Gaussian processes (GP) model has been successfully applied to the prediction of nonstationary time series. Due to the model's covariance function containing an undetermined hyperparameters, to find its maximum likelihood values one usually suffers from either susceptibility to initial conditions or large computational cost. To overcome the pitfalls mentioned above, at the same time to acquire better prediction performance, a novel multi-scale Gaussian processes (MGP) model is proposed in this paper. In the MGP model, the covariance function is constructed by a scaling function with its different dilations and translations, ensuring that the optimal value of the hyperparameter is easy to determine. Although some more time is spent on the calculation of covariance function, MGP takes much less time to determine hyperparameter. Therefore, the total training time of MGP is competitive to GP. Experiments demonstrate the prediction performance of MGP is better than GP. Moreover, the experiments also show that the performance of MGP and support vector machine (SVM) is comparable. They give better performance compared to the radial basis function (RBF) networks.
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ABSTRACT: Forecasting the evolution of complex systems is noted as one of the ten grand challenges of modern science. Time series data from complex systems capture the dynamic behaviors and causalities of the underlying processes and provide a tractable means to predict and monitor system state evolution. However, the nonlinear and nonstationary dynamics of the underlying processes pose a major challenge for accurate forecasting. For most real-world systems, the vector field of state dynamics is a nonlinear function of the state variables, i.e., the relationship connecting intrinsic state variables with their autoregressive terms and exogenous variables is nonlinear. Time series emerging from such complex systems exhibit aperiodic (chaotic) patterns even under steady state. Also, since real-world systems often evolve under transient conditions, the signals obtained therefrom tend to exhibit myriad forms of nonstationarity. Nonetheless, methods reported in the literature focus mostly on forecasting linear and stationary processes. This paper presents a review of these advancements in nonlinear and nonstationary time series forecasting models and a comparison of their performances in certain real-world manufacturing and health informatics applications. Conventional approaches do not adequately capture the system evolution (from the standpoint of forecasting accuracy, computational effort, and sensitivity to quantity and quality of a priori information) in these applications.
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