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Multiple-step ahead prediction for non linear dynamic systems: A Gaussian Process treatment with propagation of the uncertainty

MPG-Autoren
http://pubman.mpdl.mpg.de/cone/persons/resource/persons84156

Rasmussen,  CE
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons83845

Quiñonero-Candela,  J
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Zitation

Girard, A., Rasmussen, C., Quiñonero-Candela, J., & Murray-Smith, R. (2003). Multiple-step ahead prediction for non linear dynamic systems: A Gaussian Process treatment with propagation of the uncertainty. Advances in Neural Information Processing Systems 15, 529-536.


Zitierlink: http://hdl.handle.net/11858/00-001M-0000-0013-DB49-8
Zusammenfassung
We consider the problem of multi-step ahead prediction in time series analysis using the non-parametric Gaussian process model. k-step ahead forecasting of a discrete-time non-linear dynamic system can be performed by doing repeated one-step ahead predictions. For a state-space model of the form y_t = f(y_t-1},...,y_{t-L), the prediction of y at time t + k is based on the point estimates of the previous outputs. In this paper, we show how, using an analytical Gaussian approximation, we can formally incorporate the uncertainty about intermediate regressor values, thus updating the uncertainty on the current prediction.