Multiple-step ahead prediction for non linear dynamic systems – A Gaussian Process treatment with propagation of the uncertainty
نویسندگان
چکیده
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 yt = f(yt 1; : : : ; yt L), the prediction of y at time t+ k is based on the estimates ŷt+k 1; : : : ; ŷt+k L of the previous outputs. In this paper, we show how, using an analytical Gaussian approximation, we can formally incorporate the uncertainty about future regressor values, thus updating the uncertainty on the current prediction.
منابع مشابه
Gaussian Process Priors with Uncertain Inputs - Application to Multiple-Step Ahead Time Series Forecasting
We consider the problem of multi-step ahead prediction in time series analysis using the non-parametric Gaussian process model. -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 , the prediction of at time is based on the point estimates of the previous outputs. In this paper, w...
متن کاملGirard, A. and Murray-Smith, R. (2005) Gaussian processes: prediction at a noisy input and application to iterative multiple-step ahead forecasting
With the Gaussian Process model, the predictive distribution of the output corresponding to a new given input is Gaussian. But if this input is uncertain or noisy, the predictive distribution becomes non-Gaussian. We present an analytical approach that consists of computing only the mean and variance of this new distribution (Gaussian approximation). We show how, depending on the form of the co...
متن کاملGaussian Processes: Prediction at a Noisy Input and Application to Iterative Multiple-Step Ahead Forecasting of Time-Series
With the Gaussian Process model, the predictive distribution of the output corresponding to a new given input is Gaussian. But if this input is uncertain or noisy, the predictive distribution becomes non-Gaussian. We present an analytical approach that consists of computing only the mean and variance of this new distribution (Gaussian approximation). We show how, depending on the form of the co...
متن کاملGaussian Process priors with Uncertain Inputs : Multiple - Step - Ahead Prediction ∗
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 nonlinear dynamic system can be performed by doing repeated one-step ahead predictions. For a state-space model of the form yt = f(yt−1, . . . , yt−L), the prediction of y at time t + k is based on the estimates ŷt+k−1, . . ....
متن کاملMultiple-step Time Series Forecasting with Sparse Gaussian Processes
Forecasting of non-linear time series is a relevant problem in control. Furthermore, an estimate of the uncertainty of the prediction is useful for constructing robust controllers. Multiple-step ahead forecasting has recently been addressed using Gaussian processes, but direct implementations are restricted to small data sets. In this paper we consider multiple-step forecasting for sparse Gauss...
متن کامل