Multiple-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 Gaussian processes to alleviate this problem. We derive analytical expressions for multiple-step ahead prediction using the FITC approximation. On several benchmarks we compare the FITC approximation with a Gaussian process trained on a large portion of randomly drawn training samples. As a consequence of being able to handle larger data sets, we show a mean prediction that is closer to the true system response with less uncertainty.