Prediction at an Uncertain Input for Gaussian Processes and Relevance Vector Machines Application to Multiple-Step Ahead Time-Series Forecasting
We consider in this report non-linear models that map an input D-dimensional column vector x into a single dimensional output f(x). The non-linear mapping f(·) is implemented by means of a Gaussian process (GP) or a Relevance Vector Machine (RVM), see for example [Rasmussen, 1996] and [Tipping, 2001]. We are given a training data set D = {xi, yi}i=1 where the target yi relates to the input xi through yi = f(xi) + (1)