Prediction at an Uncertain Input for Gaussian Processes and Relevance Vector Machines Application to Multiple-Step Ahead Time-Series Forecasting

Abstract

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 = fx i ; y i g N i=1 where the target y i relates to the input x i through y i = f(x i ) + (1) where N (0; ) is additive i.i.d. Gaussian noise of variance.