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

Quiñonero-Candela, J; Girard, A; Rasmussen, CE

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

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

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Quiñonero-Candela, J., Girard, A., & Rasmussen, C.(2003). Prediction at an Uncertain Input for Gaussian Processes and Relevance Vector Machines - Application to Multiple-Step Ahead Time-Series Forecasting (IMM-2003-18). Kopenhagen, Denmark: Technical University of Denmark, DTU: Informatics and Mathematical Modelling.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-DDF6-7

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.