Gaussian processes: prediction at a noisy input and application to iterative multiple-step ahead forecasting of time-series

Girard, A. and Murray-Smith, R. (2005) Gaussian processes: prediction at a noisy input and application to iterative multiple-step ahead forecasting of time-series. Lecture Notes in Computer Science, 3355, pp. 158-184. (doi: 10.1007/b105497)

Abstract

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 (<i>Gaussian</i> <i>approximation</i>). We show how, depending on the form of the covariance function of the process, we can evaluate these moments exactly or approximately (within a Taylor approximation of the covariance function). We apply our results to the iterative multiple-step ahead prediction of non-linear dynamic systems with propagation of the uncertainty as we predict ahead in time. Finally, using numerical examples, we compare the <i>Gaussian</i> <i>approximation</i> to the numerical approximation of the true predictive distribution by simple Monte-Carlo.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Murray-Smith, Professor Roderick
• Authors: Girard, A., and Murray-Smith, R.
• Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
• College/School: College of Science and Engineering > School of Computing Science
• Journal Name: Lecture Notes in Computer Science
• Publisher: Springer
• ISSN: 1611-3349
• Copyright Holders: Copyright © 2005 Springer
• First Published: First published in Lecture Notes in Computer Science 3355:158-184
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher.