Propagation of Uncertainty in Bayesian Kernel Models - Application to Multiple-Step Ahead Forecasting

Joaquin Quinonero; Agathe Girard; Jan Larsen; Carl Edward Rasmussen

doi:10.1109/ICASSP.2003.1202463

Propagation of Uncertainty in Bayesian Kernel Models - Application to Multiple-Step Ahead Forecasting

Joaquin Quinonero, Agathe Girard, Jan Larsen, Carl Edward Rasmussen

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

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Abstract

The object of Bayesian modelling is predictive distribution, which, in a forecasting scenario, enables evaluation of forecasted values and their uncertainties. We focus on reliably estimating the predictive mean and variance of forecasted values using Bayesian kernel based models such as the Gaussian process and the relevance vector machine. We derive novel analytic expressions for the predictive mean and variance for Gaussian kernel shapes under the assumption of a Gaussian input distribution in the static case, and of a recursive Gaussian predictive density in iterative forecasting. The capability of the method is demonstrated for forecasting of time-series and compared to approximate methods.

Original language	English
Title of host publication	International Conference on Acoustics, Speech and Signal Processing
Publisher	IEEE
Publication date	2003
Pages	701-704
ISBN (Print)	0-7803-7663-3
DOIs	https://doi.org/10.1109/ICASSP.2003.1202463
Publication status	Published - 2003
Event	2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03). - Duration: 1 Jan 2004 → …

Conference

Conference	2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03).
Period	01/01/2004 → …

Bibliographical note

Copyright: 2004 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE

Keywords

Relevance Vector Machine
Gaussian Process
Time-Series Prediction
Uncertain Inputs

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10.1109/ICASSP.2003.1202463

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Cite this

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title = "Propagation of Uncertainty in Bayesian Kernel Models - Application to Multiple-Step Ahead Forecasting",

abstract = "The object of Bayesian modelling is predictive distribution, which, in a forecasting scenario, enables evaluation of forecasted values and their uncertainties. We focus on reliably estimating the predictive mean and variance of forecasted values using Bayesian kernel based models such as the Gaussian process and the relevance vector machine. We derive novel analytic expressions for the predictive mean and variance for Gaussian kernel shapes under the assumption of a Gaussian input distribution in the static case, and of a recursive Gaussian predictive density in iterative forecasting. The capability of the method is demonstrated for forecasting of time-series and compared to approximate methods.",

keywords = "Relevance Vector Machine, Gaussian Process, Time-Series Prediction, Uncertain Inputs",

author = "Joaquin Quinonero and Agathe Girard and Jan Larsen and Rasmussen, {Carl Edward}",

note = "Copyright: 2004 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE; 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03). ; Conference date: 01-01-2004",

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doi = "10.1109/ICASSP.2003.1202463",

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Quinonero, J, Girard, A, Larsen, J & Rasmussen, CE 2003, Propagation of Uncertainty in Bayesian Kernel Models - Application to Multiple-Step Ahead Forecasting. in International Conference on Acoustics, Speech and Signal Processing. IEEE, pp. 701-704, 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03)., 01/01/2004. https://doi.org/10.1109/ICASSP.2003.1202463

Propagation of Uncertainty in Bayesian Kernel Models - Application to Multiple-Step Ahead Forecasting. / Quinonero, Joaquin; Girard, Agathe; Larsen, Jan; Rasmussen, Carl Edward.

International Conference on Acoustics, Speech and Signal Processing. IEEE, 2003. p. 701-704.

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

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N1 - Copyright: 2004 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE

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