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

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

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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 languageEnglish
    Title of host publicationInternational Conference on Acoustics, Speech and Signal Processing
    PublisherIEEE
    Publication date2003
    Pages701-704
    ISBN (Print)0-7803-7663-3
    DOIs
    Publication statusPublished - 2003
    Event2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03). -
    Duration: 1 Jan 2004 → …

    Conference

    Conference2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03).
    Period01/01/2004 → …

    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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