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Linear Operators and Stochastic Partial Differential Equations in Gaussian Process Regression

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Book cover Artificial Neural Networks and Machine Learning – ICANN 2011 (ICANN 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6792))

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Abstract

In this paper we shall discuss an extension to Gaussian process (GP) regression models, where the measurements are modeled as linear functionals of the underlying GP and the estimation objective is a general linear operator of the process. We shall show how this framework can be used for modeling physical processes involved in measurement of the GP and for encoding physical prior information into regression models in form of stochastic partial differential equations (SPDE). We shall also illustrate the practical applicability of the theory in a simulated application.

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Author information

Authors and Affiliations

  1. Department of Biomedical Engineering and Computational Science, Aalto University, Finland

    Simo Särkkä

Authors
  1. Simo Särkkä
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Editor information

Editors and Affiliations

  1. Department of Information and Computer Science, Aalto University School of Science, P.O. Box 15400, 00076, Aalto, Finland

    Timo Honkela  & Samuel Kaski  & 

  2. School of Physics, Astronomy and Informatics, Department of Informatics, Nicolaus Copernicus University, ul. Grudziadzka 5, 87-100, Torun, Poland

    Włodzisław Duch

  3. Department of Statistical Science, University College London, 1-19 Torrington Place, WC1E 7HB, London, UK

    Mark Girolami

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Särkkä, S. (2011). Linear Operators and Stochastic Partial Differential Equations in Gaussian Process Regression. In: Honkela, T., Duch, W., Girolami, M., Kaski, S. (eds) Artificial Neural Networks and Machine Learning – ICANN 2011. ICANN 2011. Lecture Notes in Computer Science, vol 6792. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21738-8_20

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  • DOI: https://doi.org/10.1007/978-3-642-21738-8_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21737-1

  • Online ISBN: 978-3-642-21738-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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