Sparse Spatio-temporal Gaussian Processes with General Likelihoods

  • Jouni Hartikainen
  • Jaakko Riihimäki
  • Simo Särkkä
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6791)

Abstract

In this paper, we consider learning of spatio-temporal processes by formulating a Gaussian process model as a solution to an evolution type stochastic partial differential equation. Our approach is based on converting the stochastic infinite-dimensional differential equation into a finite dimensional linear time invariant (LTI) stochastic differential equation (SDE) by discretizing the process spatially. The LTI SDE is time-discretized analytically, resulting in a state space model with linear-Gaussian dynamics. We use expectation propagation to perform approximate inference on non-Gaussian data, and show how to incorporate sparse approximations to further reduce the computational complexity. We briefly illustrate the proposed methodology with a simulation study and with a real world modelling problem.

Keywords

Gaussian processes spatio-temporal data expectation propagation sparse approximations 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Jouni Hartikainen
    • 1
  • Jaakko Riihimäki
    • 1
  • Simo Särkkä
    • 1
  1. 1.Dept. of Biomedical Engineering and Computational ScienceAalto UniversityFinland

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