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. © 2011 Springer-Verlag.
CITATION STYLE
Hartikainen, J., Riihimäki, J., & Särkkä, S. (2011). Sparse spatio-temporal Gaussian processes with general likelihoods. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6791 LNCS, pp. 193–200). https://doi.org/10.1007/978-3-642-21735-7_24
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