# Efficient Gaussian Process Inference for Short-Scale Spatio-Temporal Modeling

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Jaakko Luttinen,
Alexander Ilin
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Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics, PMLR 22:741-750, 2012.

#### Abstract

This paper presents an efficient Gaussian process inference scheme for modeling shortscale phenomena in spatio-temporal datasets. Our model uses a sum of separable, compactly supported covariance functions, which yields a full covariance matrix represented in terms of small sparse matrices operating either on the spatial or temporal domain. The proposed inference procedure is based on Gibbs sampling, in which samples from the conditional distribution of the latent function values are obtained by applying a simple linear transformation to samples drawn from the joint distribution of the function values and the observations. We make use of the proposed model structure and the conjugate gradient method to compute the required transformation. In the experimental part, the proposed algorithm is compared to the standard approach using the sparse Cholesky decomposition and it is shown to be much faster and computationally feasible for 100-1000 times larger datasets. We demonstrate the advantages of the proposed method in the problem of reconstructing sea surface temperature, which requires processing of a real-world dataset with 10^6 observations.

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