Short-scale spatio-temporal Gaussian process

Abstract: This paper presents an efficient Gaussian process inference scheme for
modeling short-scale 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.

Bio: Jaakko Luttinen recieved his M.Sc. degree from HUT in 2009, and he is currently pursuing his Ph.D. at the ICS department.  He is interested in latent Gaussian models for spatio-temporal modeling.