  Gaussian processes have been successful in both supervised and unsupervised
machine learning tasks, but their computational complexity has constrained
practical applications. We introduce a new approximation for large-scale
Gaussian processes, the Gaussian Process Random Field (GPRF), in which local
GPs are coupled via pairwise potentials. The GPRF likelihood is a simple,
tractable, and parallelizeable approximation to the full GP marginal
likelihood, enabling latent variable modeling and hyperparameter selection on
large datasets. We demonstrate its effectiveness on synthetic spatial data as
well as a real-world application to seismic event location.
