  Gaussian processes are typically used for smoothing and interpolation on
small datasets. We introduce a new Bayesian nonparametric framework -- GPatt --
enabling automatic pattern extrapolation with Gaussian processes on large
multidimensional datasets. GPatt unifies and extends highly expressive kernels
and fast exact inference techniques. Without human intervention -- no hand
crafting of kernel features, and no sophisticated initialisation procedures --
we show that GPatt can solve large scale pattern extrapolation, inpainting, and
kernel discovery problems, including a problem with 383400 training points. We
find that GPatt significantly outperforms popular alternative scalable Gaussian
process methods in speed and accuracy. Moreover, we discover profound
differences between each of these methods, suggesting expressive kernels,
nonparametric representations, and exact inference are useful for modelling
large scale multidimensional patterns.
