  Recent implementations of local approximate Gaussian process models have
pushed computational boundaries for non-linear, non-parametric prediction
problems, particularly when deployed as emulators for computer experiments.
Their flavor of spatially independent computation accommodates massive
parallelization, meaning that they can handle designs two or more orders of
magnitude larger than previously. However, accomplishing that feat can still
require massive supercomputing resources. Here we aim to ease that burden. We
study how predictive variance is reduced as local designs are built up for
prediction. We then observe how the exhaustive and discrete nature of an
important search subroutine involved in building such local designs may be
overly conservative. Rather, we suggest that searching the space radially,
i.e., continuously along rays emanating from the predictive location of
interest, is a far thriftier alternative. Our empirical work demonstrates that
ray-based search yields predictors with accuracy comparable to exhaustive
search, but in a fraction of the time - bringing a supercomputer implementation
back onto the desktop.
