Speeding Up Neighborhood Search in Local Gaussian Process Prediction

Recent implementations of local approximate Gaussian process models have pushed computational boundaries for nonlinear, nonparametric 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 computational horsepower. 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, that is, 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—for many problems bringing a supercomputer implementation back onto the desktop. Supplementary materials for this article are available online.