Speeding up neighborhood search in local Gaussian process prediction

TL;DR

This paper proposes a radial search method to accelerate local Gaussian process predictions, maintaining accuracy while significantly reducing computational time, making large-scale predictions more accessible.

Contribution

It introduces a radial search approach for local design building in Gaussian processes, reducing computational costs without sacrificing prediction accuracy.

Findings

Radial search achieves similar accuracy to exhaustive search.

Significant reduction in computation time.

Enables desktop-level implementation of large-scale Gaussian process models.

Abstract

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.