Efficient Gaussian process learning via subspace projections

TL;DR

This paper introduces a new training method for Gaussian processes using lower-dimensional projections, improving accuracy and efficiency by reducing information loss and computational costs.

Contribution

The paper presents a novel projected likelihood approach for GPs, with a closed-form information loss expression and empirical evidence of its advantages over existing methods.

Findings

Projected likelihood reduces information loss.

Method outperforms exact GP training.

Enhanced efficiency on large datasets.

Abstract

We propose a novel training objective for GPs constructed using lower-dimensional linear projections of the data, referred to as \emph{projected likelihood} (PL). We provide a closed-form expression for the information loss related to the PL and empirically show that it can be reduced with random projections on the unit sphere. We show the superiority of the PL, in terms of accuracy and computational efficiency, over the exact GP training and the variational free energy approach to sparse GPs over different optimisers, kernels and datasets of moderately large sizes.