Accelerated training of Gaussian processes using banded square exponential covariances

Emily C. Ehrhardt; Felipe Tobar

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arXiv · 2601.19007

Accelerated training of Gaussian processes using banded square exponential covariances

Emily C. Ehrhardt·Felipe Tobar

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Abstract

We propose a novel approach to computationally efficient GP training based on the observation that square-exponential (SE) covariance matrices contain several off-diagonal entries extremely close to zero. We construct a principled procedure to eliminate those entries to produce a \emph{banded}-matrix approximation to the original covariance, whose inverse and determinant can be computed at a reduced computational cost, thus contributing to an efficient approximation to the likelihood function. We provide a theoretical analysis of the proposed method to preserve the structure of the original covariance in the 1D setting with SE kernel, and validate its computational efficiency against the variational free energy approach to sparse GPs.

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Emily C. Ehrhardt, Felipe Tobar. 2026-01-26. Accelerated training of Gaussian processes using banded square exponential covariances. https://arxiv.org/abs/2601.19007

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