Abstract:We introduce CUTS-GPR, a new method for performing numerically exact Gaussian process regression (GPR) in high-dimensional settings. The key component of CUTS-GPR is an extremely fast kernel matrix-vector product, which exhibits near-linear or even linear scaling with the amount of training data, $N$, and low-order polynomial scaling with dimensionality, $D$. This is obtained by combining an additive kernel with an incomplete grid and exploiting the resulting structure of the kernel matrix. We demonstrate the scalability of the matrix-vector product by running benchmarks with billions of data points and thousands of dimensions. Full GPR calculations, including hyperparameter optimization, are completed in a matter of hours for $N = 447 265$ and $D = 24$. We demonstrate that our CUTS-GPR enables Bayesian modeling of high-dimensional potential energy surfaces - a longstanding challenge in computational chemistry.
| Comments: | 51 pages, 8 figures |
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2605.08036 [cs.LG] |
| (or arXiv:2605.08036v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.08036 arXiv-issued DOI via DataCite (pending registration) |
From: Mads Højlund [view email]
[v1]
Fri, 8 May 2026 17:24:22 UTC (1,747 KB)
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