Don't Get Your Kroneckers in a Twist: Gaussian Processes on High-Dimensional Incomplete Grids
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866911663192539136 |
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| author | Højlund, Mads Greisen Lykke-Møller, August Smart Moss, Henry Christiansen, Ove |
| author_facet | Højlund, Mads Greisen Lykke-Møller, August Smart Moss, Henry Christiansen, Ove |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_08036 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Don't Get Your Kroneckers in a Twist: Gaussian Processes on High-Dimensional Incomplete Grids Højlund, Mads Greisen Lykke-Møller, August Smart Moss, Henry Christiansen, Ove Machine Learning 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. |
| title | Don't Get Your Kroneckers in a Twist: Gaussian Processes on High-Dimensional Incomplete Grids |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2605.08036 |