Don't Get Your Kroneckers in a Twist: Gaussian Processes on High-Dimensional Incomplete Grids

arXiv:2605.08036v1 Announce Type: new 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.

Source: arXiv cs.LG | 2026-05-11