Don't Get Your Kroneckers in a Twist: Gaussian Processes on High-Dimensional Incomplete Grids
For computational chemistry and other fields requiring scalable Bayesian modeling of high-dimensional functions, CUTS-GPR provides a practical solution to a longstanding challenge.
CUTS-GPR enables numerically exact Gaussian process regression on high-dimensional incomplete grids with near-linear scaling in data size and low-order polynomial scaling in dimensionality, demonstrated on benchmarks with billions of data points and thousands of dimensions, and applied to high-dimensional potential energy surfaces.
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.