GraphGP: Scalable Gaussian Processes with Vecchia's Approximation

• URL: http://arxiv.org/abs/2606.11402v1
• Date: Tue, 09 Jun 2026 19:50:27 GMT
• Title: GraphGP: Scalable Gaussian Processes with Vecchia's Approximation
• Abstract summary: Vecchia's approximation is a sparse precision matrix approximation for stationary, decaying kernels.<n>We present GraphGP, an algorithm for Vecchia's approximation that scales to nearly a billion parameters with linear time and memory requirements.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Gaussian processes are a powerful tool for modeling continuous fields, but their naive $\mathcal{O}(N^3)$ computational cost and $\mathcal{O}(N^2)$ memory requirement often limit their practical use. Vecchia's approximation is a sparse precision matrix approximation for stationary, decaying kernels that conditions each point only on its $k$ nearest neighbors. We present GraphGP, a GPU algorithm for Vecchia's approximation that scales to nearly a billion parameters with linear time and memory requirements, handling arbitrary point distributions over a large dynamic range. Our key contributions are (1) a bit-reversed k-d tree ordering that allows efficient neighbor searches while also maximizing batch parallelism, and (2) a differentiable CUDA implementation, which is substantially faster and more memory efficient than our pure JAX baseline. GraphGP provides the building blocks for inference, including forward generation, inverse application, log-determinant, and kernel parameter derivatives.

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