# Large-Scale Low-Rank Gaussian Process Prediction with Support Points

arXiv: https://arxiv.org/abs/2207.12804 · HTML: https://mlsanity.com/paper/2207.12804/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jul 2022.

## Built on by (most cited first, 3 of 3)

- [Modeling High-Resolution Spatio-Temporal Wind with Deep Echo State Networks and Stochastic Partial Differential Equations](https://mlsanity.com/paper/2412.07265/) (2024)
- [Scalable Asynchronous Federated Modeling for Spatial Data](https://mlsanity.com/paper/2510.01771/) (2025)
- [Adaptive Nystr"om for Gaussian Process Regression](https://mlsanity.com/paper/2607.27427/) (2026)

## Abstract (arXiv)

Low-rank approximation is a popular strategy to tackle the "big n problem" associated with large-scale Gaussian process regressions. Basis functions for developing low-rank structures are crucial and should be carefully specified. Predictive processes simplify the problem by inducing basis functions with a covariance function and a set of knots. The existing literature suggests certain practical implementations of knot selection and covariance estimation; however, theoretical foundations explaining the influence of these two factors on predictive processes are lacking. In this paper, the asymptotic prediction performance of the predictive process and Gaussian process predictions is derived and the impacts of the selected knots and estimated covariance are studied. We suggest the use of support points as knots, which best represent data locations. Extensive simulation studies demonstrate the superiority of support points and verify our theoretical results. Real data of precipitation and ozone are used as examples, and the efficiency of our method over other widely used low-rank approximation methods is verified.