# A class of multi-resolution approximations for large spatial datasets

arXiv: https://arxiv.org/abs/1710.08976 · HTML: https://mlsanity.com/paper/1710.08976/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Oct 2017.

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

- [Scalable Gaussian-process regression and variable selection using Vecchia approximations](https://mlsanity.com/paper/2202.12981/) (2022)
- [When the whole is greater than the sum of its parts: Scaling black-box inference to large data settings through divide-and-conquer](https://mlsanity.com/paper/2412.20323/) (2024)
- [Adaptive multi-resolution Gaussian processes: Scalable exact inference with naturally data-sparse covariance matrices](https://mlsanity.com/paper/2609.30348/) (2026)

## Abstract (arXiv)

Gaussian processes are popular and flexible models for spatial, temporal, and functional data, but they are computationally infeasible for large datasets. We discuss Gaussian-process approximations that use basis functions at multiple resolutions to achieve fast inference and that can (approximately) represent any spatial covariance structure. We consider two special cases of this multi-resolution-approximation framework, a taper version and a domain-partitioning (block) version. We describe theoretical properties and inference procedures, and study the computational complexity of the methods. Numerical comparisons and an application to satellite data are also provided.