# A multi-resolution approximation for massive spatial datasets

arXiv: https://arxiv.org/abs/1507.04789 · HTML: https://mlsanity.com/paper/1507.04789/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jul 2015.

## Built on by (most cited first, 20 of 20)

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- [Iterative Methods for Full-Scale Gaussian Process Approximations for Large Spatial Data](https://mlsanity.com/paper/2405.14492/) (2024)
- [Modeling Massive Spatial Datasets Using a Conjugate Bayesian Linear Regression Framework](https://mlsanity.com/paper/2109.04447/) (2021)
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- [Sequential Gibbs Posteriors with Applications to Principal Component Analysis](https://mlsanity.com/paper/2310.12882/) (2023)
- [LatticeVision: Image to Image Networks for Modeling Non-Stationary Spatial Data](https://mlsanity.com/paper/2505.09803/) (2025)
- [Logistic-beta processes for dependent random probabilities with beta marginals](https://mlsanity.com/paper/2402.07048/) (2024)
- [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)
- [Unsupervised cell segmentation by fast Gaussian Processes](https://mlsanity.com/paper/2505.18902/) (2025)
- [Scalable Asynchronous Federated Modeling for Spatial Data](https://mlsanity.com/paper/2510.01771/) (2025)
- [Predicting Covariate-Driven Spatial Deformation for Nonstationary Gaussian Processes](https://mlsanity.com/paper/2604.27280/) (2026)
- [Adaptive multi-resolution Gaussian processes: Scalable exact inference with naturally data-sparse covariance matrices](https://mlsanity.com/paper/2609.30348/) (2026)

## Abstract (arXiv)

Automated sensing instruments on satellites and aircraft have enabled the collection of massive amounts of high-resolution observations of spatial fields over large spatial regions. If these datasets can be efficiently exploited, they can provide new insights on a wide variety of issues. However, traditional spatial-statistical techniques such as kriging are not computationally feasible for big datasets. We propose a multi-resolution approximation (M-RA) of Gaussian processes observed at irregular locations in space. The M-RA process is specified as a linear combination of basis functions at multiple levels of spatial resolution, which can capture spatial structure from very fine to very large scales. The basis functions are automatically chosen to approximate a given covariance function, which can be nonstationary. All computations involving the M-RA, including parameter inference and prediction, are highly scalable for massive datasets. Crucially, the inference algorithms can also be parallelized to take full advantage of large distributed-memory computing environments. In comparisons using simulated data and a large satellite dataset, the M-RA outperforms a related state-of-the-art method.