# An Efficient Implementation for Spatial-Temporal Gaussian Process Regression and Its Applications

arXiv: https://arxiv.org/abs/2209.12565 · HTML: https://mlsanity.com/paper/2209.12565/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Sep 2022.

## Built on by (most cited first, 5 of 5)

- [Scalable Spatiotemporal Prediction with Bayesian Neural Fields](https://mlsanity.com/paper/2403.07657/) (2024)
- [STACI: Spatio-Temporal Aleatoric Conformal Inference](https://mlsanity.com/paper/2505.21658/) (2025)
- [Effect Decomposition of Functional-Output Computer Experiments via Orthogonal Additive Gaussian Processes](https://mlsanity.com/paper/2506.12701/) (2025)
- [Tackling Incomplete Data in Air Quality Prediction: A Bayesian Deep Learning Framework for Uncertainty Quantification](https://mlsanity.com/paper/2511.02175/) (2025)
- [Predicting and Interpolating Spatiotemporal Environmental Data: A Case Study of Groundwater Storage in Bangladesh](https://mlsanity.com/paper/2511.22378/) (2025)

## Abstract (arXiv)

Spatial-temporal Gaussian process regression is a popular method for spatial-temporal data modeling. Its state-of-art implementation is based on the state-space model realization of the spatial-temporal Gaussian process and its corresponding Kalman filter and smoother, and has computational complexity O(NM3), where N and M are the number of time instants and spatial input locations, respectively, and thus can only be applied to data with large N but relatively small M. In this paper, our primary goal is to show that by exploring the Kronecker structure of the state-space model realization of the spatial-temporal Gaussian process, it is possible to further reduce the computational complexity to O(M3+NM2) and thus the proposed implementation can be applied to data with large N and moderately large M. The proposed implementation is illustrated over applications in weather data prediction and spatially-distributed system identification. Our secondary goal is to design a kernel for both the Colorado precipitation data and the GHCN temperature data, such that while having more efficient implementation, better prediction performance can also be achieved than the state-of-art result.