# Parallel inference for massive distributed spatial data using low-rank models

arXiv: https://arxiv.org/abs/1402.1472 · HTML: https://mlsanity.com/paper/1402.1472/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Feb 2014.

## Built on by (most cited first, 2 of 2)

- [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)

Due to rapid data growth, statistical analysis of massive datasets often has to be carried out in a distributed fashion, either because several datasets stored in separate physical locations are all relevant to a given problem, or simply to achieve faster (parallel) computation through a divide-and-conquer scheme. In both cases, the challenge is to obtain valid inference that does not require processing all data at a single central computing node. We show that for a very widely used class of spatial low-rank models, which can be written as a linear combination of spatial basis functions plus a fine-scale-variation component, parallel spatial inference and prediction for massive distributed data can be carried out exactly, meaning that the results are the same as for a traditional, non-distributed analysis. The communication cost of our distributed algorithms does not depend on the number of data points. After extending our results to the spatio-temporal case, we illustrate our methodology by carrying out distributed spatio-temporal particle filtering inference on total precipitable water measured by three different satellite sensor systems.