# A parsimonious, computationally efficient machine learning method for spatial regression

arXiv: https://arxiv.org/abs/2309.16448 · HTML: https://mlsanity.com/paper/2309.16448/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 57 references that are in the map.
- First posted on arXiv 28 Sep 2023.

## Builds on (most cited first, 3 of 3)

- [Stochastic Local Interaction (SLI) Model: Interfacing Machine Learning and Geostatistics](https://mlsanity.com/paper/1501.04053/) (2015)
- [Half-tapering strategy for conditional simulation with large datasets](https://mlsanity.com/paper/1607.08372/) (2016)
- [Spatial data modeling by means of Gibbs Markov random fields based on a generalized planar rotator model](https://mlsanity.com/paper/2201.02537/) (2022)

## Abstract (arXiv)

We introduce the modified planar rotator method (MPRS), a physically inspired machine learning method for spatial/temporal regression. MPRS is a non-parametric model which incorporates spatial or temporal correlations via short-range, distance-dependent ``interactions'' without assuming a specific form for the underlying probability distribution. Predictions are obtained by means of a fully autonomous learning algorithm which employs equilibrium conditional Monte Carlo simulations. MPRS is able to handle scattered data and arbitrary spatial dimensions. We report tests on various synthetic and real-word data in one, two and three dimensions which demonstrate that the MPRS prediction performance (without parameter tuning) is competitive with standard interpolation methods such as ordinary kriging and inverse distance weighting. In particular, MPRS is a particularly effective gap-filling method for rough and non-Gaussian data (e.g., daily precipitation time series). MPRS shows superior computational efficiency and scalability for large samples. Massive data sets involving millions of nodes can be processed in a few seconds on a standard personal computer.