A parsimonious, computationally efficient machine learning method for spatial regression

TL;DR

The paper presents MPRS, a novel physically inspired machine learning method for spatial and temporal regression that is computationally efficient, scalable, and effective for complex, non-Gaussian data, outperforming traditional interpolation techniques.

Contribution

Introduction of MPRS, a non-parametric, physically inspired regression method that efficiently handles large, scattered datasets without parameter tuning.

Findings

MPRS performs competitively with kriging and IDW in various data scenarios.

MPRS is particularly effective for gap-filling non-Gaussian data like precipitation.

MPRS can process millions of data points in seconds on a standard PC.

Abstract

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.