A parsimonious, computationally efficient machine learning method for spatial regression
This provides a computationally efficient method for spatial regression, particularly effective for gap-filling in rough and non-Gaussian data like daily precipitation time series, but it is incremental as it builds on existing interpolation approaches.
The paper tackled spatial/temporal regression by introducing the modified planar rotator method (MPRS), a non-parametric model that handles scattered data and arbitrary dimensions, and demonstrated its prediction performance is competitive with standard interpolation methods like ordinary kriging and inverse distance weighting, with computational efficiency allowing processing of millions of nodes in seconds on a standard PC.
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.