A parsimonious, computationally efficient machine learning method for
  spatial regression
Milan Žukovič Dionissios T. Hristopulos
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.