  Machine learning and geostatistics are powerful mathematical frameworks for
modeling spatial data. Both approaches, however, suffer from poor scaling of
the required computational resources for large data applications. We present
the Stochastic Local Interaction (SLI) model, which employs a local
representation to improve computational efficiency. SLI combines geostatistics
and machine learning with ideas from statistical physics and computational
geometry. It is based on a joint probability density function defined by an
energy functional which involves local interactions implemented by means of
kernel functions with adaptive local kernel bandwidths. SLI is expressed in
terms of an explicit, typically sparse, precision (inverse covariance) matrix.
This representation leads to a semi-analytical expression for interpolation
(prediction), which is valid in any number of dimensions and avoids the
computationally costly covariance matrix inversion.
