Stochastic Local Interaction (SLI) model: Bridging machine learning and geostatistics

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.