Stochastic Local Interaction (SLI) Model: Interfacing Machine Learning and Geostatistics

TL;DR

The paper introduces the Stochastic Local Interaction (SLI) model, a computationally efficient framework combining machine learning and geostatistics for large-scale spatial data analysis using local interactions and sparse matrices.

Contribution

It presents the SLI model that integrates ideas from physics and geometry to improve scalability and efficiency in spatial data modeling.

Findings

SLI uses local kernel functions with adaptive bandwidths.

The model results in a sparse precision matrix for efficient computations.

SLI provides a semi-analytical interpolation method valid in multiple dimensions.

Abstract

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.