Stochastic Local Interaction (SLI) Model: Interfacing Machine Learning and Geostatistics
This addresses computational bottlenecks for researchers and practitioners in fields like geostatistics and machine learning dealing with large spatial datasets, though it appears incremental as it combines existing ideas.
The paper tackles the computational scaling problem in spatial data modeling by introducing the Stochastic Local Interaction (SLI) model, which improves efficiency through a local representation and sparse precision matrix, avoiding costly covariance matrix inversion.
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.