# Stochastic Local Interaction Model with Sparse Precision Matrix for Space-Time Interpolation

arXiv: https://arxiv.org/abs/1902.07780 · HTML: https://mlsanity.com/paper/1902.07780/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Feb 2019.

## Built on by (most cited first, 1 of 1)

- [Non-separable Covariance Kernels for Spatiotemporal Gaussian Processes based on a Hybrid Spectral Method and the Harmonic Oscillator](https://mlsanity.com/paper/2302.09580/) (2023)

## Abstract (arXiv)

The application of geostatistical and machine learning methods based on Gaussian processes to big space-time data is beset by the requirement for storing and numerically inverting large and dense covariance matrices. Computationally efficient representations of space-time correlations can be constructed using local models of conditional dependence which can reduce the computational load. We formulate a stochastic local interaction model for regular and scattered space-time data that incorporates interactions within controlled space-time neighborhoods. The strength of the interaction and the size of the neighborhood are defined by means of kernel functions and adaptive local bandwidths. Compactly supported kernels lead to finite-size local neighborhoods and consequently to sparse precision matrices that admit explicit expression. Hence, the stochastic local interaction model's requirements for storage are modest and the costly covariance matrix inversion is not needed. We also derive a semi-explicit prediction equation and express the conditional variance of the prediction in terms of the diagonal of the precision matrix. For data on regular space-time lattices, the stochastic local interaction model is equivalent to a Gaussian Markov Random Field.