LatticeVision: Image to Image Networks for Modeling Non-Stationary Spatial Data
Abstract
In many applications, we wish to fit a parametric statistical model to a small ensemble of spatially distributed random variables ('fields'). However, parameter inference using maximum likelihood estimation (MLE) is computationally prohibitive, especially for large, non-stationary fields. Thus, many recent works train neural networks to estimate parameters given spatial fields as input, sidestepping MLE completely. In this work we focus on a popular class of parametric, spatially autoregressive (SAR) models. We make a simple yet impactful observation; because the SAR parameters can be arranged on a regular grid, both inputs (spatial fields) and outputs (model parameters) can be viewed as images. Using this insight, we demonstrate that image-to-image (I2I) networks enable faster and more accurate parameter estimation for a class of non-stationary SAR models with unprecedented complexity.
Cite
@article{arxiv.2505.09803,
title = {LatticeVision: Image to Image Networks for Modeling Non-Stationary Spatial Data},
author = {Antony Sikorski and Michael Ivanitskiy and Nathan Lenssen and Douglas Nychka and Daniel McKenzie},
journal= {arXiv preprint arXiv:2505.09803},
year = {2026}
}
Comments
This work has been accepted at the 29th International Conference on Artificial Intelligence and Statistics (AISTATS)