LatticeVision: Image to Image Networks for Modeling Non-Stationary Spatial Data

TL;DR

This paper introduces LatticeVision, an image-to-image neural network approach that significantly improves the speed and accuracy of estimating parameters for complex, non-stationary spatial models by leveraging their grid-like structure.

Contribution

The work demonstrates that viewing SAR model parameters and spatial fields as images enables effective use of I2I networks for parameter estimation in complex non-stationary settings.

Findings

I2I networks outperform traditional methods in speed and accuracy.

The approach handles higher complexity non-stationary models.

Parameter estimation becomes more scalable and efficient.

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.