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

Antony Sikorski, Michael Ivanitskiy, Nathan Lenssen, Douglas Nychka, Daniel McKenzie

TL;DR: We introduce a framework for parameter estimation and emulation of non-stationary spatial data by combining image to image neural networks and spatial autoregressive models.

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.

Submission Number: 994