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

Antony Sikorski, Michael Ivanitskiy, Nathan Lenssen, Douglas Nychka, Daniel McKenzie
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:2278-2286, 2026.

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 this Paper

BibTeX
@InProceedings{pmlr-v300-sikorski26a, title = { LatticeVision: Image to Image Networks for Modeling Non-Stationary Spatial Data }, author = {Sikorski, Antony and Ivanitskiy, Michael and Lenssen, Nathan and Nychka, Douglas and McKenzie, Daniel}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {2278--2286}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/sikorski26a/sikorski26a.pdf}, url = {https://proceedings.mlr.press/v300/sikorski26a.html}, 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. } }
Endnote
%0 Conference Paper %T LatticeVision: Image to Image Networks for Modeling Non-Stationary Spatial Data %A Antony Sikorski %A Michael Ivanitskiy %A Nathan Lenssen %A Douglas Nychka %A Daniel McKenzie %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-sikorski26a %I PMLR %P 2278--2286 %U https://proceedings.mlr.press/v300/sikorski26a.html %V 300 %X 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.
APA
Sikorski, A., Ivanitskiy, M., Lenssen, N., Nychka, D. & McKenzie, D.. (2026). LatticeVision: Image to Image Networks for Modeling Non-Stationary Spatial Data . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:2278-2286 Available from https://proceedings.mlr.press/v300/sikorski26a.html.

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