# Modeling Spatial Extremes using Non-Gaussian Spatial Autoregressive Models via Convolutional Neural Networks

arXiv: https://arxiv.org/abs/2505.03034 · HTML: https://mlsanity.com/paper/2505.03034/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 49 references that are in the map.
- First posted on arXiv 5 May 2025.

## Builds on (most cited first, 17 of 17)

- [Neural Methods for Amortized Inference](https://mlsanity.com/paper/2404.12484/) (2024)
- [Likelihood-Free Parameter Estimation with Neural Bayes Estimators](https://mlsanity.com/paper/2208.12942/) (2022)
- [Neural Networks for Parameter Estimation in Intractable Models](https://mlsanity.com/paper/2107.14346/) (2021)
- [Fast covariance parameter estimation of spatial Gaussian process models using neural networks](https://mlsanity.com/paper/2012.15339/) (2020)
- [Neural Bayes Estimators for Irregular Spatial Data using Graph Neural Networks](https://mlsanity.com/paper/2310.02600/) (2023)
- [Advances in Statistical Modeling of Spatial Extremes](https://mlsanity.com/paper/2007.00774/) (2020)
- [Neural Likelihood Surfaces for Spatial Processes with Computationally Intensive or Intractable Likelihoods](https://mlsanity.com/paper/2305.04634/) (2023)
- [Modeling of spatial extremes in environmental data science: Time to move away from max-stable processes](https://mlsanity.com/paper/2401.17430/) (2024)
- [Fast parameter estimation of Generalized Extreme Value distribution using Neural Networks](https://mlsanity.com/paper/2305.04341/) (2023)
- [Extremal Quantile Regression: An Overview](https://mlsanity.com/paper/1612.06850/) (2016)
- [Modeling Extremal Streamflow using Deep Learning Approximations and a Flexible Spatial Process](https://mlsanity.com/paper/2208.03344/) (2022)
- [Neural Bayes estimators for censored inference with peaks-over-threshold models](https://mlsanity.com/paper/2306.15642/) (2023)
- [A Deep Learning Synthetic Likelihood Approximation of a Non-stationary Spatial Model for Extreme Streamflow Forecasting](https://mlsanity.com/paper/2212.07267/) (2022)
- [Modeling spatial data using local likelihood estimation and a Mat'ern to SAR translation](https://mlsanity.com/paper/2002.01124/) (2020)
- [Efficient Modeling of Spatial Extremes over Large Geographical Domains](https://mlsanity.com/paper/2112.10248/) (2021)
- [Spatial scale-aware tail dependence modeling for high-dimensional spatial extremes](https://mlsanity.com/paper/2412.07957/) (2024)
- [Modeling spatial tail dependence with Cauchy convolution processes](https://mlsanity.com/paper/2102.07094/) (2021)

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

- [LatticeVision: Image to Image Networks for Modeling Non-Stationary Spatial Data](https://mlsanity.com/paper/2505.09803/) (2025)

## Abstract (arXiv)

Data derived from remote sensing or numerical simulations often have a regular gridded structure and are large in volume, making it challenging to find accurate spatial models that can fill in missing grid cells or simulate the process effectively, especially in the presence of spatial heterogeneity and heavy-tailed marginal distributions. To overcome this issue, we present a spatial autoregressive modeling framework, which maps observations at a location and its neighbors to independent random variables. This is a highly flexible modeling approach and well-suited for non-Gaussian fields, providing simpler interpretability. In particular, we consider the SAR model with Generalized Extreme Value distribution innovations to combine the observation at a central grid location with its neighbors, capturing extreme spatial behavior based on the heavy-tailed innovations. While these models are fast to simulate by exploiting the sparsity of the key matrices in the computations, the maximum likelihood estimation of the parameters is prohibitive due to the intractability of the likelihood, making optimization challenging. To overcome this, we train a convolutional neural network on a large training set that covers a useful parameter space, and then use the trained network for fast parameter estimation. Finally, we apply this model to analyze annual maximum precipitation data from ERA-Interim-driven Weather Research and Forecasting (WRF) simulations, allowing us to explore its spatial extreme behavior across North America.