# Modeling Nonstationary Extremal Dependence via Deep Spatial Deformations

arXiv: https://arxiv.org/abs/2505.12548 · HTML: https://mlsanity.com/paper/2505.12548/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 43 references that are in the map.
- First posted on arXiv 18 May 2025.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Deep Compositional Spatial Models](https://mlsanity.com/paper/1906.02840/) (2019)
- [Modeling of spatial extremes in environmental data science: Time to move away from max-stable processes](https://mlsanity.com/paper/2401.17430/) (2024)
- [Modeling Nonstationary and Asymmetric Multivariate Spatial Covariances via Deformations](https://mlsanity.com/paper/2004.08724/) (2020)
- [Non-Stationary Dependence Structures for Spatial Extremes](https://mlsanity.com/paper/1411.3174/) (2014)
- [Constructing Large Nonstationary Spatio-Temporal Covariance Models via Compositional Warpings](https://mlsanity.com/paper/2202.03560/) (2022)
- [Joint Estimation of Extreme Spatially Aggregated Precipitation at Different Scales through Mixture Modelling](https://mlsanity.com/paper/2111.08469/) (2021)
- [Spatial deformation for non-stationary extremal dependence](https://mlsanity.com/paper/2101.07167/) (2021)
- [Flexible Modeling of Nonstationary Extremal Dependence using Spatially-Fused LASSO and Ridge Penalties](https://mlsanity.com/paper/2210.05792/) (2022)
- [Anisotropic Brown-Resnick space-time processes: estimation and model assessment](https://mlsanity.com/paper/1503.06049/) (2015)
- [Flexible models for nonstationary dependence: Methodology and examples](https://mlsanity.com/paper/2001.06642/) (2020)
- [Functional Peaks-over-threshold Analysis](https://mlsanity.com/paper/2002.02711/) (2020)
- [On the Tail Behaviour of Aggregated Random Variables](https://mlsanity.com/paper/2105.11917/) (2021)
- [Non-stationary max-stable models with an application to heavy rainfall data](https://mlsanity.com/paper/2212.11598/) (2022)

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

- [Canonical Tail Dependence for Soft Extremal Clustering of Multichannel Brain Signals](https://mlsanity.com/paper/2512.06435/) (2025)

## Abstract (arXiv)

Modeling nonstationarity that often prevails in extremal dependence of spatial data can be challenging, and typically requires bespoke or complex spatial models that are difficult to estimate. Inference for stationary and isotropic models is considerably easier, but the assumptions that underpin these models are rarely met by data observed over large or topographically complex domains. A possible approach for accommodating nonstationarity in a spatial model is to warp the spatial domain to a latent space where stationarity and isotropy can be reasonably assumed. Although this approach is very flexible, estimating the warping function can be computationally expensive, and the transformation is not always guaranteed to be bijective, which may lead to physically unrealistic transformations when the domain folds onto itself. We overcome these challenges by developing deep compositional spatial models to capture nonstationarity in extremal dependence. Specifically, we focus on modeling high threshold exceedances of process functionals by leveraging efficient inference methods for limiting r-Pareto processes. A detailed high-dimensional simulation study demonstrates the superior performance of our model in estimating the warped space. We illustrate our method by modeling UK precipitation extremes and show that we can efficiently estimate the extremal dependence structure of data observed at thousands of locations.