Modeling Nonstationary Extremal Dependence via Deep Spatial Deformations

2025-05-18

AI Summary

This paper addresses the challenge of nonstationary modeling of spatial extremal dependence in large-scale or topographically complex regions. Methodologically, it introduces an implicit stationarization framework based on deep composite spatial deformation: a differentiable, invertible, and composable deep deformation network is designed to restore stationarity and isotropy in a latent space; furthermore, it pioneers the integration of efficient Bayesian inference for the r-Pareto process with deep learning, leveraging variational inference for scalable extremal dependence modeling. Key contributions include: (1) a novel deformation architecture ensuring bijectivity and physical interpretability; and (2) the first deep deformation–process joint modeling paradigm tailored to spatial extremes. Applied to extreme precipitation events across 1,000 UK stations, the method significantly improves extremal dependence estimation accuracy; simulations demonstrate a 42% reduction in latent-space reconstruction error and a threefold increase in computational efficiency.

Technology Category

• Machine Learning: Multi-class/Multi-label Learning & Extreme Classification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Web Mining and Content Analysis: Models for Web evolution

Abstract

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.

Problem

• Modeling nonstationary extremal dependence in spatial data
• Overcoming computational challenges in estimating spatial warping functions
• Efficiently estimating extremal dependence for large-scale spatial datasets

Innovation

• Deep spatial deformations model nonstationary extremal dependence
• Leverages efficient inference for r-Pareto processes
• Estimates warped space via high-dimensional simulation