Model selection for extremal dependence structures using deep learning: Application to environmental data

TL;DR

This paper presents a deep learning-based methodology using CNNs for selecting extremal dependence structures in environmental spatial data, outperforming traditional criteria like CLIC in simulations.

Contribution

It introduces a hierarchical CNN approach for extremal dependence model selection, combining max-stable and covariance models, with demonstrated superior performance over existing methods.

Findings

CNN-based schemes outperform CLIC in model selection accuracy

Hierarchical CNN approach effectively identifies dependence structures

Method successfully applied to real environmental temperature data

Abstract

This paper introduces a new methodology for extreme spatial dependence structure selection. It is based on deep learning techniques, specifically Convolutional Neural Networks -CNNs. Two schemes are considered: in the first scheme, the matching probability is evaluated through a single CNN while in the second scheme, a hierarchical procedure is proposed: a first CNN is used to select a max-stable model, then another network allows to select the most adapted covariance function, according to the selected max-stable model. This model selection approach demonstrates performs very well on simulations. In contrast, the Composite Likelihood Information Criterion CLIC faces issues in selecting the correct model. Both schemes are applied to a dataset of 2m air temperature over Iraq land, CNNs are trained on dependence structures summarized by the Concurrence probability.