Extrapolation of extreme covariates in generalized additive regression using extreme-value theory

2026-07-09

AI Summary

This study addresses the failure of generalized additive models (GAMs) in extrapolation under covariate distributional shifts or extreme values by proposing a novel framework that integrates multivariate extreme value theory (EVT). The approach employs GAMs in the central region of the covariate space while introducing an EVT-driven asymptotic model in extreme regions, unified through a link function that establishes a coherent linear structure on latent variables or continuous responses. This work presents the first systematic embedding of extreme value theory into the GAM regression framework, substantially enhancing robustness and predictive accuracy under extreme covariate extrapolation. Empirical validation on European wildfire prediction—using environmental and meteorological covariates—demonstrates the method’s superior performance under extreme climatic conditions.

Abstract

We propose methods to enhance the predictive performance of generalized additive models (GAMs) in the context of covariate extrapolation, where predictions rely on covariates beyond their observed range. When using predictive models such as GAMs, shifts in the covariate distribution between training and prediction datasets can occur. Ignoring this issue may lead to inaccurate predictions in the tail of the covariate distributions. For example, this problem is particularly critical in climate-change scenarios, where covariates simulated from future climate scenarios are likely to contain more extreme conditions. Our approach integrates GAMs for the bulk of covariate distributions with asymptotic models from multivariate extreme-value theory at high covariate values. We consider binary responses based on a latent variable assumption, and also continuous responses. For large values of the covariates, on a specific marginal scale motivated by extreme-value theory the latent variable or continuous response is assumed to depend linearly on the covariates with an additive error term, when using an appropriate link function. In an application to wildfires in Europe, we explore how the new method can improve predictions, using environmental and meteorological covariates.

Problem

• covariate extrapolation
• generalized additive models
• extreme-value theory
• distribution shift
• tail prediction

Innovation

• generalized additive models
• extreme-value theory
• covariate extrapolation
• tail prediction
• latent variable model