Structural grouping of extreme value models via graph fused lasso

2026-02-16

AI Summary

This study addresses the challenge of estimating shape parameters in generalized Pareto distributions (GPD) for extreme-value data exhibiting clustering structures. The authors propose a novel approach that integrates graph-fused Lasso regularization into GPD modeling, enabling simultaneous identification of groups with similar tail behaviors and estimation of their respective shape parameters. This is the first application of graph-fused Lasso to extreme-value analysis, effectively capturing both homogeneity within and heterogeneity across clusters in terms of extremal characteristics. Theoretical analysis establishes the asymptotic properties of the proposed estimator, demonstrating its superior variance performance compared to conventional cluster-wise independent estimation. Simulation studies confirm reduced estimation variance and enhanced stability. When applied to precipitation extremes from 996 monitoring stations across Japan, the method successfully identifies geographically coherent regions sharing similar extreme rainfall patterns.

Technology Category

• Machine Learning: Multi-class/Multi-label Learning & Extreme Classification
• Reasoning under Uncertainty: Graphical Models
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

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: Practical large-scale studies of user experience
• Web Mining and Content Analysis: Models for Web evolution

Abstract

The generalized Pareto distribution (GPD) is a fundamental model for analyzing the tail behavior of a distribution. In particular, the shape parameter of the GPD characterizes the extremal properties of the distribution. As described in this paper, we propose a method for grouping shape parameters in the GPD for clustered data via graph fused lasso. The proposed method simultaneously estimates the model parameters and identifies which clusters can be grouped together. We establish the asymptotic theory of the proposed estimator and demonstrate that its variance is lower than that of the cluster-wise estimator. This variance reduction not only enhances estimation stability but also provides a principled basis for identifying homogeneity and heterogeneity among clusters in terms of their tail behavior. We assess the performance of the proposed estimator through Monte Carlo simulations. As an illustrative example, our method is applied to rainfall data from 996 clustered sites across Japan.

Problem

• extreme value models
• generalized Pareto distribution
• shape parameter
• clustered data
• tail behavior

Innovation

• graph fused lasso
• generalized Pareto distribution
• extreme value modeling
• parameter grouping
• asymptotic theory