Title: Extreme Quantile Regression via SVM: Achieving Out-of-Distribution Generalization with Heavy-Tailed Inputs

This study investigates quantile regression within an extrapolation context, specifically addressing scenarios where covariates assume unusually large magnitudes. By applying regular variation assumptions, we demonstrate that extreme observations can be robustly described by their angular components. This insight allows for learning strategies that prioritize the angles of the most extreme data points. We formalize this methodology by minimizing an asymptotic conditional risk, which effectively restricts the learning process to the tail of the covariate distribution.

To address high-dimensional and nonlinear environments, we introduce a novel Support Vector Machine (SVM) framework for extreme quantile regression, utilizing reproducing kernel Hilbert spaces. A key advantage of our approach is its ability to handle unbounded response variables without requiring restrictive transformations. Furthermore, we derive finite-sample learning guarantees based on mild regularity conditions. This framework bridges statistical learning theory and multivariate extreme value theory, offering a theoretically sound and computationally feasible solution for extrapolation problems. To validate the practical utility of our method, we conduct an empirical analysis using river flow data from the Danube, confirming the real-world applicability of our theoretical findings.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC