针对极端输入的分位数回归，提出基于支持向量机的新方法。
Out-of-Distribution generalization of quantile regression with heavy tailed inputs: an SVM approach
- 通过角度特征聚焦极端样本尾部，构建渐近条件风险最小化框架。
- 在多维非线性场景下实现高维极端分位数预测，无需变量变换。
- 理论保证有限样本学习性能，适用于水文等实际极端事件建模。
我们研究协变量取异常大值情形下的分位数回归问题。在正则变化假设下，极端观测可通过其方向分量有效刻画，从而设计聚焦最极端样本方向的学习策略。该方法通过最小化渐近条件风险来实现学习过程在协变量分布尾部的定位。本文提出一种新型支持向量机（SVM）框架，利用再生核希尔伯特空间处理高维与非线性场景，可适应无界响应变量，避免对数据进行限制性变换。在弱正则性假设下，建立了有限样本学习保证。所提框架融合统计学习与多元极值理论，提供了一种可计算且理论严谨的外推方法。通过在多瑙河水文数据上的实证研究，验证了方法的实际有效性。
原文摘要 · Abstract (English)
We study quantile regression in an extrapolation regime where the covariate takes unusually large values. Under regular variation assumptions, extreme observations can be effectively characterized through their angular components, enabling learning strategies that focus on the angle of the most extreme observations. This approach is formalized through the minimization of an asymptotic conditional risk that localizes learning in the tail of the covariate distribution. We propose a novel Support Vector Machine (SVM) framework for extreme quantile regression, leveraging reproducing kernel Hilbert spaces to handle high-dimensional and nonlinear settings. Our method also accommodates unbounded response variables and avoids restrictive transformations. We establish finite-sample learning guarantees under mild regularity assumptions. The proposed framework unifies ideas from statistical learning and multivariate extremes, providing a tractable and theoretically grounded approach to extrapolation. We complement our theoretical findings with an empirical study on river flow data from the Danube, demonstrating the practical relevance of our methods.
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