# Out-of-Distribution generalization of quantile regression with heavy tailed inputs: an SVM approach

arXiv: https://arxiv.org/abs/2606.00265 · HTML: https://mlsanity.com/paper/2606.00265/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 51 references that are in the map.
- First posted on arXiv 29 May 2026.

## Builds on (most cited first, 10 of 10)

- [Heavy-tailed Representations, Text Polarity Classification & Data Augmentation](https://mlsanity.com/paper/2003.11593/) (2020)
- [Validating Deep Learning Weather Forecast Models on Recent High-Impact Extreme Events](https://mlsanity.com/paper/2404.17652/) (2024)
- [Optimal Learning Rates for Localized SVMs](https://mlsanity.com/paper/1507.06615/) (2015)
- [Extremes on river networks](https://mlsanity.com/paper/1501.02663/) (2015)
- [Concentration bounds for the empirical angular measure with statistical learning applications](https://mlsanity.com/paper/2104.03966/) (2021)
- [liquidSVM: A Fast and Versatile SVM package](https://mlsanity.com/paper/1702.06899/) (2017)
- [On Regression in Extreme Regions](https://mlsanity.com/paper/2303.03084/) (2023)
- [Progression: an extrapolation principle for regression](https://mlsanity.com/paper/2410.23246/) (2024)
- [Multi-site modelling and reconstruction of past extreme skew surges along the French Atlantic coast](https://mlsanity.com/paper/2505.00835/) (2025)
- [Extrapolation in Statistical Learning with Extreme Value Theory](https://mlsanity.com/paper/2605.01909/) (2026)

## Abstract (arXiv)

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.