# On Regression in Extreme Regions

arXiv: https://arxiv.org/abs/2303.03084 · HTML: https://mlsanity.com/paper/2303.03084/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 91 references that are in the map.
- First posted on arXiv 6 Mar 2023.

## Builds on (most cited first, 22 of 22)

- [Generalizing from a Few Examples: A Survey on Few-Shot Learning](https://mlsanity.com/paper/1904.05046/) (2019)
- [Empirical risk minimization for heavy-tailed losses](https://mlsanity.com/paper/1406.2462/) (2014)
- [Heavy-tailed Representations, Text Polarity Classification & Data Augmentation](https://mlsanity.com/paper/2003.11593/) (2020)
- [Gradient boosting for extreme quantile regression](https://mlsanity.com/paper/2103.00808/) (2021)
- [Learning without Concentration for General Loss Functions](https://mlsanity.com/paper/1410.3192/) (2014)
- [Decompositions of Dependence for High-Dimensional Extremes](https://mlsanity.com/paper/1612.07190/) (2016)
- [k-means clustering of extremes](https://mlsanity.com/paper/1904.02970/) (2019)
- [Principal Component Analysis for Multivariate Extremes](https://mlsanity.com/paper/1906.11043/) (2019)
- [Sparsity in Multivariate Extremes with Applications to Anomaly Detection](https://mlsanity.com/paper/1507.05899/) (2015)
- [Extremal Random Forests](https://mlsanity.com/paper/2201.12865/) (2022)
- [Max K-armed bandit: On the ExtremeHunter algorithm and beyond](https://mlsanity.com/paper/1707.08820/) (2017)
- [Sparse regular variation](https://mlsanity.com/paper/1907.00686/) (2019)
- [Concentration bounds for the empirical angular measure with statistical learning applications](https://mlsanity.com/paper/2104.03966/) (2021)
- [On aggregation for heavy-tailed classes](https://mlsanity.com/paper/1502.07097/) (2015)
- [Determining the Dependence Structure of Multivariate Extremes](https://mlsanity.com/paper/1809.01606/) (2018)
- [Sparse Representation of Multivariate Extremes with Applications to Anomaly Ranking](https://mlsanity.com/paper/1603.09584/) (2016)
- [Identifying groups of variables with the potential of being large simultaneously](https://mlsanity.com/paper/1802.09977/) (2018)
- [Multivariate peaks over thresholds models](https://mlsanity.com/paper/1603.06619/) (2016)
- [An Extreme Value Bayesian Lasso for the Conditional Left and Right Tails](https://mlsanity.com/paper/2010.07164/) (2020)
- [A Multivariate Extreme Value Theory Approach to Anomaly Clustering and Visualization](https://mlsanity.com/paper/1907.07523/) (2019)
- [Tail inverse regression for dimension reduction with extreme response](https://mlsanity.com/paper/2108.01432/) (2021)
- [On Choice of Hyper-parameter in Extreme Value Theory based on Machine Learning Techniques](https://mlsanity.com/paper/2107.06074/) (2021)

## Built on by (most cited first, 6 of 6)

- [Progression: an extrapolation principle for regression](https://mlsanity.com/paper/2410.23246/) (2024)
- [Extreme Conformal Prediction: Reliable Intervals for High-Impact Events](https://mlsanity.com/paper/2505.08578/) (2025)
- [Multi-site modelling and reconstruction of past extreme skew surges along the French Atlantic coast](https://mlsanity.com/paper/2505.00835/) (2025)
- [A Kolmogorov-Arnold Neural Model for Cascading Extremes](https://mlsanity.com/paper/2505.13370/) (2025)
- [Extrapolation in Statistical Learning with Extreme Value Theory](https://mlsanity.com/paper/2605.01909/) (2026)
- [Out-of-Distribution generalization of quantile regression with heavy tailed inputs: an SVM approach](https://mlsanity.com/paper/2606.00265/) (2026)

## Abstract (arXiv)

We establish a statistical learning theoretical framework aimed at extrapolation, or out-of-domain generalization, on the unobserved tails of covariates in continuous regression problems. Our strategy involves performing statistical regression on a subsample of observations with continuous labels that are the furthest away from the origin, focusing specifically on their angular components. The underlying assumptions of our approach are grounded in the theory of multivariate regular variation, a cornerstone of extreme value theory. We address the stylized problem of nonparametric least squares regression with predictors chosen from a Vapnik-Chervonenkis class. This work contributes to a broader initiative to develop statistical learning theoretical foundations for supervised learning strategies that enhance performance on the supposedly heavy tails of covariates. Previous efforts in this area have focused exclusively on binary classification on extreme covariates. Although the continuous target setting necessitates different techniques and regularity assumptions, our main results echo findings from earlier studies. We quantify the predictive performance on tail regions in terms of excess risk, presenting it as a finite sample risk bound with a clear bias-variance decomposition. Numerical experiments with simulated and real data illustrate our theoretical findings.