mlsanityData to 7 Oct 2026

Extrapolation in Statistical Learning with Extreme Value Theory

arXiv 2605.01909 ↗First posted 3 May 2026stat.ML cs.LG math.STcited by 1

Not on the map. Why?

Abstract (arXiv)

Extreme value theory provides rigorous theory and statistical tools for extrapolation in machine learning, particularly in settings where traditional methods struggle due to data scarcity in the tails. A broad range of tasks benefit from these advances, including regression and classification beyond the training data, extreme quantile regression, supervised and unsupervised dimension reduction, generative artificial intelligence and anomaly detection. This review synthesizes recent developments in these fields at the intersection of statistical learning and extreme value theory, with a focus on principled methods based on asymptotically motivated representations of the tail of univariate and multivariate distributions. We consider different theoretical frameworks for both asymptotically dependent and independent data and discuss how they translate into efficient statistical methods for extrapolation to extreme regions. By addressing both theoretical and practical aspects, we offer a comprehensive overview of the state-of-the-art in this quickly evolving field, and identify promising directions for future research.

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 67 of its 146 references that are in the map. First posted on arXiv 3 May 2026.

Builds on

67 of 146 references.

References · 67

  1. 2017Attention Is All You Needcited by 59,932
  2. 2022Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language modelscited by 1,970
  3. 2020Long-tail learning via logit adjustmentcited by 605
  4. 2017Nonparametric regression using deep neural networks with ReLU activation functioncited by 431
  5. 2016Generalized Random Forestscited by 309
  6. 2023GenCast: Diffusion-based ensemble forecasting for medium-range weathercited by 169
  7. 2018Anchor regression: heterogeneous data meets causalitycited by 116
  8. 2015The Extreme Value Machinecited by 78
  9. 2020A causal framework for distribution generalizationcited by 68
  10. 2023Engression: Extrapolation through the Lens of Distributional Regressioncited by 49
  11. 2020ExGAN: Adversarial Generation of Extreme Samplescited by 28
  12. 2024Can AI weather models predict out-of-distribution gray swan tropical cyclones?cited by 26
38 more
  1. 2020Heavy-tailed Representations, Text Polarity Classification & Data Augmentationcited by 20
  2. 2022Neural Networks for Extreme Quantile Regression with an Application to Forecasting of Flood Riskcited by 19
  3. 2019Copula & Marginal Flows: Disentangling the Marginal from its Jointcited by 17
  4. 2024Validating Deep Learning Weather Forecast Models on Recent High-Impact Extreme Eventscited by 14
  5. 2025Numerical models outperform AI weather forecasts of record-breaking extremescited by 14
  6. 2016Decompositions of Dependence for High-Dimensional Extremescited by 13
  7. 2020Sparse Structures for Multivariate Extremescited by 12
  8. 2019k-means clustering of extremescited by 11
  9. 2022Regression modelling of spatiotemporal extreme U.S. wildfires via partially-interpretable neural networkscited by 11
  10. 2019Principal Component Analysis for Multivariate Extremescited by 10
  11. 2015Sparsity in Multivariate Extremes with Applications to Anomaly Detectioncited by 9
  12. 2022Extremal Random Forestscited by 9
  13. 2023A VAE Approach to Sample Multivariate Extremescited by 9
  14. 2021Concentration bounds for the empirical angular measure with statistical learning applicationscited by 8
  15. 2022COMET Flows: Towards Generative Modeling of Multivariate Extremes and Tail Dependencecited by 8
  16. 2024Tail calibration of probabilistic forecastscited by 7
  17. 2020Structure learning for extremal tree modelscited by 6
  18. 2022Statistical Inference for H"usler-Reiss Graphical Models Through Matrix Completionscited by 6
  19. 2023On Regression in Extreme Regionscited by 6
  20. 2024Progression: an extrapolation principle for regressioncited by 6
  21. 2016Sparse Representation of Multivariate Extremes with Applications to Anomaly Rankingcited by 5
  22. 2018Identifying groups of variables with the potential of being large simultaneouslycited by 5
  23. 2021Estimating a Directed Tree for Extremescited by 5
  24. 2024Extrapolation-Aware Nonparametric Statistical Inferencecited by 5
  25. 2025Extreme Conformal Prediction: Reliable Intervals for High-Impact Eventscited by 5
  26. 2018Improving precipitation forecasts using extreme quantile regressioncited by 4
  27. 2021Modeling Extremes with d-max-decreasing Neural Networkscited by 4
  28. 2021Total positivity in multivariate extremescited by 4
  29. 2023Sharp error bounds for imbalanced classification: how many examples in the minority class?cited by 4
  30. 2024Deep Learning of Multivariate Extremes via a Geometric Representationcited by 4
  31. 2025Extremes of structural causal modelscited by 4
  32. 2025GPDFlow: Generative Multivariate Threshold Exceedance Modeling via Normalizing Flowscited by 4
  33. 2019A Multivariate Extreme Value Theory Approach to Anomaly Clustering and Visualizationcited by 3
  34. 2021Spectral learning of multivariate extremescited by 3
  35. 2022Graphical models for infinite measures with applications to extremescited by 3
  36. 2023Extremes in High Dimensions: Methods and Scalable Algorithmscited by 3
  37. 2023Regular Variation in Hilbert Spaces and Principal Component Analysis for Functional Extremescited by 3
  38. 2020Linking representations for multivariate extremes via a limit setcited by 2

50 most cited of 67 All 67 (JSON)

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026Out-of-Distribution generalization of quantile regression with heavy tailed inputs: an SVM approachcited by 0