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Extremes in High Dimensions: Methods and Scalable Algorithms

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arxiv 2303.04258 v2 pith:LA6E2JWC submitted 2023-03-07 stat.ME math.STstat.TH

Johannes Lederer , Marco Oesting This is my paper · ORCID
classification stat.MEmath.STstat.TH
keywords estimatorsextremesmodelsparametersalgorithmsextremehigh-dimensionalmultivariate
verification ladder T0 review T1 audit T2 compute T3 formal
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Extreme value theory for univariate and low-dimensional observations has been explored in considerable detail, but the field is still in an early stage regarding high-dimensional settings. This paper focuses on H\"usler-Reiss models, a popular class of models for multivariate extremes similar to multivariate Gaussian distributions, and their domain of attraction. We develop estimators for the model parameters based on score matching, and we equip these estimators with theories and exceptionally scalable algorithms. Simulations and applications to weather extremes demonstrate the fact that the estimators can estimate a large number of parameters reliably and fast; for example, we show that H\"usler-Reiss models with thousands of parameters can be fitted within a couple of minutes on a standard laptop. More generally speaking, our work relates extreme value theory to modern concepts of high-dimensional statistics and convex optimization.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. An Explicit Link between Extreme Value Theory and Compositional Data Analysis

    stat.ME 2026-07 accept novelty 7.0 of 10

    Hüsler–Reiss extremal variograms/covariances and compositional log-ratio covariances are identical under a small set of projections and the variogram map, enabling direct method transfer.

  2. Clustering Tails in High Dimension

    stat.ME 2025-06 conditional novelty 6.0 of 10

    A sequential rank-based procedure partitions high-dimensional variables into clusters with a common extreme value index, with consistency guarantees and simulation support.

  3. Spatial Modeling and Risk Zoning of Global Extreme Precipitation via Graph Neural Networks and r-Pareto Processes

    stat.AP 2025-09 reject novelty 4.0 of 10

    The paper proposes a graph-neural-network and r-Pareto hybrid for extreme-precipitation risk zoning and reports improved precision over baselines, but the evaluation is self-referential.

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