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Pré-Publication, Document De Travail Année : 2023

High-dimensional variable clustering based on sub-asymptotic maxima of a weakly dependent random process

Résumé

We propose a new class of models for variable clustering called Asymptotic Independent block (AI-block) models, which defines population-level clusters based on the independence of the maxima of a multivariate stationary mixing random process among clusters. This class of models is identifiable, meaning that there exists a maximal element with a partial order between partitions, allowing for statistical inference. We also present an algorithm for recovering the clusters of variables without specifying the number of clusters \emph{a priori}. Our work provides some theoretical insights into the consistency of our algorithm, demonstrating that under certain conditions it can effectively identify clusters in the data with a computational complexity that is polynomial in the dimension. This implies that groups can be learned nonparametrically in which block maxima of a dependent process are only sub-asymptotic. To further illustrate the significance of our work, we applied our method to neuroscience and environmental real-datasets. These applications highlight the potential and versatility of the proposed approach.
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Dates et versions

hal-03969058 , version 1 (02-02-2023)
hal-03969058 , version 2 (23-09-2023)

Identifiants

  • HAL Id : hal-03969058 , version 2

Citer

Alexis Boulin, Elena Di Bernardino, Thomas Laloë, Gwladys Toulemonde. High-dimensional variable clustering based on sub-asymptotic maxima of a weakly dependent random process. 2023. ⟨hal-03969058v2⟩
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