Article Dans Une Revue Journal of the American Statistical Association Année : 2025

High-Dimensional Variable Clustering based on 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)

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Alexis Boulin, Elena Di Bernardino, Thomas Laloë, Gwladys Toulemonde. High-Dimensional Variable Clustering based on Maxima of a Weakly Dependent Random Process. Journal of the American Statistical Association, 2025, 120 (551), pp.1933-1944. ⟨10.1080/01621459.2025.2459443⟩. ⟨hal-03969058v2⟩
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