High-Dimensional Variable Clustering based on Maxima of a Weakly Dependent Random Process

Alexis Boulin, Elena Di Bernardino, Thomas Laloë and Gwladys Toulemonde

Journal of the American Statistical Association, 2025, vol. 120, issue 551, 1933-1944

Abstract: 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 depending on a tuning parameter that recovers the clusters of variables without specifying the number of clusters 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. A data-driven selection method for the tuning parameter is also proposed. 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. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Date: 2025
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DOI: 10.1080/01621459.2025.2459443

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