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

• 成果类型: Article; Early Access
• 署名作者: Boulin, Alexis; Di Bernardino, Elena; Laloe, Thomas; Toulemonde, Gwladys
• 署名单位: Universite Cote d'Azur; Centre National de la Recherche Scientifique (CNRS); Inria; Centre National de la Recherche Scientifique (CNRS); Universite de Montpellier
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2025.2459443
• 发表日期: 2025
• 关键词: block maxima; MULTIVARIATE

摘要

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.