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We propose a new class of models for variable clustering called AsymptoticIndependent block (AI-block) models, which defines population-level clustersbased on the independence of the maxima of a multivariate stationary mixingrandom process among clusters. This class of models is identifiable, meaningthat there exists a maximal element with a partial order between partitions,allowing for statistical inference. We also present an algorithm for recoveringthe clusters of variables without specifying the number of clusters \emph{apriori}. Our work provides some theoretical insights into the consistency ofour algorithm, demonstrating that under certain conditions it can effectivelyidentify clusters in the data with a computational complexity that ispolynomial in the dimension. This implies that groups can be learnednonparametrically in which block maxima of a dependent process are onlysub-asymptotic. To further illustrate the significance of our work, we appliedour method to neuroscience and environmental real-datasets. These applicationshighlight the potential and versatility of the proposed approach.

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