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 theoritical 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.

翻译：我们提出了一类新的变量聚类模型，称为渐近独立块（AI-block）模型。该模型基于多元平稳混合随机过程中簇内最大值之间的独立性来定义总体层面的聚类。此类模型具有可辨识性，这意味着在划分之间存在一个具有偏序关系的最大元素，从而允许进行统计推断。我们还提出了一种算法，无需事先指定聚类数量即可恢复变量聚类。我们的工作为算法的相合性提供了理论洞见，表明在特定条件下，该算法能够以维度多项式级的计算复杂度有效识别数据中的聚类。这意味着可以非参数地学习群组结构，其中相依过程的块最大值仅具有次渐近性质。