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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2302.00934 |
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| _version_ | 1866910513312563200 |
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| author | Boulin, Alexis Di Bernardino, Elena Laloë, Thomas Toulemonde, Gwladys |
| author_facet | Boulin, Alexis Di Bernardino, Elena Laloë, Thomas Toulemonde, Gwladys |
| contents | 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 \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. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_00934 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | High-dimensional variable clustering based on maxima of a weakly dependent random process Boulin, Alexis Di Bernardino, Elena Laloë, Thomas Toulemonde, Gwladys Statistics Theory Methodology Machine Learning 60G70, 62H05, 62M99 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 \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. 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. |
| title | High-dimensional variable clustering based on maxima of a weakly dependent random process |
| topic | Statistics Theory Methodology Machine Learning 60G70, 62H05, 62M99 |
| url | https://arxiv.org/abs/2302.00934 |