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

arXiv: https://arxiv.org/abs/2302.00934 · HTML: https://mlsanity.com/paper/2302.00934/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 101 references that are in the map.
- First posted on arXiv 2 Feb 2023.

## Builds on (most cited first, 20 of 20)

- [Decompositions of Dependence for High-Dimensional Extremes](https://mlsanity.com/paper/1612.07190/) (2016)
- [Sparse Structures for Multivariate Extremes](https://mlsanity.com/paper/2004.12182/) (2020)
- [k-means clustering of extremes](https://mlsanity.com/paper/1904.02970/) (2019)
- [Principal Component Analysis for Multivariate Extremes](https://mlsanity.com/paper/1906.11043/) (2019)
- [Sparsity in Multivariate Extremes with Applications to Anomaly Detection](https://mlsanity.com/paper/1507.05899/) (2015)
- [Sparse regular variation](https://mlsanity.com/paper/1907.00686/) (2019)
- [High-Dimensional Inference for Cluster-Based Graphical Models](https://mlsanity.com/paper/1806.05139/) (2018)
- [Determining the Dependence Structure of Multivariate Extremes](https://mlsanity.com/paper/1809.01606/) (2018)
- [Structure learning for extremal tree models](https://mlsanity.com/paper/2012.06179/) (2020)
- [Statistical Inference for H"usler-Reiss Graphical Models Through Matrix Completions](https://mlsanity.com/paper/2210.14292/) (2022)
- [Sparse Representation of Multivariate Extremes with Applications to Anomaly Ranking](https://mlsanity.com/paper/1603.09584/) (2016)
- [Identifying groups of variables with the potential of being large simultaneously](https://mlsanity.com/paper/1802.09977/) (2018)
- [Multivariate Nonparametric Estimation of the Pickands Dependence Function using Bernstein Polynomials](https://mlsanity.com/paper/1405.5228/) (2014)
- [Graphical models for infinite measures with applications to extremes](https://mlsanity.com/paper/2211.15769/) (2022)
- [Independence clustering (without a matrix)](https://mlsanity.com/paper/1703.06700/) (2017)
- [Multiple block sizes and overlapping blocks for multivariate time series extremes](https://mlsanity.com/paper/1907.09477/) (2019)
- [Extremal independence old and new](https://mlsanity.com/paper/2002.07808/) (2020)
- [Multiscale modelling of replicated nonstationary time series](https://mlsanity.com/paper/2005.09440/) (2020)
- [Rank-based Estimation under Asymptotic Dependence and Independence, with Applications to Spatial Extremes](https://mlsanity.com/paper/2008.03349/) (2020)
- [Optimal Variable Clustering for High-Dimensional Matrix Valued Data](https://mlsanity.com/paper/2112.12909/) (2021)

## Built on by (most cited first, 1 of 1)

- [Extrapolation in Statistical Learning with Extreme Value Theory](https://mlsanity.com/paper/2605.01909/) (2026)

## Abstract (arXiv)

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.