# Post-clustering Inference under Dependency

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This post is for González-Delgado, J., Cortés, J., & Neuvial, P. (2023). Post-clustering Inference under Dependency (arXiv:2310.11822). arXiv.

Gao et al. (2022): develop for independent observations identically distributed as $p$-dimensional Gaussian variables with a spherical covariance matrix, i.e., $\bfX \sim MN_{n\times p}(\mu, I_n, \sigma^2I_p)$

here, aim at extending this framework to a more convenient scenario for practical applications, where arbitrary dependence structures between observations and features are allowed

the theory is developed for hierarchical agglomerative clustering algorithm and for the k-means algorithm

the paper considers

\[\bfX \sim MN_{n\times p}(\mu, U, \Sigma)\]