Cohesion and Repulsion in Bayesian Distance Clustering

Natarajan, Abhinav; Heinecke, Andreas M.; Mayer, Emanuel; Glenn, Simon

doi:10.1080/01621459.2023.2191821

Cited by 4 publications

(1 citation statement)

References 52 publications

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“…In addition, we highlight other interesting work integrating algorithmic approaches within a Bayesian framework. This includes combining density-based methods with a Bayesian model-based approach [ 81 ]; Bayesian hierarchical clustering which builds a tree of hierarchical clustering solutions based on Bayesian nonparametric (BNP) mixture models [ 82 – 85 ] and Bayesian distance-based clustering based on pairwise distances between observations [ 86 – 89 ].…”

Section: Bayesian Cluster Analysismentioning

confidence: 99%

Bayesian cluster analysis

Wade

2023

Phil. Trans. R. Soc. A.

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Bayesian cluster analysis offers substantial benefits over algorithmic approaches by providing not only point estimates but also uncertainty in the clustering structure and patterns within each cluster. An overview of Bayesian cluster analysis is provided, including both model-based and loss-based approaches, along with a discussion on the importance of the kernel or loss selected and prior specification. Advantages are demonstrated in an application to cluster cells and discover latent cell types in single-cell RNA sequencing data to study embryonic cellular development. Lastly, we focus on the ongoing debate between finite and infinite mixtures in a model-based approach and robustness to model misspecification. While much of the debate and asymptotic theory focuses on the marginal posterior of the number of clusters, we empirically show that quite a different behaviour is obtained when estimating the full clustering structure. This article is part of the theme issue ‘Bayesian inference: challenges, perspectives, and prospects’.

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Section: Bayesian Cluster Analysismentioning

confidence: 99%

Bayesian cluster analysis

Wade

2023

Phil. Trans. R. Soc. A.

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Fast generation of exchangeable sequences of clusters data

Levin,

Betancourt

2024

Stat Comput

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Repulsion, chaos, and equilibrium in mixture models

Cremaschi,

Wertz,

De Iorio

2024

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Mixture models are commonly used in applications with heterogeneity and overdispersion in the population, as they allow the identification of subpopulations. In the Bayesian framework, this entails the specification of suitable prior distributions for the weights and locations of the mixture. Despite their popularity, the flexibility of these models often does not translate into the interpretability of the clusters. To overcome this issue, repulsive mixture models have been recently proposed. The basic idea is to include a repulsive term in the distribution of the atoms of the mixture, favouring mixture locations far apart. This approach induces well-separated clusters, aiding the interpretation of the results. However, these models are usually not easy to handle due to unknown normalizing constants. We exploit results from equilibrium statistical mechanics, where the molecular chaos hypothesis implies that nearby particles spread out over time. In particular, we exploit the connection between random matrix theory and statistical mechanics and propose a novel class of repulsive prior distributions based on Gibbs measures associated with joint distributions of eigenvalues of random matrices. The proposed framework greatly simplifies computations thanks to the availability of the normalizing constant in closed form. We investigate the theoretical properties and clustering performance of the proposed distributions.

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Cohesion and Repulsion in Bayesian Distance Clustering

Cited by 4 publications

References 52 publications

Bayesian cluster analysis

Bayesian cluster analysis

Fast generation of exchangeable sequences of clusters data

Repulsion, chaos, and equilibrium in mixture models

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