Bayesian Clustering via Fusing of Localized Densities

• 成果类型: Article; Early Access
• 署名作者: Dombowsky, Alexander; Dunson, David B.
• 署名单位: Duke University; Duke University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2024.2427935
• 发表日期: 2024
• 关键词: mixture-models; convergence-rates; strong identifiability; parameter-estimation; dirichlet mixtures; mixing measures; Finite; components; number; CLASSIFICATION

摘要

Bayesian clustering typically relies on mixture models, with each component interpreted as a different cluster. After defining a prior for the component parameters and weights, Markov chain Monte Carlo (MCMC) algorithms are commonly used to produce samples from the posterior distribution of the component labels. The data are then clustered by minimizing the expectation of a clustering loss function that favors similarity to the component labels. Unfortunately, although these approaches are routinely implemented, clustering results are highly sensitive to kernel misspecification. For example, if Gaussian kernels are used but the true density of data within a cluster is even slightly non-Gaussian, then clusters will be broken into multiple Gaussian components. To address this problem, we develop Fusing of Localized Densities (FOLD), a novel clustering method that melds components together using the posterior of the kernels. FOLD has a fully Bayesian decision theoretic justification, naturally leads to uncertainty quantification, can be easily implemented as an add-on to MCMC algorithms for mixtures, and favors a small number of distinct clusters. We provide theoretical support for FOLD including clustering optimality under kernel misspecification. In simulated experiments and real data, FOLD outperforms competitors by minimizing the number of clusters while inferring meaningful group structure. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.