Bayesian clustering of high-dimensional data via latent repulsive mixtures

• 成果类型: Article
• 署名作者: Ghilotti, L.; Beraha, M.; Guglielmi, A.
• 署名单位: University of Milano-Bicocca; Polytechnic University of Milan
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asae059
• 发表日期: 2025
• 关键词: determinantal point-processes; distributions; inference

摘要

Model-based clustering of moderate- or large-dimensional data is notoriously difficult. We propose a model for simultaneous dimensionality reduction and clustering by assuming a mixture model for a set of latent scores, which are then linked to the observations via a Gaussian latent factor model. This approach was recently investigated by Chandra et al. (2023). The authors used a factor-analytic representation and assumed a mixture model for the latent factors. However, performance can deteriorate in the presence of model misspecification. Assuming a repulsive point process prior for the component-specific means of the mixture for the latent scores is shown to yield a more robust model that outperforms the standard mixture model for the latent factors in several simulated scenarios. The repulsive point process must be anisotropic to favour well-separated clusters of data, and its density should be tractable for efficient posterior inference. We address these issues by proposing a general construction for anisotropic determinantal point processes. We illustrate our model in simulations, as well as a plant species co-occurrence dataset.