Bayesian Dynamic Clustering Factor Models

2025-05-27

AI Summary

This paper addresses the challenge of modeling multivariate longitudinal data by proposing a Bayesian framework that integrates dynamic factor models with hidden Markov models, enabling simultaneous dimensionality reduction, individual clustering, and inference of dynamic transitions among clusters. Its key innovation lies in embedding a factor structure directly into the evolution of latent states—marking the first such formulation—thereby allowing cluster definitions to vary over time. Parameter estimation and clustering are jointly learned via Gibbs sampling. In simulation studies, the method accurately recovers true parameters and group structures. Applied to a real-world cohort of individuals with opioid use disorder, it identifies clinically interpretable patient subtypes and their time-varying transition pathways. These results provide a statistically rigorous foundation for precision phenotyping and optimal timing of clinical interventions.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Bayesian Learning
• Intelligent Robots: State Estimation

Application Category

• User Modeling, Personalization and Recommendation: Studies of user behavior, including longitudinal effects of personalized systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution

Abstract

We propose novel Bayesian Dynamic Clustering Factor Models (BDCFM) for the analysis of multivariate longitudinal data. BDCFM combines factor models with hidden Markov models to concomitantly perform dimension reduction, clustering, and estimation of the dynamic transitions of subjects through clusters. We develop an efficient Gibbs sampler for exploration of the posterior distribution. An analysis of a simulated dataset shows that our inferential approach works well both at parameter estimation and clustering of subjects. Finally, we illustrate the utility of our BDCFM with an analysis of a dataset on opioid use disorder.

Problem

• Develops Bayesian Dynamic Clustering Factor Models for multivariate longitudinal data
• Combines factor models and hidden Markov models for dimension reduction and clustering
• Estimates dynamic transitions of subjects through clusters using Gibbs sampling

Innovation

• Combines factor models with hidden Markov models
• Performs dimension reduction and dynamic clustering
• Uses efficient Gibbs sampler for posterior exploration