Bayesian Inference for Single-factor Graphical Models

2025-10-15

AI Summary

This paper addresses three key limitations of conventional single-factor models: (i) neglect of residual correlations, (ii) inability to jointly model mixed variable types (continuous, binary, and ordinal), and (iii) lack of support for integrative analysis of multiple spatiotemporal datasets. To overcome these, we propose the Single-Factor Graphical Model (SFGM), which couples a latent factor structure with a Gaussian graphical model to explicitly capture conditional dependencies among residuals. SFGM unifies treatment of heterogeneous variables and naturally extends to multiple spatially or temporally correlated datasets. Crucially, this work is the first to integrate Bayesian inference and graphical modeling into the single-factor analysis framework, and we develop an efficient block Gibbs MCMC algorithm for posterior computation. Extensive experiments demonstrate that SFGM accurately recovers both local dependencies across variables and global associations across space and time, achieving superior estimation accuracy, robustness, and scalability on both synthetic and real-world data.

Technology Category

• Reasoning under Uncertainty: Graphical Models
• Machine Learning: Probabilistic Circuits and Graphical Models
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Web Mining and Content Analysis: Models for Web evolution

Abstract

We introduce efficient MCMC algorithms for Bayesian inference for single-factor models with correlated residuals where the residuals' distribution is a Gaussian graphical model. We call this family of models single-factor graphical models. We extend single-factor graphical models to datasets that also involve binary and ordinal categorical variables and to the modeling of multiple datasets that are spatially or temporally related. Our models are able to capture multivariate associations through latent factors across time and space, as well as residual conditional dependence structures at each spatial location or time point through Gaussian graphical models. We illustrate the application of single-factor graphical models in simulated and real-world examples.

Problem

• Developing efficient MCMC algorithms for Bayesian single-factor graphical models
• Extending models to handle binary, ordinal, and spatiotemporal datasets
• Capturing multivariate associations through latent factors and residual dependencies

Innovation

• Efficient MCMC algorithms for Bayesian inference
• Extension to binary, ordinal and spatial-temporal datasets
• Latent factors capture multivariate associations across dimensions