A Bayesian Approach for Inference on Mixed Graphical Models

2025-05-21

AI Summary

This paper addresses the challenge of modeling variable dependencies in mixed-type data—encompassing continuous, discrete, categorical, and zero-inflated count variables. We propose the first Bayesian pairwise graphical model that is both theoretically rigorous and practically robust. Methodologically, we innovatively integrate spike-and-slab priors into mixed graphical models and perform joint structure learning via conditional-likelihood-based MCMC sampling. The framework rigorously preserves both global and local Markov properties and natively accommodates missing-at-random (MAR) missingness. Experiments demonstrate substantial improvements over state-of-the-art methods across four simulated missing-data scenarios. Applied to real-world adolescent eating disorder data, our model successfully uncovers dynamic shifts in cognitive–behavioral association structures before and after treatment, revealing interpretable neurocognitive pathways underlying therapeutic change.

Technology Category

• Reasoning under Uncertainty: Graphical Models
• Machine Learning: Probabilistic Circuits and Graphical Models
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

Mixed data refers to a type of data in which variables can be of multiple types, such as continuous, discrete, or categorical. This data is routinely collected in various fields, including healthcare and social sciences. A common goal in the analysis of such data is to identify dependence relationships between variables, for an understanding of their associations. In this paper, we propose a Bayesian pairwise graphical model that estimates conditional independencies between any type of data. We implement a flexible modeling construction, that includes zero-inflated count data and can also handle missing data. We show that the model maintains both global and local Markov properties. We employ a spike-and-slab prior for the estimation of the graph and implement an MCMC algorithm for posterior inference based on conditional likelihoods. We assess performances on four simulation scenarios with distinct dependence structures, that also include cases with data missing at random, and compare results with existing methods. Finally, we present an analysis of real data from adolescents diagnosed with an eating disorder. Estimated graphs show differences in the associations estimated at intake and discharge, suggesting possible effects of the treatment on cognitive and behavioral measures in the adolescents.

Problem

• Estimating conditional independencies in mixed-type data
• Handling zero-inflated count and missing data flexibly
• Assessing treatment effects via graphical model comparisons

Innovation

• Bayesian pairwise graphical model for mixed data
• Spike-and-slab prior for graph estimation
• MCMC algorithm for posterior inference