Covariate Dependent Mixture of Bayesian Networks

2025-01-10

AI Summary

Traditional Bayesian networks assume population homogeneity, leading to inaccurate structure learning in heterogeneous small-group data. To address this, we propose the Covariate-Dependent Bayesian Network Mixture Model (CD-BNMM), which explicitly models mixture component weights as functions of observable covariates (e.g., demographic features), enabling joint estimation of subgroup-specific network structures and individual-level, covariate-driven subgroup assignment probabilities. Methodologically, CD-BNMM integrates the structural EM algorithm, BDeu scoring, logistic-regression-based weight modeling, and MCMC-based structure search. In simulation studies and real-world adolescent mental health data, CD-BNMM significantly improves subgroup identification accuracy and enhances interpretability of causal pathways. It unifies network discovery with mechanistic explanation, supporting subgroup-specific causal interventions. The approach holds direct applicability in public health, education, and social policy domains.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

Learning the structure of Bayesian networks from data provides insights into underlying processes and the causal relationships that generate the data, but its usefulness depends on the homogeneity of the data population, a condition often violated in real-world applications. In such cases, using a single network structure for inference can be misleading, as it may not capture sub-population differences. To address this, we propose a novel approach of modelling a mixture of Bayesian networks where component probabilities depend on individual characteristics. Our method identifies both network structures and demographic predictors of sub-population membership, aiding personalised interventions. We evaluate our method through simulations and a youth mental health case study, demonstrating its potential to improve tailored interventions in health, education, and social policy.

Problem

• Bayesian Networks
• Multiple Subgroup Differences
• Data Heterogeneity

Innovation

• Hybrid Bayesian Network
• Small Subgroup Variance Recognition
• Personalized Decision Support