Profile Graphical Models

2026-03-30

AI Summary

This study addresses the challenge of modeling how external risk factors influence multivariate conditional independence structures within a unified graphical framework. To this end, the authors propose a novel class of models termed “profile graphical models,” formally defining this family for the first time and showing that both multigraphs and chain graphs arise as special cases. They further establish the compatibility of profile graphical models with the independence interpretation of two-block LWF chain graphs. Building upon a continuous spike-and-slab prior, they develop a Bayesian inference procedure for Gaussian undirected profile graphical models and devise an efficient EM algorithm for implementation. Empirical evaluations on both synthetic data and protein signaling networks in acute myeloid leukemia demonstrate that the proposed model yields more parsimonious network representations and significantly improves the capture of patient heterogeneity compared to existing approaches.

Abstract

We introduce a novel class of graphical models, termed profile graphical models, that represent, within a single graph, how an external factor influences the dependence structure of a multivariate set of variables. This class is quite general and includes multiple graphs and chain graphs as special cases. Profile graphical models capture the conditional distributions of a multivariate random vector given different levels of a risk factor, and learn how the conditional independence structure among variables may vary across these risk profiles; we formally define this family of models and establish their corresponding Markov properties. We derive key structural and probabilistic properties that underpin a more powerful inferential framework than existing approaches, underscoring that our contribution extends beyond a novel graphical representation.Furthermore, we show that the resulting profile undirected graphical models are independence-compatible with two-block LWF chain graph models.We then develop a Bayesian approach for Gaussian undirected profile graphical models based on continuous spike-and-slab priors to learn shared sparsity structures across different levels of the risk factor. We also design a fast EM algorithm for efficient inference. Inferential properties are explored through simulation studies, including the comparison with competing methods. The practical utility of this class of models is demonstrated through the analysis of protein network data from various subtypes of acute myeloid leukemia. Our results show a more parsimonious network and greater patient heterogeneity than its competitors, highlighting its enhanced ability to capture subject-specific differences.

Problem

• profile graphical models
• conditional independence
• risk factor
• multivariate dependence
• graphical representation

Innovation

• profile graphical models
• conditional independence
• spike-and-slab priors
• EM algorithm
• heterogeneous networks