Individual-Specific Gaussian Graphical Models for Heterogeneous Populations with Application to Epigenetic Gene Regulation in Lung Adenocarcinoma

Inter-patient molecular heterogeneity is a fundamental challenge in precision oncology: population-level multi-omics networks reveal average biology aggregated across the population but obscure individual variations that drive differential clinical outcomes. We introduce SIREN (Sample-specific Inference via Regularized Empirical-Bayes Networks), a method that estimates one partial correlation network per sample across omics layers by combining a population-level empirical Bayes prior with a rank-1 individual-specific update. Since a sample-specific precision matrix cannot be estimated from a single observation, SIREN uses a conjugate Inverse Wishart prior whose mean is the Oracle Approximating Shrinkage estimator, yielding closed-form individual-specific posteriors without MCMC. On simulated heterogeneous populations, SIREN achieves superior edge recovery over population-average methods including OAS, Ledoit-Wolf, and graphical Lasso, while remaining competitive in homogeneous settings. Applied to paired transcriptomic and methylomic profiles from lung adenocarcinoma, SIREN identifies individual-specific gene-methylation regulatory edges that stratify patients by survival in ways population-level analysis cannot, implicating chromatin remodeling and WNT signaling pathways in epigenetic heterogeneity. SIREN is computationally scalable and available as a Python package.