Robust Heterogeneity Adjustment for Gaussian Graphical Model With Latent Variables

Graphical models serve as fundamental tools for encoding conditional dependence structures in multivariate biological data, with latent variable Gaussian graphical models playing a pivotal role in capturing complex dependencies in the presence of unobserved confounding variables. However, practical implementations often face two critical challenges: systematic heterogeneity arising from unobserved subpopulations (e.g., tumor subtypes, cell clusters, or patient stratifications) and outliers (e.g., technical artifacts or rare phenotypic variations), both of which can substantially distort the underlying network structure. To address these issues, we extend the latent variable Gaussian graphical model by integrating a mixture model, proposing a robust framework tailored for data heterogeneity. The proposed method can simultaneously achieve network structure estimation (after removing shared effects from latent variables), outlier detection, and subgroup membership identification. An effective computational algorithm is developed. Extensive experimental evaluations demonstrate that the proposed method offers a reliable graphical estimate in the presence of heterogeneity, maintaining robustness even against a significant proportion of outliers. The heterogeneity analysis of a breast cancer dataset further illustrates the practical applicability of the proposed approach and its sound biological implications.