Module-Structured Mixture Factor Models to Identify Outcome-Specific Signatures in Gene Expression Data

Abstract

High-throughput gene expression data exhibit high dimensionality, complex intergene dependence, and pronounced biological heterogeneity across samples, presenting major challenges for unsupervised clustering and disease subtype discovery. We introduce a module-structured mixture factor model that combines finite mixture modelling with low-rank latent factor representations defined at the gene-module level. By explicitly modelling gene modules in both the mean and covariance structure, the proposed framework decomposes expression variability into global gene-specific effects, cluster-specific module-level shifts, latent dependence within modules, and gene-specific residual noise. An Expectation--Conditional Maximisation algorithm is developed for parameter estimation, allowing stable and scalable inference in high-dimensional transcriptomic settings. This framework enables interpretable unsupervised identification of disease-associated molecular subtypes and phenotypic heterogeneity across two autoimmune diseases using a large clinical transcriptomic dataset.