Learning Covariate-Dependent Gene Networks

Title:

Learning Covariate-Dependent Gene Networks 

Abstract: 
In many genomic studies, gene co-expression networks are shaped by subject-level covariates such as single nucleotide polymorphisms (SNPs). Traditional Gaussian graphical models, however, estimate only population-level networks and ignore these covariate effects, potentially obscuring important heterogeneity across individuals. To address this limitation, we develop covariate-dependent Gaussian graphical regression models, which directly regress the precision matrix on covariates to characterize how network structures vary with high-dimensional subject-specific features.

To estimate the model efficiently, we propose a multi-task learning framework that achieves lower estimation error than node-wise regressions. Yet, statistical inference for such models remains largely unexplored. We therefore introduce a class of debiased estimators based on multi-task learners, which can be computed independently and efficiently. A key methodological contribution is a novel projection technique for estimating the inverse covariance matrix, reducing computational complexity to scale linearly with the sample size n. The resulting estimators exhibit fast convergence and asymptotic normality, enabling valid inference. Simulation studies demonstrate strong empirical performance, and an application to a brain cancer gene-expression dataset reveals biologically meaningful network patterns.