High-Dimensional Semiparametric Analysis of Differential Network Analysis for Matrix-Variate

Differential network analysis provides a powerful framework for characterizing how biological networks change across different conditions or external stimuli. With recent advances in high-throughput technologies, matrix-valued data have become increasingly common in biostatistics and medical research. However, most existing differential network methods are designed for vector-valued observations. As a result, they do not fully exploit the structural information inherent in matrix-valued data. In addition, many of these approaches rely on multivariate normality, an assumption that is often violated in practice, motivating the need for robust inference procedures. In this paper, we develop a semiparametric matrix-variate differential network model that accommodates heavy-tailed or non-Gaussian data distributions. We introduce a rank-based D-trace loss with an ℓ1 penalty to directly estimate the spatial differential partial correlation matrix. The resulting optimization problem is solved using an efficient ADMM algorithm. We establish the theoretical properties of the proposed estimator, including its consistency under high-dimensional scaling. Extensive simulation studies and real-data analyses further demonstrate that our robust procedure substantially outperforms existing non-robust alternatives.