Supervised Heterogeneous Gaussian Graphical Models

Mixture regression models are widely employed for analyzing heterogeneous data. Currently, network-based heterogeneity analysis methods predominantly focus on unsupervised learning, intending to uncover subgroup structures within data and estimate multiple graphs/networks. However, in many real-world scenarios, there is a significant emphasis on both prediction performance of the model and meaningful interpretation of the identified subgroups. In this study, we propose a supervised heterogeneous Gaussian graphical model that accommodates both continuous and discrete response variables. A high-dimensional expectation-conditional-maximization (ECM) algorithm is developed for estimation. We provide a non-asymptotic statistical analysis of the outputs generated from the ECM algorithm. Additionally, numerical studies are conducted to demonstrate the superior performance of our approach, which is further illustrated through an analysis of spectrometric data. Supplementary materials are available online.