Study of across-graph association in Gaussian graphical models for paired data

The subject of this work is the family of coloured graphical models, which are graphical models characterized by the presence of symmetries between edges and vertices. A particular interest is given to a subfamily of coloured graphical models, called pdRCON models, used in the paired data setting, meaning graphs comprised of two groups that are dependent of each other. The graphical lasso for paired data, developed by Ranciati & Roverato (2024a), provides a method for model selection within the pdRCON family. The main objective is to evaluate the impact of across-graph association assumptions on inference for each group-specific subgraph. To do so, a simulation study investigates whether performance measures about structure recovery and accuracy estimation of the two groups vary with these assumptions. Some differences can emerge, especially in the scenarios with higher graph density and more symmetries; however, due to the high computational cost of the model selection procedure, a limited iterations number results in considerable variability. pdRCON subclasses with different across-graph structure are then applied to a high-dimensional, real-world dataset on breast cancer gene expression. The models obtained, characterized by low graph density, show few differences across the two group-level subgraphs, particularly when using eBIC for model selection.