Gaussian graphical models are nowadays commonly applied to the comparison of groups sharing the same variables, by jointy learning their independence structures. We consider the case where there are exactly two dependent groups and the association structure is represented by a family of coloured Gaussian graphical models suited to deal with paired data problems. To learn the two dependent graphs, together with their across-graph association structure, we implement a fused graphical lasso penalty. We carry out a comprehensive analysis of this approach, with special attention to the role played by some relevant submodel classes. In this way, we provide a broad set of tools for the application of Gaussian graphical models to paired data problems. These include results useful for the specification of penalty values in order to obtain a path of lasso solutions and an ADMM algorithm that solves the fused graphical lasso optimization problem. Finally, we present an application of our method to cancer genomics where it is of interest to compare cancer cells with a control sample from histologically normal tissues adjacent to the tumor. All the methods described in this article are implemented in the $\texttt{R}$ package $\texttt{pdglasso}$ availabe at: https://github.com/savranciati/pdglasso.

翻译：高斯图模型现今常被应用于比较共享相同变量的组群，通过联合学习其独立性结构。我们考虑恰好存在两个相依组群的情况，其关联结构由一系列适用于处理配对数据问题的着色高斯图模型表示。为学习这两个相依图及其跨图关联结构，我们实现了融合图套索惩罚。我们对该方法进行了全面分析，特别关注某些相关子模型类别所起的作用。通过这种方式，我们为高斯图模型在配对数据问题中的应用提供了一套广泛的工具。这些工具包括有助于设定惩罚值以获得套索解路径的结果，以及解决融合图套索优化问题的ADMM算法。最后，我们将该方法应用于癌症基因组学，旨在比较癌细胞与肿瘤相邻组织学正常组织的对照样本。本文所述的所有方法均实现在$\texttt{R}$软件包$\texttt{pdglasso}$中，可通过https://github.com/savranciati/pdglasso获取。