We consider the problem of estimating differences in two Gaussian graphical models (GGMs) which are known to have similar structure. The GGM structure is encoded in its precision (inverse covariance) matrix. In many applications one is interested in estimating the difference in two precision matrices to characterize underlying changes in conditional dependencies of two sets of data. Existing methods for differential graph estimation are based on single-attribute (SA) models where one associates a scalar random variable with each node. In multi-attribute (MA) graphical models, each node represents a random vector. In this paper, we analyze a group lasso penalized D-trace loss function approach for differential graph learning from multi-attribute data. An alternating direction method of multipliers (ADMM) algorithm is presented to optimize the objective function. Theoretical analysis establishing consistency in support recovery and estimation in high-dimensional settings is provided. Numerical results based on synthetic as well as real data are presented.

翻译：我们考虑估计两个已知具有相似结构的高斯图模型（GGMs）之间差异的问题。GGM的结构由其精度（逆协方差）矩阵编码。在许多应用中，人们感兴趣的是估计两个精度矩阵之间的差异，以表征两组数据条件依赖关系的潜在变化。现有的差分图估计方法基于单属性（SA）模型，其中每个节点关联一个标量随机变量。而在多属性（MA）图模型中，每个节点表示一个随机向量。本文分析了一种用于从多属性数据中学习差分图的组Lasso惩罚D-trace损失函数方法。我们提出了一种交替方向乘子法（ADMM）算法来优化目标函数。提供了在高维背景下支持恢复和估计一致性的理论分析。还展示了基于合成数据和真实数据的数值实验结果。