We consider the problem of inferring the conditional independence graph (CIG) of high-dimensional Gaussian vectors from multi-attribute data. Most existing methods for graph estimation are based on single-attribute models where one associates a scalar random variable with each node. In multi-attribute graphical models, each node represents a random vector. In this paper, we present a sparse-group lasso based penalized log-likelihood approach for graph learning from multi-attribute data. Existing works on multi-attribute graphical modeling have considered only group lasso penalty. The main objective of this paper is to explore the use of sparse-group lasso for multi-attribute graph estimation. An alternating direction method of multipliers (ADMM) algorithm is presented to optimize the objective function to estimate the inverse covariance matrix. Sufficient conditions for consistency and sparsistency of the estimator are provided. Numerical results based on synthetic as well as real data are presented.

中文翻译：

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稀疏组套索，用于从多属性数据中学习图形

我们考虑了从多属性数据中推论高维高斯向量的条件独立图（CIG）的问题。大多数现有的图估计方法都是基于单属性模型，其中将标量随机变量与每个节点相关联。在多属性图形模型中，每个节点代表一个随机向量。在本文中，我们提出了一种基于稀疏组套索的惩罚对数似然方法，用于从多属性数据中学习图。现有的关于多属性图形建模的工作仅考虑了组套索惩罚。本文的主要目的是探索稀疏组套索在多属性图估计中的应用。提出了一种交替方向乘数法（ADMM）算法，以优化目标函数来估计逆协方差矩阵。提供了用于估计器一致性和稀疏性的充分条件。给出了基于合成数据和实际数据的数值结果。