Estimation of Markov Random Field and covariance models from high-dimensional
data represents a canonical problem that has received a lot of attention in the
literature. A key assumption, widely employed, is that of {\em sparsity} of the
underlying model. In this paper, we study the problem of estimating such models
exhibiting a more intricate structure comprising simultaneously of {\em sparse,
structured sparse} and {\em dense} components. Such structures naturally arise
in several scientific fields, including molecular biology, finance, and
political science. We introduce a general framework based on a novel structured
norm that enables us to estimate such complex structures from high-dimensional
data. The resulting optimization problem is convex and we introduce a
linearized multi-block alternating direction method of multipliers (ADMM)
algorithm to solve it efficiently. We illustrate the superior performance of
the proposed framework on a number of synthetic data sets generated from both
random and structured networks. Further, we apply the method to a number of
real data sets and discuss the results.

通过提出一种基于新型结构规范的通用框架，以及使用线性化的多块交替方向乘数法算法来高效地解决该问题，我们研究了从高维数据中估计稀疏、结构稀疏和密集组件的模型。在合成和实际数据集上的实验证实了这种方法的优越性。