Sparse graphical modelling has attained widespread attention across various academic fields. We propose two new graphical model approaches, Gslope and Tslope, which provide sparse estimates of the precision matrix by penalizing its sorted L1-norm, and relying on Gaussian and T-student data, respectively. We provide the selections of the tuning parameters which provably control the probability of including false edges between the disjoint graph components and empirically control the False Discovery Rate for the block diagonal covariance matrices. In extensive simulation and real world analysis, the new methods are compared to other state-of-the-art sparse graphical modelling approaches. The results establish Gslope and Tslope as two new effective tools for sparse network estimation, when dealing with both Gaussian, t-student and mixture data.

翻译：稀疏图模型已在各学术领域获得广泛关注。本文提出两种新型图模型方法——Gslope和Tslope，分别基于高斯分布和t分布数据，通过惩罚排序L1范数实现精度矩阵的稀疏估计。我们提供了调参选择方案，可证明控制不相关图分量间引入虚假边的概率，并通过经验方法控制块对角协方差矩阵的错误发现率。在大量仿真实验与真实数据分析中，新方法与其他前沿稀疏图模型方法进行了比较。结果表明，Gslope和Tslope在处理高斯分布、t分布及混合数据时，是两种高效的稀疏网络估计新工具。