On Sparse Complex Gaussian Graphical Model Selection
On Sparse Complex Gaussian Graphical Model Selection
复制标题
稀疏复杂高斯图模型选择
DOI：
10.1109/mlsp.2019.8918691
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
Jitendra Tugnait
中科院分区：
文献类型：
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作者：
Jitendra Tugnait
研究了稀疏高维真复值高斯图模型（CGGM）的条件独立图（CIG）的估计问题。与具有p个顶点的无向图相关联的p变量CGGM被定义为服从由图的边集所隐含的条件独立性限制的复高斯分布族。本文的重点是理论分析最近提出的图形套索方法的基础上$\ell_{1} -$惩罚对数似然目标函数估计稀疏逆协方差矩阵。给出了逆协方差估计的相合性和稀疏性的充分条件。
We consider the problem of estimating the conditional independence graph (CIG) of a sparse, high-dimensional proper complex-valued Gaussian graphical model (CGGM). A p-variate CGGM associated with an undirected graph with p vertices is defined as the family of complex Gaussian distributions that obey the conditional independence restrictions implied by the edge set of the graph. The focus of this paper is on theoretical analysis of a recently proposed graphical lasso approach based on an $\ell_{1} -$penalized log-likelihood objective function to estimate the sparse inverse covariance matrix. Sufficient conditions for consistency and sparsistency of the inverse covariance estimator are provided.