Motivated by analysis of gene expression data measured in different tissues or disease states, we consider joint estimation of multiple precision matrices to effectively utilize the partially shared graphical structures of the corresponding graphs. The procedure is based on a weighted constrained ℓ∞/ℓ1 minimization, which can be effectively implemented by a second-order cone programming. Compared to separate estimation methods, the proposed joint estimation method leads to estimators converging to the true precision matrices faster. Under certain regularity conditions, the proposed procedure leads to an exact graph structure recovery with a probability tending to 1. Simulation studies show that the proposed joint estimation methods outperform other methods in graph structure recovery. The method is illustrated through an analysis of an ovarian cancer gene expression data. The results indicate that the patients with poor prognostic subtype lack some important links among the genes in the apoptosis pathway.

中文翻译：

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多个高维精度矩阵的联合估计


通过分析不同组织或疾病状态下测量的基因表达数据，我们考虑联合估计多个精度矩阵，以有效利用相应图的部分共享图形结构。该过程基于加权约束 ℓ∞/ℓ1 最小化，可以通过二阶锥规划有效地实现。与单独的估计方法相比，所提出的联合估计方法使估计器更快地收敛到真实精度矩阵。在一定的规律性条件下，所提出的过程导致精确的图结构恢复，概率趋于1。仿真研究表明，所提出的联合估计方法在图结构恢复方面优于其他方法。通过对卵巢癌基因表达数据的分析来说明该方法。结果表明，预后不良亚型患者的凋亡通路中的基因之间缺乏一些重要的联系。