Cai T Tony, Li Hongzhe, Liu Weidong, Xie Jichun
Professor of Statistics, Department of Statistics, The Wharton School, University of Pennsylvania, Philadelphia, PA 19104.
Professor of Biostatistics, University of Pennsylvania Perelman School of Medicine, Philadelphia, PA 19104.
Stat Sin. 2016 Apr;26(2):445-464. doi: 10.5705/ss.2014.256.
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 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.
受在不同组织或疾病状态下测量的基因表达数据分析的推动，我们考虑对多个精度矩阵进行联合估计，以有效利用相应图形的部分共享图形结构。该过程基于加权约束最小化，可通过二阶锥规划有效实现。与单独估计方法相比，所提出的联合估计方法导致估计器更快地收敛到真实精度矩阵。在某些正则性条件下，所提出的过程导致以趋于1的概率精确恢复图形结构。模拟研究表明，所提出的联合估计方法在图形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，预后不良亚型的患者在凋亡途径中的基因之间缺乏一些重要联系。
