Selection of the Regularization Parameter in Graphical Models Using Network Characteristics
Selection of the Regularization Parameter in Graphical Models Using Network Characteristics
复制标题
利用网络特性选择图模型中的正则化参数
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
C. Mayer
中科院分区：
文献类型：
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作者：
Adrià Caballé Mestres;N. Bochkina;C. Mayer
抽象的高斯图形模型代表随机变量之间条件依赖性的基础图结构，可以使用其部分相关或精确矩阵确定。在高维设置中，通过添加惩罚项来估算精度矩阵，该矩阵通过添加惩罚项来控制精度矩阵中的稀疏性量，并完全表征图形的复杂性和结构。最常用的惩罚项是由正则化参数缩放的精度矩阵的L1规范，该矩阵确定了图形的稀疏性与数据拟合之间的权衡。在本文中，我们提出了几个过程，以在图形模型的估计中选择正则化参数，这些过程侧重于可靠地恢复图形的适当网络结构。我们进行了广泛的仿真研究，以表明所提出的方法为不同的网络拓扑产生了有用的结果。这些方法还应用于基因表达数据的高维案例研究，目的是发现与结肠癌相关的基因。使用这些数据，我们找到了图形结构，这些结构经过验证以显示重要的生物学基因关联。补充材料可在线获得。
ABSTRACT Gaussian graphical models represent the underlying graph structure of conditional dependence between random variables, which can be determined using their partial correlation or precision matrix. In a high-dimensional setting, the precision matrix is estimated using penalized likelihood by adding a penalization term, which controls the amount of sparsity in the precision matrix and totally characterizes the complexity and structure of the graph. The most commonly used penalization term is the L1 norm of the precision matrix scaled by the regularization parameter, which determines the trade-off between sparsity of the graph and fit to the data. In this article, we propose several procedures to select the regularization parameter in the estimation of graphical models that focus on recovering reliably the appropriate network structure of the graph. We conduct an extensive simulation study to show that the proposed methods produce useful results for different network topologies. The approaches are also applied in a high-dimensional case study of gene expression data with the aim to discover the genes relevant to colon cancer. Using these data, we find graph structures, which are verified to display significant biological gene associations. Supplementary material is available online.
DOI：
10.1073/pnas.95.25.14863
发表时间：
1998-12-08
影响因子：
11.1
作者：
Eisen, MB;Spellman, PT;Botstein, D
通讯作者：
Botstein, D