NETWORK EXPLORATION VIA THE ADAPTIVE LASSO AND SCAD PENALTIES
NETWORK EXPLORATION VIA THE ADAPTIVE LASSO AND SCAD PENALTIES
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DOI：
10.1214/08-aoas215
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发表时间：
2009-06-01
影响因子：
1.8
通讯作者：
Wu, Yichao
中科院分区：
文献类型：
--
作者：
Fan, Jianqing;Feng, Yang;Wu, Yichao
图形模型经常被用来探索网络，如遗传网络，在一组变量中。这通常是通过探索所考虑的变量的精度矩阵的稀疏性来进行的。惩罚似然法常用于此类探索。然而，精度矩阵的正定性约束使得优化问题具有挑战性。我们引入了非凹惩罚和自适应LASSO惩罚来减弱网络估计中的偏差问题。通过对非凹罚函数的局部线性逼近，将精度矩阵估计问题重新转换为具有加权L-1罚的惩罚似然问题序列，并使用Friedman等人的有效算法[Biostatistics 9（2008）432-441]求解。我们的估计方案适用于两个真实的数据集。仿真实验和渐近理论被用来证明我们提出的方法。
Graphical models are frequently used to explore networks, such as genetic networks, among a set of variables. This is usually carried out via exploring the sparsity of the precision matrix of the variables under consideration. Penalized likelihood methods are often used in such explorations. Yet, positive-definiteness constraints of precision matrices make the optimization problem challenging. We introduce nonconcave penalties and the adaptive LASSO penalty to attenuate the bias problem in the network estimation. Through the local linear approximation to the nonconcave penalty functions, the problem of precision matrix estimation is recast as a sequence of penalized likelihood problems with a weighted L-1 penalty and solved using the efficient algorithm of Friedman et al. [Biostatistics 9 (2008) 432-441]. Our estimation schemes are applied to two real datasets. Simulation experiments and asymptotic theory are used to justify our proposed methods.