Regularized estimation of large-scale gene association networks using graphical Gaussian models.
Regularized estimation of large-scale gene association networks using graphical Gaussian models.
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DOI：
10.1186/1471-2105-10-384
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发表时间：
2009-11-24
影响因子：
3
通讯作者：
Boulesteix AL
中科院分区：
文献类型：
--
作者：
Krämer N;Schäfer J;Boulesteix AL
图形高斯模型是从微阵列数据中估计(非定向)基因关联网络的流行工具。当变量数量大大超过样本数量时，一个关键问题是部分相关矩阵的估计。在这种情况下，由于样本协方差矩阵的(Moore-Penrose)逆导致较差的估计，标准方法是不合适的，需要适当的正则化技术。流行的方法包括协方差矩阵的有偏估计和高维回归方案，如套索和偏最小二乘法。在这篇文章中，我们研究了一个将正则化回归方法与图形高斯模型估计相结合的通用框架。该框架包括现有的各种方法以及分别基于岭回归和自适应套索的两种新方法。这些方法在模拟研究中和通过对六个不同的真实数据集的应用进行了定性和定量的广泛比较。此外，所有提出的算法都在R包“parcor”中实现，该包可从R库CRAN获得。在我们的仿真研究中，所研究的非稀疏回归方法，即岭回归和偏最小二乘，在结合(局部)错误发现率多重测试来确定网络中是否存在边时，表现出相当保守的行为。对于密度较高的网络，这两种方法的性能差异减小。对于稀疏网络，我们确认了套索选择过多边的众所周知的倾向，而两阶段自适应套索是一个有趣的替代方案，它提供了更稀疏的解决方案。在我们的模拟中，稀疏和非稀疏方法都能够重建具有簇结构的网络。在六个真实数据集上，我们也清楚地区分了非稀疏方法和稀疏方法的结果，其中正则化参数的指定自动意味着模型的选择。在六个数据集中的五个中，偏最小二乘法选择非常密集的网络。此外，对于违反不相关观测假设的数据(由于重复)，套索和自适应套索产生非常复杂的结构，这表明它们在这些条件下可能不适合。当使用二次抽样时，收缩方法比基于回归的方法更稳定。
Graphical Gaussian models are popular tools for the estimation of (undirected) gene association networks from microarray data. A key issue when the number of variables greatly exceeds the number of samples is the estimation of the matrix of partial correlations. Since the (Moore-Penrose) inverse of the sample covariance matrix leads to poor estimates in this scenario, standard methods are inappropriate and adequate regularization techniques are needed. Popular approaches include biased estimates of the covariance matrix and high-dimensional regression schemes, such as the Lasso and Partial Least Squares. In this article, we investigate a general framework for combining regularized regression methods with the estimation of Graphical Gaussian models. This framework includes various existing methods as well as two new approaches based on ridge regression and adaptive lasso, respectively. These methods are extensively compared both qualitatively and quantitatively within a simulation study and through an application to six diverse real data sets. In addition, all proposed algorithms are implemented in the R package "parcor", available from the R repository CRAN. In our simulation studies, the investigated non-sparse regression methods, i.e. Ridge Regression and Partial Least Squares, exhibit rather conservative behavior when combined with (local) false discovery rate multiple testing in order to decide whether or not an edge is present in the network. For networks with higher densities, the difference in performance of the methods decreases. For sparse networks, we confirm the Lasso's well known tendency towards selecting too many edges, whereas the two-stage adaptive Lasso is an interesting alternative that provides sparser solutions. In our simulations, both sparse and non-sparse methods are able to reconstruct networks with cluster structures. On six real data sets, we also clearly distinguish the results obtained using the non-sparse methods and those obtained using the sparse methods where specification of the regularization parameter automatically means model selection. In five out of six data sets, Partial Least Squares selects very dense networks. Furthermore, for data that violate the assumption of uncorrelated observations (due to replications), the Lasso and the adaptive Lasso yield very complex structures, indicating that they might not be suited under these conditions. The shrinkage approach is more stable than the regression based approaches when using subsampling.
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影响因子：
7
作者：
Ma, Shisong;Gong, Qingqiu;Bohnert, Hans J.
通讯作者：
Bohnert, Hans J.
影响因子：
9.5
作者：
Boulesteix, Anne-Laure;Strimmer, Korbinian
通讯作者：
Strimmer, Korbinian
影响因子：
2.1
作者：
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5.8
作者：
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作者：
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通讯作者：
Zhu, Ji