Gaussian graphical models are usually estimated from unreplicated data. The data are, however, likely to comprise signal and noise. These two cannot be deconvoluted from unreplicated data. Pragmatically, the noise is then ignored in practice. We point out the consequences of this practice for the reconstruction of the conditional independence graph of the signal. Replicated data allow for the deconvolution of signal and noise and the reconstruction of former's conditional independence graph. Hereto we present a penalized Expectation-Maximization algorithm. The penalty parameter is chosen to maximize the F-fold cross-validated log-likelihood. Sampling schemes of the folds from replicated data are discussed. By simulation we investigate the effect of replicates on the reconstruction of the signal's conditional independence graph. Moreover, we compare the proposed method to several obvious competitors. In an application we use data from oncogenomic studies with replicates to reconstruct the gene-gene interaction networks, operationalized as conditional independence graphs. This yields a realistic portrait of the effect of ignoring other sources but sampling variation. In addition, it bears implications on the reproducibility of inferred gene-gene interaction networks reported in literature.

中文翻译：

---

根据具有重复项的数据对高斯图模型进行惩罚估计


高斯图模型通常是根据未重复的数据估计的。然而，数据可能包括信号和噪声。这两者无法从未复制的数据中解卷积。实际上，在实践中噪声被忽略。我们指出了这种做法对重建信号条件独立图的影响。复制数据允许对信号和噪声进行反卷积并重建前者的条件独立图。在此，我们提出了一种惩罚性期望最大化算法。选择惩罚参数以最大化F倍交叉验证对数似然。讨论了复制数据的折叠采样方案。通过模拟，我们研究了重复对信号条件独立图重建的影响。此外，我们将所提出的方法与几个明显的竞争对手进行了比较。在一个应用程序中，我们使用来自肿瘤基因组研究的数据和重复数据来重建基因-基因相互作用网络，并将其操作为条件独立图。这产生了忽略其他来源但采样变化的影响的真实描述。此外，它对文献中报道的推断基因-基因相互作用网络的可重复性也有影响。