Abstract Updating of the Gaussian graphical model via shrinkage estimation is studied. This shrinkage is towards a nonzero parameter value representing prior quantitative information. Once new data become available, the previously estimated parameter needs updating. Shrinkage provides the means to this end, using the latter as a shrinkage target to acquire an updated estimate. The process of iteratively updating the Gaussian graphical model in shrinkage fashion is shown to yield an improved fit and an asymptotically unbiased and consistent estimator. The workings of updating via shrinkage are elucidated by linking it to Bayesian updating and through the inheritance by the update of eigen-properties of the previous estimate. The effect of shrinkage on the moments and loss of the estimator are pointed out. Practical issues possibly hampering updating are identified and solutions outlined. The presented updating procedure is illustrated through the reconstruction of a gene–gene interaction network using transcriptomic data.

中文翻译：

---

通过有针对性的惩罚估计更新高斯图模型

摘要 研究了通过收缩估计更新高斯图模型。这种收缩趋向于表示先验定量信息的非零参数值。一旦有新数据可用，先前估计的参数需要更新。收缩为此提供了手段，使用后者作为收缩目标来获取更新的估计。显示以收缩方式迭代更新高斯图形模型的过程会产生改进的拟合和渐近无偏且一致的估计量。通过将收缩更新与贝叶斯更新联系起来并通过更新先前估计的特征属性的继承来阐明通过收缩更新的工作原理。指出了收缩对估计量的矩和损失的影响。确定了可能妨碍更新的实际问题并概述了解决方案。通过使用转录组数据重建基因-基因相互作用网络来说明所提出的更新程序。