Revealing biological networks is one key objective in systems biology. With microarrays, researchers now routinely measure expression profiles at the genome level under various conditions, and such data may be used to statistically infer gene regulation networks. Gaussian graphical models (GGMs) have proven useful for this purpose by modeling the Markovian dependence among genes. However, a single GGM may not be adequate to describe the potentially differing networks across various conditions, and hence it is more natural to infer multiple GGMs from such data. In this article we propose a class of nonconvex penalty functions aiming at the estimation of multiple GGMs with a flexible joint sparsity constraint. We illustrate the property of our proposed nonconvex penalty functions by simulation study. We then apply the method to a gene expression dataset from the GenCord Project, and show that our method can identify prominent pathways across different conditions. Supplementary materials for this article are available online.

中文翻译：

---

具有联合稀疏高斯图形模型的基因调控网络推理

揭示生物网络是系统生物学的一个关键目标。借助微阵列，研究人员现在可以在各种条件下定期测量基因组水平的表达谱，这些数据可用于统计推断基因调控网络。高斯图形模型 (GGM) 已通过对基因之间的马尔可夫依赖性建模来证明可用于此目的。然而，单个 GGM 可能不足以描述各种条件下潜在的不同网络，因此从此类数据推断多个 GGM 更为自然。在本文中，我们提出了一类非凸惩罚函数，旨在通过灵活的联合稀疏约束来估计多个 GGM。我们通过模拟研究说明了我们提出的非凸惩罚函数的特性。然后，我们将该方法应用于来自 GenCord 项目的基因表达数据集，并表明我们的方法可以识别不同条件下的突出途径。本文的补充材料可在线获取。