We propose a new method to learn the structure of a Gaussian graphical model with finite sample false discovery rate control. Our method builds on the knockoff framework of Barber and Candès for linear models. We extend their approach to the graphical model setting by using a local (node-based) and a global (graph-based) step: we construct knockoffs and feature statistics for each node locally, and then solve a global optimization problem to determine a threshold for each node. We then estimate the neighbourhood of each node, by comparing its feature statistics to its threshold, resulting in our graph estimate. Our proposed method is very flexible, in the sense that there is freedom in the choice of knockoffs, feature statistics and the way in which the final graph estimate is obtained. For any given data set, it is not clear a priori what choices of these hyperparameters are optimal. We therefore use a sample-splitting-recycling procedure that first uses half of the samples to select the hyperparameters, and then learns the graph using all samples, in such a way that the finite sample FDR control still holds. We compare our method to several competitors in simulations and on a real data set.

中文翻译：

---

GGM 仿冒滤波器：高斯图形模型的错误发现率控制

我们提出了一种新方法来学习具有有限样本错误发现率控制的高斯图模型的结构。我们的方法建立在 Barber 和 Candès 的线性模型仿冒框架之上。我们通过使用局部（基于节点）和全局（基于图）步骤将他们的方法扩展到图形模型设置：我们在本地为每个节点构建仿制品和特征统计，然后解决全局优化问题以确定阈值对于每个节点。然后我们通过将每个节点的特征统计与其阈值进行比较来估计每个节点的邻域，从而得到我们的图估计。我们提出的方法非常灵活，因为在选择仿冒品、特征统计和获得最终图估计的方式方面存在自由。对于任何给定的数据集，尚不清楚这些超参数的哪些选择是最佳的。因此，我们使用样本分割再循环过程，首先使用一半样本来选择超参数，然后使用所有样本学习图形，这样有限样本 FDR 控制仍然有效。我们在模拟和真实数据集上将我们的方法与几个竞争对手进行比较。