In this article, we introduce the concept of confidence graphs (CG) for graphical model selection. CG first identifies two nested graphical models—called small and large confidence graphs (SCG and LCG)—trapping the true graphical model in between at a given level of confidence, just like the endpoints of traditional confidence interval capturing the population parameter. Therefore, SCG and LCG provide us with more insights about the simplest and most complex forms of dependence structure the true model can possibly be, and their difference also offers us a measure of model selection uncertainty. In addition, rather than relying on a single selected model, CG consists of a group of graphical models between SCG and LCG as the candidates. The proposed method can be coupled with many popular model selection methods, making it an ideal tool for comparing model selection uncertainty as well as measuring reproducibility. We also propose a new residual bootstrap procedure for graphical model settings to approximate the sampling distribution of the selected models and to obtain CG. To visualize the distribution of selected models and its associated uncertainty, we further develop new graphical tools, such as grouped model selection distribution plot. Numerical studies further illustrate the advantages of the proposed method.

在本文中，我们介绍了用于图形模型选择的置信图 (CG) 概念。CG 首先识别两个嵌套的图形模型——称为小置信图和大置信图（SCG 和 LCG）——在给定的置信水平下捕获真正的图形模型，就像捕获总体参数的传统置信区间的端点一样。因此，SCG 和 LCG 为我们提供了更多关于真实模型可能是最简单和最复杂的依赖结构形式的见解，它们的差异也为我们提供了模型选择不确定性的度量。此外，CG 不是依赖于单个选定的模型，而是由 SCG 和 LCG 之间的一组图形模型作为候选。所提出的方法可以与许多流行的模型选择方法相结合，使其成为比较模型选择不确定性和测量再现性的理想工具。我们还为图形模型设置提出了一种新的残差引导程序，以近似所选模型的采样分布并获得 CG。为了可视化所选模型的分布及其相关不确定性，我们进一步开发了新的图形工具，例如分组模型选择分布图。数值研究进一步说明了所提出方法的优点。我们进一步开发了新的图形工具，例如分组模型选择分布图。数值研究进一步说明了所提出方法的优点。我们进一步开发了新的图形工具，例如分组模型选择分布图。数值研究进一步说明了所提出方法的优点。