Abstract Identifying large-scale conditional dependence structures through graphical models is a challenging yet practical problem. Under ultra-high dimensional settings, a screening procedure is generally suggested before variable selection to reduce computational costs. However, most existing screening methods examine the marginal correlations, thus not suitable to discover the conditional dependence in graphical models. To overcome this issue, we propose a new procedure called graphical uniform joint screening (GUS) for edge identification in graphical models. Instead of screening out edges nodewisely, GUS utilizes a uniform threshold for all statistics indicating the significance of different edges to adapt to various kinds of graphical structures. We demonstrate that GUS enjoys the sure screening property and even the screening consistency by preserving the rankings of the significant edges. Furthermore, a scalable implementation of GUS is developed for big data applications. Simulation and real data studies are provided to illustrate the effectiveness of the proposed method.

中文翻译：

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超高维图形模型的统一联合筛选

摘要 通过图形模型识别大规模条件依赖结构是一个具有挑战性但实际的问题。在超高维设置下，通常建议在变量选择之前进行筛选程序以降低计算成本。然而，大多数现有的筛选方法检查边际相关性，因此不适合发现图形模型中的条件依赖性。为了克服这个问题，我们提出了一种称为图形统一联合筛选 (GUS) 的新程序，用于图形模型中的边缘识别。GUS 不是逐节点筛选边，而是对所有统计数据使用统一的阈值，指示不同边的重要性以适应各种图形结构。我们通过保留显着边缘的排名来证明 GUS 享有确定的筛选属性甚至筛选一致性。此外，还为大数据应用开发了可扩展的 GUS 实现。提供了仿真和实际数据研究来说明所提出方法的有效性。