For the problem of inferring a Gaussian graphical model (GGM), this work explores the application of a recent approach from the multiple testing literature for graph inference. The main idea of the method by Rebafka et al. (2022) is to model the data by a latent variable model, the so-called noisy stochastic block model (NSBM), and then use the associated ${\ell}$-values to infer the graph. The inferred graph controls the false discovery rate, that means that the proportion of falsely declared edges does not exceed a user-defined nominal level. Here it is shown that any test statistic from the GGM literature can be used as input for the NSBM approach to perform GGM inference. To make the approach feasible in practice, a new, computationally efficient inference algorithm for the NSBM is developed relying on a greedy approach to maximize the integrated complete-data likelihood. Then an extensive numerical study illustrates that the NSBM approach outperforms the state of the art for any of the here considered GGM-test statistics. In particular in sparse settings and on real datasets a significant gain in power is observed.

翻译：针对高斯图模型（GGM）推断问题，本文探索了多重检验文献中一种新近方法在图推断中的应用。Rebafka等人（2022）方法的核心思想是：通过潜变量模型（即所谓的噪声随机块模型NSBM）对数据进行建模，并利用其关联的$\ell$值来推断图结构。推断所得的图能够控制错误发现率，即误判边的比例不超过用户预设的名义水平。本文证明，GGM文献中的任何检验统计量均可作为NSBM方法的输入进行GGM推断。为使该方法具备实践可行性，我们开发了一种计算高效的新型NSBM推断算法，该算法基于贪心策略最大化完整数据积分似然。随后的大规模数值研究表明，就本文所考察的所有GGM检验统计量而言，NSBM方法的性能均优于现有技术。特别是在稀疏场景和真实数据集上，我们观察到其统计功效获得了显著提升。