The Gaussian graphical model (GGM) incorporates an undirected graph to represent the conditional dependence between variables, with the precision matrix encoding partial correlation between pair of variables given the others. To achieve flexible and accurate estimation and inference of GGM, we propose the novel method FLAG, which utilizes the random effects model for pairwise conditional regression to estimate the precision matrix and applies statistical tests to recover the graph. Compared with existing methods, FLAG has several unique advantages: (i) it provides accurate estimation without sparsity assumptions on the precision matrix, (ii) it allows for element-wise inference of the precision matrix, (iii) it achieves computational efficiency by developing an efficient PX-EM algorithm and a MM algorithm accelerated with low-rank updates, and (iv) it enables joint estimation of multiple graphs using FLAG-Meta or FLAG-CA. The proposed methods are evaluated using various simulation settings and real data applications, including gene expression in the human brain, term association in university websites, and stock prices in the U.S. financial market. The results demonstrate that FLAG and its extensions provide accurate precision estimation and graph recovery.

翻译：高斯图模型（GGM）通过无向图表示变量间的条件依赖关系，其中精度矩阵刻画了给定其他变量时两个变量间的偏相关性。为实现GGM的灵活精确估计与推断，我们提出新颖的FLAG方法，该方法利用成对条件回归的随机效应模型估计精度矩阵，并通过统计检验恢复图结构。与现有方法相比，FLAG具有以下独特优势：（i）无需对精度矩阵施加稀疏性假设即可实现精确估计；（ii）支持对精度矩阵进行逐元素推断；（iii）通过开发高效的PX-EM算法和低秩更新的MM加速算法，实现计算高效性；（iv）利用FLAG-Meta或FLAG-CA实现多图联合估计。通过多种仿真设置及实际数据应用（包括人脑基因表达、大学网站术语关联、美国金融市场股价）评估所提方法，结果表明FLAG及其扩展方法能提供精确的精度估计与图恢复。