Reproducible Learning of Gaussian Graphical Models via Graphical Lasso Multiple Data Splitting  

作　　者：Kang Hu Danning Li Binghui Liu 

机构地区：[1]KLAS and School of Mathematics&Statistics,Northeast Normal University,Changchun 130024,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2025年第2期553-568,共16页数学学报(英文版)

基　　金：partially supported by the National Natural Science Foundation of China(Grant No.12171079);the National Key R&D Program of China(Grant No.2020YFA0714102);partially supported by the National Natural Science Foundation of China(Grant No.12101116);the National Key Research and Development Program of China(Grant No.2022YFA1003701)。

摘　　要：Gaussian graphical models(GGMs) are widely used as intuitive and efficient tools for data analysis in several application domains. To address the reproducibility issue of structure learning of a GGM, it is essential to control the false discovery rate(FDR) of the estimated edge set of the graph in terms of the graphical model. Hence, in recent years, the problem of GGM estimation with FDR control is receiving more and more attention. In this paper, we propose a new GGM estimation method by implementing multiple data splitting. Instead of using the node-by-node regressions to estimate each row of the precision matrix, we suggest directly estimating the entire precision matrix using the graphical Lasso in the multiple data splitting, and our calculation speed is p times faster than the previous. We show that the proposed method can asymptotically control FDR, and the proposed method has significant advantages in computational efficiency. Finally, we demonstrate the usefulness of the proposed method through a real data analysis.

关 键 词：False discovery rate Gaussian graphical model multiple data splitting graphical Lasso 

分 类 号：O157.5[理学—数学]