Topology Adaptive Graph Estimation in High Dimensions

Mathematics

Christian L. Müller¹  Johannes Lederer² 

[1] Center for Computational Mathematics, Flatiron Institute, New York, NY 10010, USA;Department of Mathematics, Ruhr-University Bochum, Universitätsstraße 150, 44801 Bochum, Germany;

关键词: graphical models;    tuning parameters;    high-dimensional statistics;   

DOI  :  10.3390/math10081244

来源: DOAJ

【 摘 要 】

We introduce Graphical TREX (GTREX), a novel method for graph estimation in high-dimensional Gaussian graphical models. By conducting neighborhood selection with TREX, GTREX avoids tuning parameters and is adaptive to the graph topology. We compared GTREX with standard methods on a new simulation setup that was designed to assess accurately the strengths and shortcomings of different methods. These simulations showed that a neighborhood selection scheme based on Lasso and an optimal (in practice unknown) tuning parameter outperformed other standard methods over a large spectrum of scenarios. Moreover, we show that GTREX can rival this scheme and, therefore, can provide competitive graph estimation without the need for tuning parameter calibration.

【 授权许可】

Unknown