Topology Adaptive Graph Estimation in High Dimensions

Johannes Lederer and Christian L. Müller
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Johannes Lederer: Department of Mathematics, Ruhr-University Bochum, Universitätsstraße 150, 44801 Bochum, Germany
Christian L. Müller: Center for Computational Mathematics, Flatiron Institute, New York, NY 10010, USA

Mathematics, 2022, vol. 10, issue 8, 1-10

Abstract: 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.

Keywords: graphical models; tuning parameters; high-dimensional statistics (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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