Topology Adaptive Graph Estimation in High Dimensions
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 se...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-04-01
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| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/10/8/1244 |
| _version_ | 1797410247296417792 |
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| author | Johannes Lederer Christian L. Müller |
| author_facet | Johannes Lederer Christian L. Müller |
| author_sort | Johannes Lederer |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T04:26:10Z |
| format | Article |
| id | doaj.art-c4d11a9137fd45919c865d3708f8402c |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T04:26:10Z |
| publishDate | 2022-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-c4d11a9137fd45919c865d3708f8402c2023-12-03T13:40:08ZengMDPI AGMathematics2227-73902022-04-01108124410.3390/math10081244Topology Adaptive Graph Estimation in High DimensionsJohannes Lederer0Christian L. Müller1Department of Mathematics, Ruhr-University Bochum, Universitätsstraße 150, 44801 Bochum, GermanyCenter for Computational Mathematics, Flatiron Institute, New York, NY 10010, USAWe 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.https://www.mdpi.com/2227-7390/10/8/1244graphical modelstuning parametershigh-dimensional statistics |
| spellingShingle | Johannes Lederer Christian L. Müller Topology Adaptive Graph Estimation in High Dimensions Mathematics graphical models tuning parameters high-dimensional statistics |
| title | Topology Adaptive Graph Estimation in High Dimensions |
| title_full | Topology Adaptive Graph Estimation in High Dimensions |
| title_fullStr | Topology Adaptive Graph Estimation in High Dimensions |
| title_full_unstemmed | Topology Adaptive Graph Estimation in High Dimensions |
| title_short | Topology Adaptive Graph Estimation in High Dimensions |
| title_sort | topology adaptive graph estimation in high dimensions |
| topic | graphical models tuning parameters high-dimensional statistics |
| url | https://www.mdpi.com/2227-7390/10/8/1244 |
| work_keys_str_mv | AT johanneslederer topologyadaptivegraphestimationinhighdimensions AT christianlmuller topologyadaptivegraphestimationinhighdimensions |