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Topology Adaptive Graph Estimation in High Dimensions

Author

Listed:
  • 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
    Department of Statistics, LMU Muünchen, 80539 Munich, Germany
    Institute of Computational Biology, Helmholtz Zentrum München, 85764 Neuherberg, Germany)

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.

Suggested Citation

  • Johannes Lederer & Christian L. Müller, 2022. "Topology Adaptive Graph Estimation in High Dimensions," Mathematics, MDPI, vol. 10(8), pages 1-10, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:8:p:1244-:d:790655
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    References listed on IDEAS

    as
    1. Jacob Bien & Irina Gaynanova & Johannes Lederer & Christian L. Müller, 2019. "Prediction error bounds for linear regression with the TREX," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 451-474, June.
    2. Ming Yuan & Yi Lin, 2007. "Model selection and estimation in the Gaussian graphical model," Biometrika, Biometrika Trust, vol. 94(1), pages 19-35.
    3. Lam, Clifford & Fan, Jianqing, 2009. "Sparsistency and rates of convergence in large covariance matrix estimation," LSE Research Online Documents on Economics 31540, London School of Economics and Political Science, LSE Library.
    Full references (including those not matched with items on IDEAS)

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