Topology Adaptive Graph Estimation in High Dimensions
This work addresses graph estimation for high-dimensional data, offering a parameter-free method that is competitive but incremental compared to existing approaches.
The authors tackled the problem of graph estimation in high-dimensional Gaussian graphical models by introducing GTREX, a method that avoids tuning parameters and adapts to graph topology, showing it can rival Lasso-based schemes with optimal tuning in simulations.
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 compare GTREX with standard methods on a new simulation set-up that is designed to assess accurately the strengths and shortcomings of different methods. These simulations show that a neighborhood selection scheme based on Lasso and an optimal (in practice unknown) tuning parameter outperforms 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.