Topology Adaptive Graph Estimation in High Dimensions

TL;DR

GTREX is a new graph estimation method for high-dimensional Gaussian models that adapts to topology and avoids tuning parameters, performing competitively with tuned Lasso-based methods.

Contribution

Introduction of GTREX, a tuning-free, topology-adaptive graph estimation method for high-dimensional Gaussian graphical models.

Findings

GTREX performs comparably to tuned Lasso neighborhood selection.

Simulations show GTREX's robustness across various scenarios.

GTREX avoids the need for tuning parameter calibration.

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 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.