TIGER: A Tuning-Insensitive Approach for Optimally Estimating Gaussian Graphical Models

TL;DR

TIGER is a new high-dimensional Gaussian graphical model estimation method that is tuning-insensitive, computationally efficient, and theoretically minimax optimal, demonstrated through simulations and real data.

Contribution

It introduces a tuning-insensitive estimator for Gaussian graphical models that simplifies parameter selection and improves computational speed.

Findings

Faster than existing methods due to tuning-insensitivity

Minimax optimal estimator under various norms

Effective in simulated and real data applications

Abstract

We propose a new procedure for estimating high dimensional Gaussian graphical models. Our approach is asymptotically tuning-free and non-asymptotically tuning-insensitive: it requires very few efforts to choose the tuning parameter in finite sample settings. Computationally, our procedure is significantly faster than existing methods due to its tuning-insensitive property. Theoretically, the obtained estimator is simultaneously minimax optimal for precision matrix estimation under different norms. Empirically, we illustrate the advantages of our method using thorough simulated and real examples. The R package bigmatrix implementing the proposed methods is available on the Comprehensive R Archive Network: http://cran.r-project.org/.