Family-wise error rate control in Gaussian graphical model selection via Distributionally Robust Optimization

Abstract

Recently, a special case of precision matrix estimation based on a distributionally robust optimization (DRO) framework has been shown to be equivalent to the graphical lasso. From this formulation, a method for choosing the regularization term, i.e., for graphical model selection, was proposed. In this work, we establish a theoretical connection between the confidence level of graphical model selection via the DRO formulation and the asymptotic family-wise error rate of estimating false edges. Simulation experiments and real data analyses illustrate the utility of the asymptotic family-wise error rate control behavior even in finite samples.

References in corpus (5)

• Extended Bayesian Information Criteria for Gaussian Graphical Models
• Robust Wasserstein Profile Inference and Applications to Machine Learning
• Multiple Testing and Error Control in Gaussian Graphical Model Selection
• Statistical paleoclimate reconstructions via Markov random fields
• Distributionally Robust Inverse Covariance Estimation: The Wasserstein Shrinkage Estimator