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

TL;DR

This paper links distributionally robust optimization-based graphical model selection to family-wise error rate control, demonstrating its effectiveness through theory, simulations, and real data analysis.

Contribution

It establishes a theoretical connection between DRO-based graphical model selection confidence levels and family-wise error rate, enhancing error control understanding.

Findings

DRO formulation controls family-wise error rate asymptotically.

Simulation results confirm finite-sample error rate control.

Real data analysis demonstrates practical utility.

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.