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, that is, 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.

FROSTY: A High-Dimensional Scale-Free Bayesian Network Learning Method

“…RobSel algorithm only requires bootstrapped sample covariance matrices to determine λ α , without requiring computationally expensive cross-validation. Furthermore, in the recent work of Tran et al (2022), it has been shown that α in RobSel is the upper bound of the asymptotic family-wise error rate of estimating at least one erroneous nonzero in . Since the DRO formulation is to minimize the worst-case scenario, RobSel tends to be conservative even for large values of α, and, in fact, a large value of α is recommended, e.g., α = 0.99 was routinely used with good results.…”