A challenging problem in estimating high-dimensional graphical models is to choose the regularization parameter in a data-dependent way. The standard techniques include K -fold cross-validation ( K -CV), Akaike information criterion (AIC), and Bayesian information criterion (BIC). Though these methods work well for low-dimensional problems, they are not suitable in high dimensional settings. The method has a clear interpretation: we use the least amount of regularization that simultaneously makes a graph sparse and replicable under random sampling. This interpretation requires essentially no conditions.

A challenging problem in estimating high-dimensional graphical models is to choose the regularization parameter in a data-dependent way. The standard techniques include $K$-fold cross-validation ($K$-CV), Akaike information criterion (AIC), and Bayesian information criterion (BIC). Though these methods work well for low-dimensional problems, they are not suitable in high dimensional settings. The method has a clear interpretation: we use the least amount of regularization that simultaneously makes a graph sparse and replicable under random sampling. This interpretation requires essentially no conditions.