Stability approach to regularization selection (stars) is a natural way to select optimal regularization parameter for all three estimation methods.
It selects the optimal graph by variability of subsamplings and tends to overselect edges in Gaussian graphical models.
Besides selecting the regularization parameters, stars can also provide an additional estimated graph by merging the corresponding subsampled graphs using the frequency counts.
The subsampling procedure in stars may NOT be very efficient, we also provide the recent developed highly efficient, rotation information criterion approach (ric).
Instead of tuning over a grid by cross-validation or subsampling, we directly estimate the optimal regularization paramter based on random Rotations.
However, ric usually has very good empirical performances but suffers from underselections sometimes.
Therefore, we suggest if user are sensitive of false negative rates, they should either consider increasing r.num argument or applying the stars to model selection.
Extended Bayesian information criterion (ebic) is another competive approach, but the ebic.gamma argument can only be tuned by experience.
Note: This text comes from huge.select function which belongs to R huge package.