# glasso- Assumptions of Meinhausen-Buhlmann approximation?

First off, This is not an R question - it is a conceptual question, so there is no need to perform any code.

Problem: I'm trying to invert a large dimensional covariance matrix of p features. For large p, even using a graphical LASSO with a regularization parameter, inverting this matrix takes a long time. In the past, I have elected instead to use the Meinhausen-Buhlmann approximation to speed the inversion up, using R's glasso() method from the glasso package. You can specify the approximation by setting the parameter approx to TRUE: glasso(cov.matrix, rho=0.15, approx=TRUE). This makes the inversion of even a large covariance matrix, very speedy.

However, I'm looking at my resulting graphical structure and I worry I don't trust the approximation, because the clustering of the nodes isn't very organized/interpretable. I expect to see clusters based on annotation groups each node belongs to.

Do I have reason to distrust the Meinhausen-Bulhmann approximation? What assumptions does it make? The original paper is a bit out of my depth, so I would appreciate help in digesting how the approximation works from experts/smarter people.

Thanks for any insights!

:-)

Estimation quality of a precision matrix in high dimensions $p>>n$ through any procedure is dependent on assumptions--in short there's no free lunch, and I rather doubt there is a useful estimator that is minimax in the space of all precision matrices.