Hi all,

I'm using GraphLASSO to estimate the graphical model and precision 
matrix of my variables. It is well known that GraphLASSO and related 
methods are very sensitive to contaminated data and their estimates have 
low break-down points:
http://arxiv.org/abs/1501.01219

As suggested by the authors in the above paper I'd like to use 
GraphLASSO with robust correlation matrices to estimate the precision 
matrix.  When I looked at the source code of GraphLASSO however, it 
seemed like there's no way to supply the fit method with a 
pre-calculated correlation matrix, as it is calculated internally and 
automatically using the empirical_covariance() method.

I know that if I rank my data column-wise before applying GraphLASSO 
I'll get Spearman correlation. I tried this, and it already improves the 
performance of GraphLASSO with outliers, so I'd advise adding this trick 
to the documentation to raise awareness of this issue.

But the authors suggest the Gaussian rank correlation works even better 
than Spearman, because it handles normally distributed variables better, 
while still having high break-down point as Spearman. Therefore I'd like 
to calculate a Gaussian rank correlation matrix and supply it to the 
GraphLASSO method. Is there any way with the current implementation to 
do this or should I rewrite the GraphLASSO class to make this possible?

Cheers,
Daniel