I have a covariance matrix and want to calculate an inverse covariance matrix. For calculating the covariance matrix, I use the package QUIC (cran.r-project.org/web/packages/QUIC/QUIC.pdf) As soon as I have the inverse covariance matrix, I want to generate a graph representing the correlations between the random variables, so I am only interested in non-zero entries who are not on the diagonal.

But I don't know how I should choose the regularization parameter... if I choose 1 as regularization parameter, all entries of the inverse covariance matrix are zero, expect the ones on the diagonal. Thats bad, so I also tried several other values for the parameter and it worked. Now, I have differnet inverse covariance matrixes, but I don't know how to find out which one fits my data best.

I have also thought about using cross-validation, for example a k-fold-cross-validation. There is no problem in dividing my dataset into different pieces and generateing the inverse covariance matrix, but I don't know how to calculate an error for matrices... is it even possible?

And sorry if you might think that my question is dumb or something. I have only little expierience in the field of statistics.