Implicit Differentiation for Hyperparameter Tuning the Weighted
  Graphical Lasso
Can Pouliquen Paulo Gonçalves Mathurin Massias Titouan Vayer
We provide a framework and algorithm for tuning the hyperparameters of the
Graphical Lasso via a bilevel optimization problem solved with a first-order
method. In particular, we derive the Jacobian of the Graphical Lasso solution
with respect to its regularization hyperparameters.