A nonconvex variational approach for robust graphical lasso

In recent years, there has been a growing interest in problems in graph estimation and model selection, which all share very similar matrix variational formulations, the most popular one being probably GLASSO. Unfortunately, the standard GLASSO formulation does not take into account noise corrupting the data: this shortcoming leads us to propose a novel criterion, where the regularization function is decoupled in two terms, one acting only on the eigenvalues of the matrix and the other on the matrix elements. Incorporating noise information into the model has the side-effect to make the cost function non-convex. To overcome this difficulty, we adopt a majorization-minimization approach, where at each iteration a convex approximation of the original cost function is minimized via the Douglas-Rachford procedure. The achieved results are very promising w.r.t. classical approaches.