Thresholded Adaptive Validation: Tuning the Graphical Lasso for Graph Recovery

Many Machine Learning algorithms are formulated as regularized optimization\nproblems, but their performance hinges on a regularization parameter that needs\nto be calibrated to each application at hand. In this paper, we propose a\ngeneral calibration scheme for regularized optimization problems and apply it\nto the graphical lasso, which is a method for Gaussian graphical modeling. The\nscheme is equipped with theoretical guarantees and motivates a thresholding\npipeline that can improve graph recovery. Moreover, requiring at most one line\nsearch over the regularization path, the calibration scheme is computationally\nmore efficient than competing schemes that are based on resampling. Finally, we\nshow in simulations that our approach can improve on the graph recovery of\nother approaches considerably.\n