Thresholded Adaptive Validation: Tuning the Graphical Lasso for Graph Recovery
This addresses the need for efficient and accurate parameter tuning in graphical modeling, though it appears incremental as it builds on existing methods like the graphical lasso.
The paper tackles the problem of calibrating regularization parameters in machine learning algorithms, specifically applying a proposed general calibration scheme to the graphical lasso for Gaussian graphical modeling, resulting in improved graph recovery in simulations.
Many Machine Learning algorithms are formulated as regularized optimization problems, but their performance hinges on a regularization parameter that needs to be calibrated to each application at hand. In this paper, we propose a general calibration scheme for regularized optimization problems and apply it to the graphical lasso, which is a method for Gaussian graphical modeling. The scheme is equipped with theoretical guarantees and motivates a thresholding pipeline that can improve graph recovery. Moreover, requiring at most one line search over the regularization path, the calibration scheme is computationally more efficient than competing schemes that are based on resampling. Finally, we show in simulations that our approach can improve on the graph recovery of other approaches considerably.