Thresholded Adaptive Validation: Tuning the Graphical Lasso for Graph Recovery

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 a...

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Bibliographic Details
Published inarXiv.org
Main Authors Laszkiewicz, Mike, Fischer, Asja, Lederer, Johannes
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 30.03.2021
Subjects
Calibration
Computer simulation
Parameters
Recovery
Regularization
Resampling
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Summary: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.
ISSN:2331-8422