Thresholded Adaptive Validation: Tuning the Graphical Lasso for Graph Recovery

Mike Laszkiewicz, Asja Fischer, Johannes Lederer
Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, PMLR 130:1864-1872, 2021.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v130-laszkiewicz21a, title = { Thresholded Adaptive Validation: Tuning the Graphical Lasso for Graph Recovery }, author = {Laszkiewicz, Mike and Fischer, Asja and Lederer, Johannes}, booktitle = {Proceedings of The 24th International Conference on Artificial Intelligence and Statistics}, pages = {1864--1872}, year = {2021}, editor = {Banerjee, Arindam and Fukumizu, Kenji}, volume = {130}, series = {Proceedings of Machine Learning Research}, month = {13--15 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v130/laszkiewicz21a/laszkiewicz21a.pdf}, url = {https://proceedings.mlr.press/v130/laszkiewicz21a.html}, abstract = { 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. } }
Endnote
%0 Conference Paper %T Thresholded Adaptive Validation: Tuning the Graphical Lasso for Graph Recovery %A Mike Laszkiewicz %A Asja Fischer %A Johannes Lederer %B Proceedings of The 24th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2021 %E Arindam Banerjee %E Kenji Fukumizu %F pmlr-v130-laszkiewicz21a %I PMLR %P 1864--1872 %U https://proceedings.mlr.press/v130/laszkiewicz21a.html %V 130 %X 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.
APA
Laszkiewicz, M., Fischer, A. & Lederer, J.. (2021). Thresholded Adaptive Validation: Tuning the Graphical Lasso for Graph Recovery . Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 130:1864-1872 Available from https://proceedings.mlr.press/v130/laszkiewicz21a.html.

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