The Solution Path of SLOPE

Xavier Dupuis, Patrick Tardivel
Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, PMLR 238:775-783, 2024.

Abstract

The SLOPE estimator has the particularity of having null components (sparsity) and components that are equal in absolute value (clustering). The number of clusters depends on the regularization parameter of the estimator. This parameter can be chosen as a trade-off between interpretability (with a small number of clusters) and accuracy (with a small mean squared error or a small prediction error). Finding such a compromise requires to compute the solution path, that is the function mapping the regularization parameter to the estimator. We provide in this article an algorithm to compute the solution path of SLOPE and show how it can be used to adjust the regularization parameter.

Cite this Paper

BibTeX
@InProceedings{pmlr-v238-dupuis24a, title = {The Solution Path of SLOPE}, author = {Dupuis, Xavier and Tardivel, Patrick}, booktitle = {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics}, pages = {775--783}, year = {2024}, editor = {Dasgupta, Sanjoy and Mandt, Stephan and Li, Yingzhen}, volume = {238}, series = {Proceedings of Machine Learning Research}, month = {02--04 May}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v238/dupuis24a/dupuis24a.pdf}, url = {https://proceedings.mlr.press/v238/dupuis24a.html}, abstract = {The SLOPE estimator has the particularity of having null components (sparsity) and components that are equal in absolute value (clustering). The number of clusters depends on the regularization parameter of the estimator. This parameter can be chosen as a trade-off between interpretability (with a small number of clusters) and accuracy (with a small mean squared error or a small prediction error). Finding such a compromise requires to compute the solution path, that is the function mapping the regularization parameter to the estimator. We provide in this article an algorithm to compute the solution path of SLOPE and show how it can be used to adjust the regularization parameter.} }
Endnote
%0 Conference Paper %T The Solution Path of SLOPE %A Xavier Dupuis %A Patrick Tardivel %B Proceedings of The 27th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2024 %E Sanjoy Dasgupta %E Stephan Mandt %E Yingzhen Li %F pmlr-v238-dupuis24a %I PMLR %P 775--783 %U https://proceedings.mlr.press/v238/dupuis24a.html %V 238 %X The SLOPE estimator has the particularity of having null components (sparsity) and components that are equal in absolute value (clustering). The number of clusters depends on the regularization parameter of the estimator. This parameter can be chosen as a trade-off between interpretability (with a small number of clusters) and accuracy (with a small mean squared error or a small prediction error). Finding such a compromise requires to compute the solution path, that is the function mapping the regularization parameter to the estimator. We provide in this article an algorithm to compute the solution path of SLOPE and show how it can be used to adjust the regularization parameter.
APA
Dupuis, X. & Tardivel, P.. (2024). The Solution Path of SLOPE. Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 238:775-783 Available from https://proceedings.mlr.press/v238/dupuis24a.html.

Related Material