Coordinate Descent for SLOPE
(2023) 26th International Conference on Artificial Intelligence and Statistics, AISTATS 2023 In Proceedings of Machine Learning Research 206. p.4802-4821- Abstract
The lasso is the most famous sparse regression and feature selection method. One reason for its popularity is the speed at which the underlying optimization problem can be solved. Sorted L-One Penalized Estimation (SLOPE) is a generalization of the lasso with appealing statistical properties. In spite of this, the method has not yet reached widespread interest. A major reason for this is that current software packages that fit SLOPE rely on algorithms that perform poorly in high dimensions. To tackle this issue, we propose a new fast algorithm to solve the SLOPE optimization problem, which combines proximal gradient descent and proximal coordinate descent steps. We provide new results on the directional derivative of the SLOPE penalty... (More)
The lasso is the most famous sparse regression and feature selection method. One reason for its popularity is the speed at which the underlying optimization problem can be solved. Sorted L-One Penalized Estimation (SLOPE) is a generalization of the lasso with appealing statistical properties. In spite of this, the method has not yet reached widespread interest. A major reason for this is that current software packages that fit SLOPE rely on algorithms that perform poorly in high dimensions. To tackle this issue, we propose a new fast algorithm to solve the SLOPE optimization problem, which combines proximal gradient descent and proximal coordinate descent steps. We provide new results on the directional derivative of the SLOPE penalty and its related SLOPE thresholding operator, as well as provide convergence guarantees for our proposed solver. In extensive benchmarks on simulated and real data, we demonstrate our method's performance against a long list of competing algorithms.
(Less)
- author
- Larsson, Johan LU ; Klopfenstein, Quentin ; Massias, Mathurin and Wallin, Jonas LU
- organization
- publishing date
- 2023
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- host publication
- Proceedings of the 26th international conference on artificial intelligence and statistics
- series title
- Proceedings of Machine Learning Research
- editor
- Ruiz, Francisco ; Dy, Jennifer and van de Meent, Jan-Willem
- volume
- 206
- pages
- 20 pages
- conference name
- 26th International Conference on Artificial Intelligence and Statistics, AISTATS 2023
- conference location
- Valencia, Spain
- conference dates
- 2023-04-25 - 2023-04-27
- external identifiers
-
- scopus:85165164923
- scopus:85165164923
- project
- Optimization and Algorithms for Sparse Regression
- language
- English
- LU publication?
- yes
- id
- d8bb60fa-3ca6-4d89-88c7-830f57d5707b
- alternative location
- https://proceedings.mlr.press/v206/larsson23a/larsson23a.pdf
- date added to LUP
- 2023-06-15 13:24:58
- date last changed
- 2023-11-22 22:29:35
@inproceedings{d8bb60fa-3ca6-4d89-88c7-830f57d5707b, abstract = {{<p>The lasso is the most famous sparse regression and feature selection method. One reason for its popularity is the speed at which the underlying optimization problem can be solved. Sorted L-One Penalized Estimation (SLOPE) is a generalization of the lasso with appealing statistical properties. In spite of this, the method has not yet reached widespread interest. A major reason for this is that current software packages that fit SLOPE rely on algorithms that perform poorly in high dimensions. To tackle this issue, we propose a new fast algorithm to solve the SLOPE optimization problem, which combines proximal gradient descent and proximal coordinate descent steps. We provide new results on the directional derivative of the SLOPE penalty and its related SLOPE thresholding operator, as well as provide convergence guarantees for our proposed solver. In extensive benchmarks on simulated and real data, we demonstrate our method's performance against a long list of competing algorithms.</p>}}, author = {{Larsson, Johan and Klopfenstein, Quentin and Massias, Mathurin and Wallin, Jonas}}, booktitle = {{Proceedings of the 26th international conference on artificial intelligence and statistics}}, editor = {{Ruiz, Francisco and Dy, Jennifer and van de Meent, Jan-Willem}}, language = {{eng}}, pages = {{4802--4821}}, series = {{Proceedings of Machine Learning Research}}, title = {{Coordinate Descent for SLOPE}}, url = {{https://proceedings.mlr.press/v206/larsson23a/larsson23a.pdf}}, volume = {{206}}, year = {{2023}}, }