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title: "Coordinate Descent for SLOPE" | ||
author: | ||
author: | ||
- Johan Larsson | ||
- Quentin Klopfenstein | ||
- Mathurin Massias | ||
- Jonas Wallin | ||
date: 2022-10-26 | ||
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 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 show that our method outperforms a long list of competing | ||
algorithms. | ||
date: 2023-04-25 | ||
citation: | ||
DOI: 10.48550/arXiv.2210.14780 | ||
number: "arXiv:2210.14780" | ||
publisher: arXiv | ||
source: arXiv.org | ||
title: Coordinate descent for SLOPE | ||
type: article | ||
URL: http://arxiv.org/abs/2210.14780 | ||
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 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 show that our method outperforms a long list of competing | ||
algorithms. | ||
editor: | ||
- Ruiz Francisco | ||
- Jennifer Dy | ||
- Jan-Willem van de Meent | ||
collection-title: Proceedings of machine learning research | ||
container-title: >- | ||
Proceedings of the 26th international conference on artificial intelligence | ||
and statistics | ||
event-place: Valencia, Spain | ||
event-title: AISTATS 2023 | ||
issued: 2023-04-25 | ||
page: 4802–4821 | ||
publisher: PMLR | ||
publisher-place: Valencia, Spain | ||
type: paper-conference | ||
url: https://proceedings.mlr.press/v206/larsson23a.html | ||
volume: '206' | ||
github: jolars/slopecd | ||
url: https://proceedings.mlr.press/v206/larsson23a.html | ||
pdf: https://proceedings.mlr.press/v206/larsson23a/larsson23a.pdf | ||
arxiv: 2210.14780 | ||
categories: | ||
- SLOPE | ||
- Optimization | ||
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