{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/efficient-designs-of-slope-penalty-sequences","title":"Efficient Designs of SLOPE Penalty Sequences in Finite Dimension","arxiv_id":"2102.07211","date":"2021-02-14","proceeding":null,"authors":["Yiliang Zhang","Zhiqi Bu"],"abstract":"In linear regression, SLOPE is a new convex analysis method that generalizes the Lasso via the sorted L1 penalty: larger fitted coefficients are penalized more heavily. This magnitude-dependent regularization requires an input of penalty sequence $\\lambda$, instead of a scalar penalty as in the Lasso case, thus making the design extremely expensive in computation. In this paper, we propose two efficient algorithms to design the possibly high-dimensional SLOPE penalty, in order to minimize the mean squared error. For Gaussian data matrices, we propose a first order Projected Gradient Descent (PGD) under the Approximate Message Passing regime. For general data matrices, we present a zero-th order Coordinate Descent (CD) to design a sub-class of SLOPE, referred to as the k-level SLOPE. Our CD allows a useful trade-off between the accuracy and the computation speed. We demonstrate the performance of SLOPE with our designs via extensive experiments on synthetic data and real-world datasets.","url_abs":"https://arxiv.org/abs/2102.07211v3","url_pdf":"https://arxiv.org/pdf/2102.07211v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"efficient-designs-of-slope-penalty-sequences","repo_url":"https://github.com/yiliangzhang96/K-level-SLOPE","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}