{"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/adaptive-multi-penalty-regularization-based","title":"Adaptive multi-penalty regularization based on a generalized Lasso path","arxiv_id":"1710.03971","date":"2017-10-11","proceeding":null,"authors":["Markus Grasmair","Timo Klock","Valeriya Naumova"],"abstract":"For many algorithms, parameter tuning remains a challenging and critical\ntask, which becomes tedious and infeasible in a multi-parameter setting.\nMulti-penalty regularization, successfully used for solving undetermined sparse\nregression of problems of unmixing type where signal and noise are additively\nmixed, is one of such examples. In this paper, we propose a novel algorithmic\nframework for an adaptive parameter choice in multi-penalty regularization with\na focus on the correct support recovery. Building upon the theory of\nregularization paths and algorithms for single-penalty functionals, we extend\nthese ideas to a multi-penalty framework by providing an efficient procedure\nfor the construction of regions containing structurally similar solutions,\ni.e., solutions with the same sparsity and sign pattern, over the whole range\nof parameters. Combining this with a model selection criterion, we can choose\nregularization parameters in a data-adaptive manner. Another advantage of our\nalgorithm is that it provides an overview on the solution stability over the\nwhole range of parameters. This can be further exploited to obtain additional\ninsights into the problem of interest. We provide a numerical analysis of our\nmethod and compare it to the state-of-the-art single-penalty algorithms for\ncompressed sensing problems in order to demonstrate the robustness and power of\nthe proposed algorithm.","url_abs":"http://arxiv.org/abs/1710.03971v1","url_pdf":"http://arxiv.org/pdf/1710.03971v1.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":"adaptive-multi-penalty-regularization-based","repo_url":"https://github.com/soply/mpgraph","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"model-selection","task_name":"Model Selection"},{"task_slug":"compressed-sensing","task_name":"compressed sensing"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}