{"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/a-path-algorithm-for-the-fused-lasso-signal","title":"A path algorithm for the Fused Lasso Signal Approximator","arxiv_id":"0910.0526","date":"2009-10-03","proceeding":null,"authors":["Holger Hoefling"],"abstract":"The Lasso is a very well known penalized regression model, which adds an $L_{1}$ penalty with parameter $\\lambda_{1}$ on the coefficients to the squared error loss function. The Fused Lasso extends this model by also putting an $L_{1}$ penalty with parameter $\\lambda_{2}$ on the difference of neighboring coefficients, assuming there is a natural ordering. In this paper, we develop a fast path algorithm for solving the Fused Lasso Signal Approximator that computes the solutions for all values of $\\lambda_1$ and $\\lambda_2$. In the supplement, we also give an algorithm for the general Fused Lasso for the case with predictor matrix $\\bX \\in \\mathds{R}^{n \\times p}$ with $\\text{rank}(\\bX)=p$.","url_abs":"https://arxiv.org/abs/0910.0526v1","url_pdf":"https://arxiv.org/pdf/0910.0526v1.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":"a-path-algorithm-for-the-fused-lasso-signal","repo_url":"https://github.com/goepp/graphseg","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"regression-1","task_name":"regression"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}