{"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/the-lasso-distribution-properties-sampling","title":"The Lasso Distribution: Properties, Sampling Methods, and Applications in Bayesian Lasso Regression","arxiv_id":"2506.07394","date":"2025-06-09","proceeding":null,"authors":["Mohammad Javad Davoudabadi","Jonathon Tidswell","Samuel Muller","Garth Tarr","John T. Ormerod"],"abstract":"In this paper, we introduce a new probability distribution, the Lasso distribution. We derive several fundamental properties of the distribution, including closed-form expressions for its moments and moment-generating function. Additionally, we present an efficient and numerically stable algorithm for generating random samples from the distribution, facilitating its use in both theoretical and applied settings. We establish that the Lasso distribution belongs to the exponential family. A direct application of the Lasso distribution arises in the context of an existing Gibbs sampler, where the full conditional distribution of each regression coefficient follows this distribution. This leads to a more computationally efficient and theoretically grounded sampling scheme. To facilitate the adoption of our methodology, we provide an R package, BayesianLasso, available on CRAN, implementing the proposed methods. Our findings offer new insights into the probabilistic structure underlying the Lasso penalty and provide practical improvements in Bayesian inference for high-dimensional regression problems.","url_abs":"https://arxiv.org/abs/2506.07394v2","url_pdf":"https://arxiv.org/pdf/2506.07394v2.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":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"the-lasso-distribution-properties-sampling","repo_url":"https://github.com/garthtarr/BayesianLasso","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}