{"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/analytic-solution-and-stationary-phase","title":"Analytic solution and stationary phase approximation for the Bayesian lasso and elastic net","arxiv_id":"1709.08535","date":"2017-09-25","proceeding":"NeurIPS 2018 12","authors":["Tom Michoel"],"abstract":"The lasso and elastic net linear regression models impose a\ndouble-exponential prior distribution on the model parameters to achieve\nregression shrinkage and variable selection, allowing the inference of robust\nmodels from large data sets. However, there has been limited success in\nderiving estimates for the full posterior distribution of regression\ncoefficients in these models, due to a need to evaluate analytically\nintractable partition function integrals. Here, the Fourier transform is used\nto express these integrals as complex-valued oscillatory integrals over\n\"regression frequencies\". This results in an analytic expansion and stationary\nphase approximation for the partition functions of the Bayesian lasso and\nelastic net, where the non-differentiability of the double-exponential prior\nhas so far eluded such an approach. Use of this approximation leads to highly\naccurate numerical estimates for the expectation values and marginal posterior\ndistributions of the regression coefficients, and allows for Bayesian inference\nof much higher dimensional models than previously possible.","url_abs":"http://arxiv.org/abs/1709.08535v3","url_pdf":"http://arxiv.org/pdf/1709.08535v3.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":"analytic-solution-and-stationary-phase","repo_url":"https://github.com/tmichoel/bayonet","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"bayesian-inference","task_name":"Bayesian Inference"},{"task_slug":"variable-selection","task_name":"Variable Selection"},{"task_slug":"regression-1","task_name":"regression"}],"methods":[{"method_slug":"linear-regression","method_name":"Linear Regression"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}