{"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/accelerating-cross-validation-in-multinomial","title":"Accelerating Cross-Validation in Multinomial Logistic Regression with $\\ell_1$-Regularization","arxiv_id":"1711.05420","date":"2017-11-15","proceeding":null,"authors":["Tomoyuki Obuchi","Yoshiyuki Kabashima"],"abstract":"We develop an approximate formula for evaluating a cross-validation estimator\nof predictive likelihood for multinomial logistic regression regularized by an\n$\\ell_1$-norm. This allows us to avoid repeated optimizations required for\nliterally conducting cross-validation; hence, the computational time can be\nsignificantly reduced. The formula is derived through a perturbative approach\nemploying the largeness of the data size and the model dimensionality. An\nextension to the elastic net regularization is also addressed. The usefulness\nof the approximate formula is demonstrated on simulated data and the ISOLET\ndataset from the UCI machine learning repository.","url_abs":"http://arxiv.org/abs/1711.05420v2","url_pdf":"http://arxiv.org/pdf/1711.05420v2.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":"accelerating-cross-validation-in-multinomial","repo_url":"https://github.com/T-Obuchi/AcceleratedCVonMLR_matlab","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok","spdx":"GPL-3.0"}},{"paper_slug":"accelerating-cross-validation-in-multinomial","repo_url":"https://github.com/T-Obuchi/AcceleratedCVonMLR_python","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok","spdx":"GPL-3.0"}}],"tasks":[{"task_slug":"machine-learning","task_name":"BIG-bench Machine Learning"},{"task_slug":"regression-1","task_name":"regression"}],"methods":[{"method_slug":"logistic-regression","method_name":"Logistic Regression"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1711.05420","atlas_url":"https://app.syntology.ai/?focus=1711.05420","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}