{"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/efficient-primal-dual-algorithms-for-large","title":"Efficient Primal-Dual Algorithms for Large-Scale Multiclass Classification","arxiv_id":"1902.03755","date":"2019-02-11","proceeding":null,"authors":["Dmitry Babichev","Dmitrii Ostrovskii","Francis Bach"],"abstract":"We develop efficient algorithms to train $\\ell_1$-regularized linear\nclassifiers with large dimensionality $d$ of the feature space, number of\nclasses $k$, and sample size $n$. Our focus is on a special class of losses\nthat includes, in particular, the multiclass hinge and logistic losses. Our\napproach combines several ideas: (i) passing to the equivalent saddle-point\nproblem with a quasi-bilinear objective; (ii) applying stochastic mirror\ndescent with a proper choice of geometry which guarantees a favorable accuracy\nbound; (iii) devising non-uniform sampling schemes to approximate the matrix\nproducts. In particular, for the multiclass hinge loss we propose a\n\\textit{sublinear} algorithm with iterations performed in $O(d+n+k)$ arithmetic\noperations.","url_abs":"http://arxiv.org/abs/1902.03755v1","url_pdf":"http://arxiv.org/pdf/1902.03755v1.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":"efficient-primal-dual-algorithms-for-large","repo_url":"https://github.com/flykiller/sublinear-svm","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"classification-1","task_name":"Classification"},{"task_slug":"classification","task_name":"General Classification"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1902.03755","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}