{"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/consistent-algorithms-for-multi-label","title":"Consistent algorithms for multi-label classification with macro-at-$k$ metrics","arxiv_id":"2401.16594","date":"2024-01-29","proceeding":null,"authors":["Erik Schultheis","Wojciech Kotłowski","Marek Wydmuch","Rohit Babbar","Strom Borman","Krzysztof Dembczyński"],"abstract":"We consider the optimization of complex performance metrics in multi-label classification under the population utility framework. We mainly focus on metrics linearly decomposable into a sum of binary classification utilities applied separately to each label with an additional requirement of exactly $k$ labels predicted for each instance. These \"macro-at-$k$\" metrics possess desired properties for extreme classification problems with long tail labels. Unfortunately, the at-$k$ constraint couples the otherwise independent binary classification tasks, leading to a much more challenging optimization problem than standard macro-averages. We provide a statistical framework to study this problem, prove the existence and the form of the optimal classifier, and propose a statistically consistent and practical learning algorithm based on the Frank-Wolfe method. Interestingly, our main results concern even more general metrics being non-linear functions of label-wise confusion matrices. Empirical results provide evidence for the competitive performance of the proposed approach.","url_abs":"https://arxiv.org/abs/2401.16594v3","url_pdf":"https://arxiv.org/pdf/2401.16594v3.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":"consistent-algorithms-for-multi-label","repo_url":"https://github.com/mwydmuch/xcolumns","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"consistent-algorithms-for-multi-label","repo_url":"https://github.com/mwydmuch/macro-measures-in-xmlc","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"binary-classification","task_name":"Binary Classification"},{"task_slug":"classification-1","task_name":"Classification"},{"task_slug":"multi-label-classification-2","task_name":"MUlTI-LABEL-ClASSIFICATION"},{"task_slug":"multi-label-classification","task_name":"Multi-Label Classification"}],"methods":[{"method_slug":"focus","method_name":"Focus"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2401.16594","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2401.16594"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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