{"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/a-convex-surrogate-operator-for-general-non","title":"A Convex Surrogate Operator for General Non-Modular Loss Functions","arxiv_id":"1604.03373","date":"2016-04-12","proceeding":null,"authors":["Jiaqian Yu","Matthew Blaschko"],"abstract":"Empirical risk minimization frequently employs convex surrogates to\nunderlying discrete loss functions in order to achieve computational\ntractability during optimization. However, classical convex surrogates can only\ntightly bound modular loss functions, sub-modular functions or supermodular\nfunctions separately while maintaining polynomial time computation. In this\nwork, a novel generic convex surrogate for general non-modular loss functions\nis introduced, which provides for the first time a tractable solution for loss\nfunctions that are neither super-modular nor submodular. This convex surro-gate\nis based on a submodular-supermodular decomposition for which the existence and\nuniqueness is proven in this paper. It takes the sum of two convex surrogates\nthat separately bound the supermodular component and the submodular component\nusing slack-rescaling and the Lov{\\'a}sz hinge, respectively. It is further\nproven that this surrogate is convex , piecewise linear, an extension of the\nloss function, and for which subgradient computation is polynomial time.\nEmpirical results are reported on a non-submodular loss based on the\nS{{\\o}}rensen-Dice difference function, and a real-world face track dataset\nwith tens of thousands of frames, demonstrating the improved performance,\nefficiency, and scalabil-ity of the novel convex surrogate.","url_abs":"http://arxiv.org/abs/1604.03373v1","url_pdf":"http://arxiv.org/pdf/1604.03373v1.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":"a-convex-surrogate-operator-for-general-non","repo_url":"https://github.com/yjq8812/aistats2016","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}