{"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/submodular-relaxation-for-inference-in-markov","title":"Submodular relaxation for inference in Markov random fields","arxiv_id":"1501.03771","date":"2015-01-15","proceeding":null,"authors":["Anton Osokin","Dmitry Vetrov"],"abstract":"In this paper we address the problem of finding the most probable state of a\ndiscrete Markov random field (MRF), also known as the MRF energy minimization\nproblem. The task is known to be NP-hard in general and its practical\nimportance motivates numerous approximate algorithms. We propose a submodular\nrelaxation approach (SMR) based on a Lagrangian relaxation of the initial\nproblem. Unlike the dual decomposition approach of Komodakis et al., 2011 SMR\ndoes not decompose the graph structure of the initial problem but constructs a\nsubmodular energy that is minimized within the Lagrangian relaxation. Our\napproach is applicable to both pairwise and high-order MRFs and allows to take\ninto account global potentials of certain types. We study theoretical\nproperties of the proposed approach and evaluate it experimentally.","url_abs":"http://arxiv.org/abs/1501.03771v1","url_pdf":"http://arxiv.org/pdf/1501.03771v1.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":"submodular-relaxation-for-inference-in-markov","repo_url":"https://github.com/aosokin/submodular-relaxation","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}