{"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/vector-space-markov-random-fields-via","title":"Vector-Space Markov Random Fields via Exponential Families","arxiv_id":"1505.05117","date":"2015-05-19","proceeding":null,"authors":["Wesley Tansey","Oscar Hernan Madrid Padilla","Arun Sai Suggala","Pradeep Ravikumar"],"abstract":"We present Vector-Space Markov Random Fields (VS-MRFs), a novel class of\nundirected graphical models where each variable can belong to an arbitrary\nvector space. VS-MRFs generalize a recent line of work on scalar-valued,\nuni-parameter exponential family and mixed graphical models, thereby greatly\nbroadening the class of exponential families available (e.g., allowing\nmultinomial and Dirichlet distributions). Specifically, VS-MRFs are the joint\ngraphical model distributions where the node-conditional distributions belong\nto generic exponential families with general vector space domains. We also\npresent a sparsistent $M$-estimator for learning our class of MRFs that\nrecovers the correct set of edges with high probability. We validate our\napproach via a set of synthetic data experiments as well as a real-world case\nstudy of over four million foods from the popular diet tracking app\nMyFitnessPal. Our results demonstrate that our algorithm performs well\nempirically and that VS-MRFs are capable of capturing and highlighting\ninteresting structure in complex, real-world data. All code for our algorithm\nis open source and publicly available.","url_abs":"http://arxiv.org/abs/1505.05117v1","url_pdf":"http://arxiv.org/pdf/1505.05117v1.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":"vector-space-markov-random-fields-via","repo_url":"https://github.com/tansey/vsmrfs","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}