{"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-learning-of-optimal-markov-network","title":"Efficient Learning of Optimal Markov Network Topology with k-Tree Modeling","arxiv_id":"1801.06900","date":"2018-01-21","proceeding":null,"authors":["Liang Ding","Di Chang","Russell Malmberg","Aaron Martinez","David Robinson","Matthew Wicker","Hongfei Yan","Liming Cai"],"abstract":"The seminal work of Chow and Liu (1968) shows that approximation of a finite\nprobabilistic system by Markov trees can achieve the minimum information loss\nwith the topology of a maximum spanning tree. Our current paper generalizes the\nresult to Markov networks of tree width $\\leq k$, for every fixed $k\\geq 2$. In\nparticular, we prove that approximation of a finite probabilistic system with\nsuch Markov networks has the minimum information loss when the network topology\nis achieved with a maximum spanning $k$-tree. While constructing a maximum\nspanning $k$-tree is intractable for even $k=2$, we show that polynomial\nalgorithms can be ensured by a sufficient condition accommodated by many\nmeaningful applications. In particular, we prove an efficient algorithm for\nlearning the optimal topology of higher order correlations among random\nvariables that belong to an underlying linear structure.","url_abs":"http://arxiv.org/abs/1801.06900v1","url_pdf":"http://arxiv.org/pdf/1801.06900v1.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-learning-of-optimal-markov-network","repo_url":"https://github.com/Aaron-Martinez/OMkT","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"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}