{"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/copula-variational-bayes-inference-via","title":"Copula Variational Bayes inference via information geometry","arxiv_id":"1803.10998","date":"2018-03-29","proceeding":null,"authors":["Viet Hung Tran"],"abstract":"Variational Bayes (VB), also known as independent mean-field approximation,\nhas become a popular method for Bayesian network inference in recent years. Its\napplication is vast, e.g. in neural network, compressed sensing, clustering,\netc. to name just a few. In this paper, the independence constraint in VB will\nbe relaxed to a conditional constraint class, called copula in statistics.\nSince a joint probability distribution always belongs to a copula class, the\nnovel copula VB (CVB) approximation is a generalized form of VB. Via\ninformation geometry, we will see that CVB algorithm iteratively projects the\noriginal joint distribution to a copula constraint space until it reaches a\nlocal minimum Kullback-Leibler (KL) divergence. By this way, all mean-field\napproximations, e.g. iterative VB, Expectation-Maximization (EM), Iterated\nConditional Mode (ICM) and k-means algorithms, are special cases of CVB\napproximation.\n  For a generic Bayesian network, an augmented hierarchy form of CVB will also\nbe designed. While mean-field algorithms can only return a locally optimal\napproximation for a correlated network, the augmented CVB network, which is an\noptimally weighted average of a mixture of simpler network structures, can\npotentially achieve the globally optimal approximation for the first time. Via\nsimulations of Gaussian mixture clustering, the classification's accuracy of\nCVB will be shown to be far superior to that of state-of-the-art VB, EM and\nk-means algorithms.","url_abs":"http://arxiv.org/abs/1803.10998v1","url_pdf":"http://arxiv.org/pdf/1803.10998v1.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":"copula-variational-bayes-inference-via","repo_url":"https://github.com/VietTran86/PCA_MUSIC","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"},{"task_slug":"compressed-sensing","task_name":"compressed sensing"}],"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}