{"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/variational-mixture-models-with-gamma-or","title":"Variational Mixture Models with Gamma or inverse-Gamma components","arxiv_id":"1607.07573","date":"2016-07-26","proceeding":null,"authors":["A. Llera","D. Vidaurre","R. H. R. Pruim","C. F. Beckmann"],"abstract":"Mixture models with Gamma and or inverse-Gamma distributed mixture components\nare useful for medical image tissue segmentation or as post-hoc models for\nregression coefficients obtained from linear regression within a Generalised\nLinear Modeling framework (GLM), used in this case to separate stochastic\n(Gaussian) noise from some kind of positive or negative \"activation\" (modeled\nas Gamma or inverse-Gamma distributed). To date, the most common choice in this\ncontext it is Gaussian/Gamma mixture models learned through a maximum\nlikelihood (ML) approach; we recently extended such algorithm for mixture\nmodels with inverse-Gamma components. Here, we introduce a fully analytical\nVariational Bayes (VB) learning framework for both Gamma and/or inverse-Gamma\ncomponents. We use synthetic and resting state fMRI data to compare the\nperformance of the ML and VB algorithms in terms of area under the curve and\ncomputational cost. We observed that the ML Gaussian/Gamma model is very\nexpensive specially when considering high resolution images; furthermore, these\nsolutions are highly variable and they occasionally can overestimate the\nactivations severely. The Bayesian Gauss-Gamma is in general the fastest\nalgorithm but provides too dense solutions. The maximum likelihood\nGaussian/inverse-Gamma is also very fast but provides in general very sparse\nsolutions. The variational Gaussian/inverse-Gamma mixture model is the most\nrobust and its cost is acceptable even for high resolution images. Further, the\npresented methodology represents an essential building block that can be\ndirectly used in more complex inference tasks, specially designed to analyse\nMRI-fMRI data; such models include for example analytical variational mixture\nmodels with adaptive spatial regularization or better source models for new\nspatial blind source separation approaches.","url_abs":"http://arxiv.org/abs/1607.07573v1","url_pdf":"http://arxiv.org/pdf/1607.07573v1.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":"variational-mixture-models-with-gamma-or","repo_url":"https://github.com/allera/One_Dim_Mixture_Models","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"blind-source-separation","task_name":"blind source separation"},{"task_slug":"regression-1","task_name":"regression"}],"methods":[{"method_slug":"linear-regression","method_name":"Linear Regression"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}