{"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/negative-binomial-process-count-and-mixture","title":"Negative Binomial Process Count and Mixture Modeling","arxiv_id":"1209.3442","date":"2012-09-15","proceeding":null,"authors":["Mingyuan Zhou","Lawrence Carin"],"abstract":"The seemingly disjoint problems of count and mixture modeling are united\nunder the negative binomial (NB) process. A gamma process is employed to model\nthe rate measure of a Poisson process, whose normalization provides a random\nprobability measure for mixture modeling and whose marginalization leads to an\nNB process for count modeling. A draw from the NB process consists of a Poisson\ndistributed finite number of distinct atoms, each of which is associated with a\nlogarithmic distributed number of data samples. We reveal relationships between\nvarious count- and mixture-modeling distributions and construct a\nPoisson-logarithmic bivariate distribution that connects the NB and Chinese\nrestaurant table distributions. Fundamental properties of the models are\ndeveloped, and we derive efficient Bayesian inference. It is shown that with\naugmentation and normalization, the NB process and gamma-NB process can be\nreduced to the Dirichlet process and hierarchical Dirichlet process,\nrespectively. These relationships highlight theoretical, structural and\ncomputational advantages of the NB process. A variety of NB processes,\nincluding the beta-geometric, beta-NB, marked-beta-NB, marked-gamma-NB and\nzero-inflated-NB processes, with distinct sharing mechanisms, are also\nconstructed. These models are applied to topic modeling, with connections made\nto existing algorithms under Poisson factor analysis. Example results show the\nimportance of inferring both the NB dispersion and probability parameters.","url_abs":"http://arxiv.org/abs/1209.3442v3","url_pdf":"http://arxiv.org/pdf/1209.3442v3.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":"negative-binomial-process-count-and-mixture","repo_url":"https://github.com/rmehta1987/CoZINB","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"bayesian-inference","task_name":"Bayesian Inference"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1209.3442","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}