[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-144476-105":59,"doc-detail-144476-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","beta-negative-binomial-process-and-exchangeable-random-partitions-for-mixed-membership-modeling","Beta-Negative Binomial Process and Exchangeable Random Partitions for Mixed-Membership Modeling","","This paper introduces the integer-valued Beta-Negative Binomial Process (BNBP) for partitioning a count vector into a latent column-exchangeable random count matrix. The contributions include proposing an exchangeable partition probability function (EPPF) for mixed-membership modeling, deriving a prediction rule for simulating exchangeable random partitions in grouped data governed by the BNBP, constructing a fully collapsed Gibbs sampler with closed-form update equations, and demonstrating that the BNBP topic model exhibits fast convergence, good mixing, and state-of-the-art prediction performance for corpus representation. The model and inference sections detail the Beta Negative Binomial Process, augmented representation, group size dependent mixture model, conditional likelihood, exchangeable cluster and partition probability functions, prediction rule for simulated exchangeable random partitions, mixed-membership modeling with the BNBP topic model, parameter inference, and a comparison with the HDP-LDA collapsed Gibbs sampler.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/beta-negative-binomial-process-and-exchangeable-random-partitions-for-mixed-membership-modeling/144476/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/beta-negative-binomial-process-and-exchangeable-random-partitions-for-mixed-membership-modeling/144476.png","ImageObject",300,407,{"name":92,"@type":93},"Caleb Sterling","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-08-26",true,{"@type":102,"interactionType":103,"userInteractionCount":44},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What is the main contribution of this paper regarding probability functions?","Question",{"text":112,"@type":113},"The paper proposes an exchangeable partition probability function (EPPF) specifically designed for mixed-membership modeling.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What are the key aspects of the BNBP topic model's performance identified in the paper?",{"text":117,"@type":113},"The BNBP topic model is shown to converge quickly, mix well, and achieve state-of-the-art prediction performance, especially when a compact corpus representation is desired.",{"name":119,"@type":110,"acceptedAnswer":120},"What inference method is employed in this research?",{"text":121,"@type":113},"A fully collapsed Gibbs sampler is constructed for parameter inference, featuring closed-form update equations for the model parameters.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},144476,1787703030,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":44,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":8,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":129,"read_time":81},962084925290,"https://ap-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45","Beta-­‐Nega(ve Binomial Process and Exchangeable Random Par((ons for Mixed-­‐Membership Modeling  \nMingyuan Zhou  \nDepartment of Informa(on, Risk, and Opera(ons Management, McCombs School of Business  \nThe University of Texas at Aus(n, Aus(n, TX, USA  \nIntroduc(on  \nThe integer-­‐valued beta-­‐nega1ve binomial process (BNBP) is employed to par11on a count vector into a latent columnexchangeable random count matrix . The paper makes the following contribu1ons:  \n􀀡An exchangeable par11on probability func1on (EPPF) for mixed-­‐membership modeling is proposed.  \n􀀡The predic1on rule to simulate the exchangeable random par11ons for grouped data governed by the BNBP is derived.  \n􀀡A fully collapsed Gibbs sampler, with closed-­‐form update equa1ons for model parameters, is constructed.  \n􀀡The BNBP topic model is shown to converge fast, mix well, and provide state-­‐of-­‐the-­‐art predic1on performance when a compact representa1on of the corpus is desired.  \nModel and Inference  \n􀀢 Beta Nega(ve Binomial Process  \nAugmented representa1on:  \n􀀢Group size dependent mixture model  \nCondi1onal Likelihood:  \nExchangeable Cluster Probability Func1on:  \nExchangeable Par11on Probability Func1on:  \nPredic(on Rule Simulated Exchangeable Random Par((ons  \nMixed-­‐Membership Modeling  \n􀀢 BNBP Topic Model  \n􀀢 Parameter Inference  \n􀀢 HDP-­‐LDA Collapsed Gibbs Sampler  \n􀀢 BNBP Collapsed Gibbs Sampler","cbCaiuuBupZ9TQ6X","https://ap.wps.com/l/cbCaiuuBupZ9TQ6X","pdf",1488830,"English","# Model and Inference\n## Beta Negative Binomial Process\n## Group size dependent mixture model\n## Conditional Likelihood\n## Exchangeable Cluster Probability Function\n## Exchangeable Partition Probability Function\n## Prediction Rule Simulated Exchangeable Random Partitions\n## Mixed-Membership Modeling\n### BNBP Topic Model\n### Parameter Inference\n### HDP-LDA Collapsed Gibbs Sampler\n### BNBP Collapsed Gibbs Sampler","[{\"question\":\"What is the main contribution of this paper regarding probability functions?\",\"answer\":\"The paper proposes an exchangeable partition probability function (EPPF) specifically designed for mixed-membership modeling.\"},{\"question\":\"What are the key aspects of the BNBP topic model's performance identified in the paper?\",\"answer\":\"The BNBP topic model is shown to converge quickly, mix well, and achieve state-of-the-art prediction performance, especially when a compact corpus representation is desired.\"},{\"question\":\"What inference method is employed in this research?\",\"answer\":\"A fully collapsed Gibbs sampler is constructed for parameter inference, featuring closed-form update equations for the model parameters.\"}]","Beta-Negative Binomial Process and Exchangeable Random Partitions for Mixed-Membership Modeling | PDF"]