[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-122327-en":3,"doc-seo-122327-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},122327,687197207057,"Sage","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",8,"Research & Report","Efficient Inference for Dynamic Flexible Interactions of Neural Populations","Hawkes process provides an effective statistical framework for analyzing neural spiking interactions, yet the classic form cannot capture inhibitory effects within neural populations. A nonlinear Hawkes variant is introduced using sigmoid nonlinearity to model both excitatory and inhibitory influence patterns. To facilitate inference, auxiliary latent variables (Polya-Gamma, latent marked Poisson processes, and sparsity variables) are added to obtain Gaussian functional forms and closed-form updates. Efficient Gibbs sampling, EM, and mean-field algorithms are derived, and a dynamic extension using a Markov state process addresses time-varying systems, outperforming state-of-the-art methods on synthetic and real neural data.","E􀀎cient Inference for Dynamic Flexible Interactions of  \nNeural Populations  \nFeng Zhou1;[2](2 zhoufeng6288@tsinghua.edu.cn)[ zhoufeng6288@tsinghua.edu.cn](2 zhoufeng6288@tsinghua.edu.cn)  \nQuyu Kong3;[4](4 quyu.kong@anu.edu.au)[ quyu.kong@anu.edu.au](4 quyu.kong@anu.edu.au)  \n[Zhijie Deng](Zhijie Deng1 dzj17@mails.tsinghua.edu.cn)[1](Zhijie Deng1 dzj17@mails.tsinghua.edu.cn)[ dzj17@mails.tsinghua.edu.cn](Zhijie Deng1 dzj17@mails.tsinghua.edu.cn)  \n[Jichao Kan](Jichao Kan4 jichao.kan@student.uts.edu.au)[4](Jichao Kan4 jichao.kan@student.uts.edu.au)[ jichao.kan@student.uts.edu.au](Jichao Kan4 jichao.kan@student.uts.edu.au)  \nYixuan [Zhang](Zhang4 yixuan.zhang@student.uts.edu.au)[4](Zhang4 yixuan.zhang@student.uts.edu.au)[ yixuan.zhang@student.uts.edu.au](Zhang4 yixuan.zhang@student.uts.edu.au)  \nCheng Feng2;[5](5 cheng.feng@siemens.com)[ cheng.feng@siemens.com](5 cheng.feng@siemens.com)  \nJun Zhu 1 ;2 􀀃 [dcszj@tsinghua.edu.cn](dcszj@tsinghua.edu.cn)  \n[1](1 Dept. of Comp. Sci. & Tech)[ Dept. of Comp. Sci. & Tech](1 Dept. of Comp. Sci. & Tech). , [BNRist Center](BNRist Center), [THU-Bosch Joint ML Center](THU-Bosch Joint ML Center), [Tsinghua University](Tsinghua University)[ ](Tsinghua University)[2](2 THU-Siemens Joint Research Center for Industrial Intelligence and Internet of Things)[ THU-Siemens Joint Research Center for Industrial Intelligence and Internet of Things](2 THU-Siemens Joint Research Center for Industrial Intelligence and Internet of Things)  \n3 Research School of Computer Science, Australian National University  \n4 Data Science Institute, University of Technology Sydney  \n5 Siemens AG  \nEditor: David Sontag  \nAbstract  \nHawkes process provides an e􀀋ective statistical framework for analyzing the interactions of neural spiking activities. Although utilized in many real applications, the classic Hawkes process is incapable of modeling inhibitory interactions among neural population. Instead, the nonlinear Hawkes process allows for modeling a more 􀀍exible in􀀍uence pattern withexcitatory or inhibitory interactions. This work proposes a 􀀍exible nonlinear Hawkes process variant based on sigmoid nonlinearity. To ease inference, three sets of auxiliary latent variables (P􀀓olya-Gamma variables, latent marked Poisson processes and sparsity variables) are augmented to make functional connection weights appear in a Gaussian form, which enables simple iterative algorithms with analytical updates. As a result, the e􀀎cient Gibbs sampler, expectation-maximization (EM) algorithm and mean-􀀌eld (MF) approximation are derived to estimate the interactions among neural populations. Furthermore, to reconcile with time-varying neural systems, the proposed time-invariant model is extended to a dynamic version by introducing a Markov state process. Similarly, three analytical iterative inference algorithms: Gibbs sampler, EM algorithm and mean-􀀌eld approximation are derived. We compare the accuracy and e􀀎ciency of these inference algorithms on synthetic data, and further experiment on real neural recordings to demonstrate that the developed models achieve superior performance over the state-of-the-art competitors.  \nKeywords: nonlinear Hawkes process, P􀀓olya-Gamma augmentation, conditional conjugate, time-varying interaction  \n1. Introduction  \nOne of the most important tasks in neuroscience is to examine the neuronal activity in the cerebral cortex under varying experimental conditions. Recordings of neuronal activity are  \n􀀃 . The corresponding author  \n􀀍c2022 Feng Zhou, Quyu Kong, Zhijie Deng, Jichao Kan, Yixuan Zhang, Cheng Feng and Jun Zhu.  \nLicense: CC-BY 4.0, see [https://creativecommons.org/licenses/by/4.0/](https://creativecommons.org/licenses/by/4.0/. Attribution)[. Attribution](https://creativecommons.org/licenses/by/4.0/. Attribution) requirements are provided  \nat [http://jmlr.org/papers/v23/21-1273.html](http://jmlr.org/papers/v23/21-1273.html).  \nZhou, Kong, Deng, Kan, Zhang, Feng and Zhu  \nrepresented through a series o","cbCaiekzUP9AVIXc","https://ap.wps.com/l/cbCaiekzUP9AVIXc","pdf",4748482,1,49,"English","en",105,"# Introduction\n# Model and Inference Approach\n## Efficient Gibbs Sampling\n## EM Algorithm\n## Mean-Field Approximation\n# Dynamic Extension for Time-Varying Interactions\n# Experiments and Evaluation","[{\"question\":\"Why is the classic Hawkes process insufficient for neuroscience neural populations?\",\"answer\":\"The classic Hawkes process uses a linearly additive intensity, which mainly supports excitatory interactions; inhibitory interactions cannot be represented properly when a negative firing rate would occur.\"},{\"question\":\"What modeling change enables both excitatory and inhibitory interactions?\",\"answer\":\"The proposed nonlinear Hawkes process variant uses sigmoid nonlinearity, allowing a more flexible influence pattern that includes both excitatory and inhibitory effects.\"},{\"question\":\"How does the method make inference computationally efficient?\",\"answer\":\"Three sets of auxiliary latent variables are augmented so that functional connection weights take a Gaussian form, enabling iterative algorithms with analytical updates, including Gibbs sampling, EM, and mean-field approximation.\"}]","Efficient Inference for Dynamic Flexible Interactions of Neural Populations | PDF",1785810028,123,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"efficient-inference-for-dynamic-flexible-interactions-of-neural-populations","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/efficient-inference-for-dynamic-flexible-interactions-of-neural-populations/122327/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-04",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"Why is the classic Hawkes process insufficient for neuroscience neural populations?","Question",{"text":75,"@type":76},"The classic Hawkes process uses a linearly additive intensity, which mainly supports excitatory interactions; inhibitory interactions cannot be represented properly when a negative firing rate would occur.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What modeling change enables both excitatory and inhibitory interactions?",{"text":80,"@type":76},"The proposed nonlinear Hawkes process variant uses sigmoid nonlinearity, allowing a more flexible influence pattern that includes both excitatory and inhibitory effects.",{"name":82,"@type":73,"acceptedAnswer":83},"How does the method make inference computationally efficient?",{"text":84,"@type":76},"Three sets of auxiliary latent variables are augmented so that functional connection weights take a Gaussian form, enabling iterative algorithms with analytical updates, including Gibbs sampling, EM, and mean-field approximation.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]