[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-81623-en":3,"doc-seo-81623-105":30,"detail-sidebar-cat-0-en-105":92},{"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":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},81623,8796095360427,"Lucas Martin","https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d",8,"Research & Report","Kronecker-Structured Nonparametric Spatiotemporal Point Processes","Events in spatiotemporal domains are central to applications such as weather, traffic, disasters, epidemics, and migration, where event-relation discovery and reliable prediction are key. Classical Poisson/Hawkes models impose restrictive parametric kernels, while neural point process methods often encode interactions implicitly, limiting interpretability. KSTPP introduces a Kronecker-structured nonparametric spatiotemporal point process with GP background intensity and spatiotemporal GP influence kernels, enabling explicit excitation/inhibition/neutrality and time-varying effects. Separable product kernels and Kronecker algebra reduce computation, with tensor-product Gauss-Legendre quadrature for tractable likelihood integrals.","Kronecker-Structured Nonparametric Spatiotemporal Point Processes  \nZhitong Xu 1 Qiwei Yuan 1 Yinghao Chen 1 Yan Sun2 Bin Shen3 Shandian Zhe 1  \n1 Kahlert School of Computing, The University of Utah  \n2 College of Arts & Sciences, Utah State University  \n3 Celonis AI  \narXiv :2603 .23746v2 [ cs .LG] 9 Jul 2026  \nAbstract  \nEvents in spatiotemporal domains arise in numerous real-world applications, where uncovering event relationships and enabling accurate prediction are central challenges. Classical Poisson and Hawkes processes rely on restrictive parametric assumptions that limit their ability to capture complex interaction patterns, while recent neural point process models increase representational capacity but integrate event information ina black-box manner, hindering interpretable relationship discovery. To address these limitations, we propose a Kronecker-Structured Nonparametric Spatiotemporal Point Process (KSTPP) that enables transparent event-wise relationship discovery while retaining high modeling flexibility. We model the background intensity with a spatial Gaussian process (GP) and the influence kernel as a spatiotemporal GP, allowing rich interaction patterns including excitation, inhibition, neutrality, and time-varying effects. To enable scalable training and prediction, we adopt separable product kernels and represent the GPs on structured grids, inducing Kronecker-structured covariance matrices. Exploiting Kronecker algebra substantially reduces computational cost and allows the model to scale to large event collections. In addition, we develop a tensor-product Gauss-Legendre quadrature scheme to efficiently evaluate intractable likelihood integrals. Extensive experiments demonstrate the effectiveness of our framework. The code is released at [https://github.com/](https://github.com/)[ ](https://github.com/)BayesianAIGroup/KSTPP.  \n1 INTRODUCTION  \nSpatiotemporal events arise in many real-world domains, including weather dynamics, traffic accidents, natural disasters, epidemics, and population migration. Modeling such events for relationship discovery and predictive analysis is crucial. Understanding interactions among events facilitates uncovering the underlying mechanisms driving these phenomena, while accurate prediction enables risk monitoring, early warning, and timely intervention.  \nExisting spatiotemporal point process models—though widely used—face several limitations. Classical Poisson processes assume event independence and thus ignore mutual influences. Hawkes processes [Hawkes, 1971] introduce self-excitation via triggering effects from past events but typically rely on parametric kernels (e.g., exponential forms), which restrict their ability to capture diverse temporal patterns and inhibitory interactions.  \nAt the other extreme, recent neural point process models directly parameterize the conditional intensity using deep architectures. For example, Neural Hawkes processes [Mei and Eisner, 2017] and Recurrent Marked Point Processes [Du et al., 2016] encode event histories via recurrent neural networks; Neural Spatial Temporal Point Processes [Chen et al., 2021] and Neural Jump Stochastic Differential Equations [Jia and Benson, 2019] incorporate continuous latent dynamics; and Transformer Hawkes Processes [Zuo et al., 2020] and Self-Attentive Hawkes Processes [Zhang et al., 2020] leverage transformer-based encoders. Although these approaches substantially enhance representational capacity, event interactions are encoded implicitly within latent states, hindering explicit and interpretable relationship discovery.  \nTo address these limitations, we propose KSTPP, a Kronecker-Structured Nonparametric Spatiotemporal Point Process. Our framework enables transparent and explicit discovery of event-wise relationships while retaining high modeling flexibility to capture complex interaction patterns,  \nincluding excitation, inhibition, neutrality, and time-varying effects. Our main contributions are sum","cbCaigqiToDE68G2","https://ap.wps.com/l/cbCaigqiToDE68G2","pdf",3116773,5,1,19,"English","en",105,"# Abstract\n# Introduction\n# Preliminaries","[{\"question\":\"What problem does KSTPP address compared with classical Poisson and Hawkes processes?\",\"answer\":\"KSTPP targets the limitations of restrictive parametric assumptions in classical Poisson/Hawkes models, which can’t represent complex excitation/inhibition patterns and diverse temporal behaviors effectively.\"},{\"question\":\"How does KSTPP make event relationships more transparent and interpretable?\",\"answer\":\"KSTPP uses a spatial Gaussian process for background intensity and a spatiotemporal Gaussian process for the influence kernel, explicitly modeling aggregated past-event influence rather than hiding interactions inside deep latent states.\"},{\"question\":\"How does KSTPP achieve scalable training and prediction?\",\"answer\":\"It employs separable product kernels and structured-grid GP representations that yield Kronecker-structured covariance matrices, enabling major computational cost reductions, and uses a tensor-product Gauss-Legendre quadrature scheme to evaluate intractable likelihood and density integrals efficiently.\"}]",1784174901,48,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":87,"head_meta":89,"extra_data":91,"updated_unix":28},"kronecker-structured-nonparametric-spatiotemporal-point-processes","",{"@graph":36,"@context":86},[37,54,69],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":21},"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/kronecker-structured-nonparametric-spatiotemporal-point-processes/81623/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":24,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-07-25","2026-07-16",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72,78,82],{"name":73,"@type":74,"acceptedAnswer":75},"What problem does KSTPP address compared with classical Poisson and Hawkes processes?","Question",{"text":76,"@type":77},"KSTPP targets the limitations of restrictive parametric assumptions in classical Poisson/Hawkes models, which can’t represent complex excitation/inhibition patterns and diverse temporal behaviors effectively.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"How does KSTPP make event relationships more transparent and interpretable?",{"text":81,"@type":77},"KSTPP uses a spatial Gaussian process for background intensity and a spatiotemporal Gaussian process for the influence kernel, explicitly modeling aggregated past-event influence rather than hiding interactions inside deep latent states.",{"name":83,"@type":74,"acceptedAnswer":84},"How does KSTPP achieve scalable training and prediction?",{"text":85,"@type":77},"It employs separable product kernels and structured-grid GP representations that yield Kronecker-structured covariance matrices, enabling major computational cost reductions, and uses a tensor-product Gauss-Legendre quadrature scheme to evaluate intractable likelihood and density integrals efficiently.","https://schema.org",{"og:url":52,"og:type":88,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":90,"canonical":52},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":93},[94,98,102,106,110,115,120,123,128,131,135],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":95,"show_sort_weight":96,"slug":97},"Story & 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