[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-125453-en":3,"doc-seo-125453-105":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},125453,1099514068365,"Aurelia","https://ap-avatar.wpscdn.com/avatar/10000253d8d9f28188e?_k=1776742907772140068",8,"Research & Report","Adaptive transformer modelling of density function for nonparametric survival analysis","Survival analysis plays an essential role across economics, engineering, and healthcare by supporting time-invariant and time-varying data such as customer churn, material degradation, and medical outcomes. Conventional approaches often produce cluttered probability distribution functions, show limited sensitivity for censoring prediction, focus only on static datasets, or depend on recurrent networks for dynamic modeling. This paper introduces UniSurv, a transformer-based nonparametric survival regression method that generates high-quality unimodal PDFs without prior distribution assumptions, using a Margin-Mean-Variance loss.","Adaptive transformer modelling of density function for nonparametric survival analysis  \nXin Zhang1,2 · Deval Mehta2,3 · Yanan Hu4 · Chao Zhu5 · David Darby5 · Zhen Yu2,3 · Daniel Merlo5 · Melissa Gresle5 · Anneke van der Walt5,6 · Helmut Butzkueven5,6 · Zongyuan Ge2,3  \nReceived: 30 May 2024 / Revised: 6 August 2024 / Accepted: 12 December 2024 /  \nPublished online: 27 January 2025 © The Author(s) 2025  \nAbstract  \nSurvival analysis holds a crucial role across diverse disciplines, such as economics, engineering and healthcare. It empowers researchers to analyze both time-invariant and timevarying data, encompassing phenomena like customer churn, material degradation and various medical outcomes. Given the complexity and heterogeneity of such data, recent endeavors have demonstrated successful integration of deep learning methodologies to address limitations in conventional statistical approaches. However, current methods typically involve cluttered probability distribution function (PDF), have lower sensitivity in censoring prediction, only model static datasets, or only rely on recurrent neural networks for dynamic modelling. In this paper, we propose a novel survival regression method capable of producing high-quality unimodal PDFs without any prior distribution assumption, by optimizing novel Margin-Mean-Variance loss and leveraging the flexibility of Transformer to handle both temporal and non-temporal data, coined UniSurv. Extensive experiments on several datasets demonstrate that UniSurv places a significantly higher emphasis on censoring compared to other methods.  \nKeywords Survival analysis · Transformer · Margin-Mean-Variance loss · Deep learning  \n1 Introduction  \nThe primary task of survival analysis is to determine the timing of one or multiple events, which can signify the moment of a mechanical system malfunction, the period of transition from corporate deficit to surplus, the instance of patient fatality or so on, depending on the specific circumstance (Lee & Whitmore, 2006) . Among all scenarios, survival analysis for medical data poses the most severe challenges (Collett, 2023) . Some medical datasets are longitudinal, as exemplified by electronic health records (EHRs), where multiple observations of each patient’s covariates over time are recorded. Survival models must be capable of handling such measurements and learning from their continuous temporal trends.  \nEditors: Kee-Eung Kim, Shou-De Lin.  \nExtended author information available on the last page of the article  \nMoreover, observations in longitudinal data are often sparse, necessitating the effective handling of missing values for any reliable survival model, even when the missing rates are exceedingly high (Singer & Willett, 1991) . Additionally, censoring represents a fundamental aspect of survival data, referring to cases in which complete information regarding the survival time or event occurrence of a subject is not fully observed or available within the study period (Leung et al., 1997) . The occurrence of censoring signifies the unknown exact timing of the event, consequently lacking ground truth for comparative learning. This, in turn, poses significant challenges for deep survival learning. Existing deep learning approaches aim at mitigating this issue by typically guaranteeing non-occurrence of events before censoring. Notwithstanding, detailed elucidation pertaining to the temporal aspect of events subsequent to censoring frequently remains inadequately explored.  \nDeveloping survival analysis models requires regressing the probability of survival over a defined period. A high-quality estimation of probability distribution is essential for the time-to-event prediction. As the initial category, parametric survival models are capable of generating high-quality probability density function (PDF) or survival curve by predetermining stochastic distribution, however, their precision is contingent upon the validity of all underlying assumptions.","cbCaivcj9RrGL4ln","https://ap.wps.com/l/cbCaivcj9RrGL4ln","pdf",2726562,1,24,"English","en",105,"# Abstract\n# 1 Introduction\n## Motivation and challenges in survival learning\n## Parametric vs non-parametric modeling\n# 2 Literature\n## Parametric and proportional hazards approaches","[{\"question\":\"What problem does UniSurv target in survival analysis?\",\"answer\":\"UniSurv targets limitations of existing deep survival methods, including cluttered PDFs, weaker censoring prediction, and insufficient handling of dynamic, longitudinal, and missing-value data.\"},{\"question\":\"How does UniSurv produce probability density functions without prior assumptions?\",\"answer\":\"UniSurv is designed as a non-parametric survival regression method that generates high-quality unimodal PDFs without relying on any predetermined event-time distribution.\"},{\"question\":\"Why is censoring prediction emphasized in UniSurv?\",\"answer\":\"The paper states that UniSurv places significantly higher emphasis on censoring compared with other methods, improving accuracy when exact event timing is not fully observed.\"}]","Adaptive transformer modelling of density function for nonparametric survival analysis | PDF",1785899086,60,{"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},"adaptive-transformer-modelling-of-density-function-for-nonparametric-survival-analysis","",{"@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/adaptive-transformer-modelling-of-density-function-for-nonparametric-survival-analysis/125453/",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","2026-08-05",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},"What problem does UniSurv target in survival analysis?","Question",{"text":75,"@type":76},"UniSurv targets limitations of existing deep survival methods, including cluttered PDFs, weaker censoring prediction, and insufficient handling of dynamic, longitudinal, and missing-value data.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does UniSurv produce probability density functions without prior assumptions?",{"text":80,"@type":76},"UniSurv is designed as a non-parametric survival regression method that generates high-quality unimodal PDFs without relying on any predetermined event-time distribution.",{"name":82,"@type":73,"acceptedAnswer":83},"Why is censoring prediction emphasized in UniSurv?",{"text":84,"@type":76},"The paper states that UniSurv places significantly higher emphasis on censoring compared with other methods, improving accuracy when exact event timing is not fully observed.","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},[93,97,101,105,109,114,119,122,127,130,134],{"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":29,"slug":108},5,"Comic","comic",{"id":110,"doc_module":4,"doc_module_name":46,"category_name":111,"show_sort_weight":112,"slug":113},6,"Technology",50,"technology",{"id":115,"doc_module":4,"doc_module_name":46,"category_name":116,"show_sort_weight":117,"slug":118},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":120,"slug":121},30,"research-report",{"id":123,"doc_module":4,"doc_module_name":46,"category_name":124,"show_sort_weight":125,"slug":126},9,"Religion & Spirituality",20,"religion-spirituality",{"id":125,"doc_module":4,"doc_module_name":46,"category_name":128,"show_sort_weight":125,"slug":129},"World Cup","world-cup",{"id":131,"doc_module":4,"doc_module_name":46,"category_name":132,"show_sort_weight":131,"slug":133},10,"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":46,"category_name":136,"show_sort_weight":106,"slug":137},19,"General","general"]