[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-85784-en":3,"doc-seo-85784-105":29,"detail-sidebar-cat-0-en-105":83},{"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":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":13,"seo_description":14,"update_tm":27,"read_time":28},85784,8796095462418,"Noah","https://ap-avatar.wpscdn.com/avatar/80000253c1241d02b47?x-image-process=image/resize,m_fixed,w_180,h_180&k=1778826106357471780",8,"Research & Report","Manifold Constrained Conformal Prediction for Spatial Events","A new conformal prediction framework constructs calibrated prediction sets for collections of spatial events, including tropical cyclone genesis and earthquake locations. Spatial point clouds are represented as empirical measures and scored via sliced Wasserstein distance, yielding distribution-valued prediction sets. These sets are constrained to lie near the training-data manifold, improving practical validity. A coverage lower bound is derived for the intersected sets, and a data-adaptive criterion can tighten the coverage gap. Because the sets are not analytically tractable, a flow-based sampling ensemble is introduced. Synthetic and real-event experiments show near-nominal coverage with reduced energy and manifold distance versus HDR and generative baselines.","MANIFOLD CONSTRAINED CONFORMAL PREDICTION FOR SPATIAL EVENTS  \nCollin Nill  \nDepartment of Statistics University of Connecticut Storrs, CT 06269 [collin.nill@uconn.edu](collin.nill@uconn.edu)  \nTrevor A. Harris  \nDepartment of Statistics University of Connecticut Storrs, CT 06269  \n[trevor.a.harris@uconn.edu](trevor.a.harris@uconn.edu)  \narXiv :2607 . 10008v1 [ stat .ML] 10 Jul 2026  \nJason Adams  \nSandia National Laboratories Albuquerque, NM 87123 [jradams@sandia.gov](jradams@sandia.gov)  \nABSTRACT  \nWe introduce a new conformal prediction method that constructs calibrated prediction sets over collections of spatial events, such as tropical cyclone genesis and earthquake locations. Forecasting natural hazards has become increasingly important, due to their significant economic impact, and quantifying the uncertainty of predictions is critical for accurate risk assessment. Our approach works by representing spatial point clouds as empirical measures so that we can score them using (sliced) Wasserstein distance, then constraining the resulting distribution-valued prediction set to be supported only near the training data manifold. We derive a coverage lower bound for the intersected sets and show that, in practice, this gap can be made small through a simple data-adaptive selection criterion. Because the resulting set is not analytically tractable, we introduce a modified flow-based sampling procedure, which allows us to represent and apply these prediction sets in practice as ensembles. Numerical experiments on synthetic data, tropical cyclone genesis, and earthquake occurrences show that our method achieves near-nominal coverage, with significantly lower energy distance and manifold distance than highest predictive density region (HDR) baselines along with generative model baselines.  \n1 INTRODUCTION  \nNatural disasters are among the most consequential and difficult-to-predict phenomena in Geoscience. Tropical cyclones, earthquakes, and wildfires collectively account for trillions of dollars in economic losses and hundreds of thousands of deaths each year (Merz et al., 2020; Beven et al., 2018) . These hazards manifest as discrete, spatially organized configurations of events rather than as continuous fields. For example, the genesis locations of tropical cyclones in a given season, epicenters of earthquake sequences, ignition points of wildfire outbreaks. The number, positions, and spatial arrangement of these events are all meaningful, and the differences are particularly consequential for compound and extreme hazards, where dependence structure and spatial spread drive the largest risks (Davison & Huser, 2015; Zscheischler et al., 2018; Abbaszadeh et al., 2022) . Uncertainty quantification for these phenomena cannot be reduced to scalar or low-dimensional summaries.  \nModern forecasting systems are increasingly capable of operating at the level of event configurations. Climate models, stochastic simulators, and deep learning approaches all produce distributions over possible configurations, either through parameterized likelihood maps or through stochastic ensembles (Leutbecher & Palmer, 2008; Jordan et al., 2011; Zhou et al., 2022; Mukherjee et al., 2025) . Figure 1 shows examples of such configurations for tropical cyclone genesis and earthquake events. None of these approaches are guaranteed to produce calibrated uncertainty, i.e. taking the 90th percentile of an ensemble does not automatically imply 90% coverage of the true event cloud. The many interacting  \nFigure 1: Examples of event clouds on the sphere. Right: tropical cyclone genesis locations from one season (Gahtan et al., 2026), concentrated in tropical oceanic basins. Center: significant earthquake epicenters from the NGDC/WDS database (U.S. Geological Survey, 2026), tracing the global fault network. Left: a simulated calibration ensemble from a Hawkes process on the sphere (Section E) . Each panel is a finite point cloud on S2 of variable cardinality.  \nproc","cbCaimMiDwN9FOTq","https://ap.wps.com/l/cbCaimMiDwN9FOTq","pdf",13319741,1,21,"English","en",105,"# Introduction\n## Conformal prediction and coverage guarantees\n## Measure-based conformity scores and optimal transport\n## Motivation for manifold-constrained uncertainty","[{\"question\":\"What performance gains are reported in experiments?\",\"answer\":\"Numerical experiments on synthetic data and real spatial hazards show near-nominal coverage with significantly lower energy distance and manifold distance than HDR and generative-model baselines.\"}]",1784206270,53,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":78,"head_meta":80,"extra_data":82,"updated_unix":27},"manifold-constrained-conformal-prediction-for-spatial-events","",{"@graph":35,"@context":77},[36,53,68],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/manifold-constrained-conformal-prediction-for-spatial-events/85784/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-17","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71],{"name":72,"@type":73,"acceptedAnswer":74},"What performance gains are reported in experiments?","Question",{"text":75,"@type":76},"Numerical experiments on synthetic data and real spatial hazards show near-nominal coverage with significantly lower energy distance and manifold distance than HDR and generative-model baselines.","Answer","https://schema.org",{"og:url":51,"og:type":79,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":81,"canonical":51},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":84},[85,89,93,97,102,107,112,115,120,123,127],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":86,"show_sort_weight":87,"slug":88},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":90,"show_sort_weight":91,"slug":92},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":45,"category_name":94,"show_sort_weight":95,"slug":96},"Exam",70,"exam",{"id":98,"doc_module":4,"doc_module_name":45,"category_name":99,"show_sort_weight":100,"slug":101},5,"Comic",60,"comic",{"id":103,"doc_module":4,"doc_module_name":45,"category_name":104,"show_sort_weight":105,"slug":106},6,"Technology",50,"technology",{"id":108,"doc_module":4,"doc_module_name":45,"category_name":109,"show_sort_weight":110,"slug":111},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":113,"slug":114},30,"research-report",{"id":116,"doc_module":4,"doc_module_name":45,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":45,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":124,"doc_module":4,"doc_module_name":45,"category_name":125,"show_sort_weight":124,"slug":126},10,"Lifestyle","lifestyle",{"id":128,"doc_module":4,"doc_module_name":45,"category_name":129,"show_sort_weight":98,"slug":130},19,"General","general"]