[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-125466-en":3,"doc-seo-125466-105":30,"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":27,"seo_description":14,"update_tm":28,"read_time":29},125466,1099514068365,"Aurelia","https://ap-avatar.wpscdn.com/avatar/10000253d8d9f28188e?_k=1776742907772140068",8,"Research & Report","Rectifying Conformity Scores for Better Conditional Coverage","We present a new method for generating confidence sets within the split conformal prediction framework. The approach learns a trainable transformation of any given conformity score to improve conditional coverage while keeping exact marginal coverage. The transformation relies on an estimate of the conditional quantile of conformity scores, enabling adaptive confidence sets in multi-output settings. A theoretical bound quantifies how quantile-estimation accuracy affects approximate conditional validity, and experiments show strong conditional coverage gains over existing methods.","Rectifying Conformity Scores for Better Conditional Coverage  \nVincent Plassier * 1 Alexander Fishkov * 2 3 Victor Dheur * 4 Mohsen Guizani 2 Souhaib Ben Taieb 2 4  \nMaxim Panov 2 Eric Moulines 2 5  \nAbstract  \nWe present a new method for generating confidence sets within the split conformal prediction framework. Our method performs a trainable transformation of any given conformity score to improve conditional coverage while ensuring exact marginal coverage. The transformation is based on an estimate of the conditional quantile of conformity scores. The resulting method is particularly beneficial for constructing adaptive confidence sets in multi-output problems where standard conformal quantile regression approaches have limited applicability. We develop a theoretical bound that captures the influence of the accuracy of the quantile estimate on the approximate conditional validity, unlike classical bounds for conformal prediction methods that only offer marginal coverage. We experimentally show that our method is highly adaptive to the local data structure and outperforms existing methods in terms of conditional coverage, improving the reliability of statistical inference in various applications.  \n1. Introduction  \nThe widespread deployment of AI models emphasizes the need for reliable uncertainty quantification (Gruber et al., 2023) . Although highly flexible in capturing complex statistical dependencies, these models can produce unreliable or overly confident predictions (Nalisnick et al., 2018) . Conformal prediction (CP; Vovk et al. (2005); Shafer & Vovk (2008)) offers a robust, distribution-free framework for predictions with finite-sample validity guarantees (Angelopoulos et al., 2023 ; 2024) .  \n*Equal contribution 1Lagrange Mathematics and Computing Research Center 2Mohamed bin Zayed University of Artificial Intelligence 3 Skolkovo Institute of Science and Technology 4University of Mons 5´Ecole Polytechnique. Correspondence to: Maxim Panov \u003C[maxim.panov@mbzuai.ac.ae](maxim.panov@mbzuai.ac.ae) >.  \nProceedings of the 42 nd International Conference on Machine Learning, Vancouver, Canada. PMLR 267, 2025 . Copyright 2025 by the author(s) .  \nClassical CP approaches guarantee marginal validity but fail to ensure the more desirable property of conditional validity, which customizes prediction regions to specific covariates. Prior studies have shown constructing meaningful prediction regions with exact conditional validity is infeasible without additional distributional assumptions (Vovk, 2012; Lei & Wasserman, 2014; Foygel Barber et al., 2021) . Consequently, current research emphasizes developing conformal methods that maintain marginal validity and achieve approximate conditional validity (Colombo, 2024; Gibbs et al., 2025) .  \nA typical relaxation of exact conditional coverage in earlier work involves group-conditional guarantees (Jung et al., 2023; Ding et al., 2024), which provide coverage guarantees for a predefined set of groups. Another branch of work partitions the covariate space X into multiple regions and applies CP within each set in the partition (LeRoy & Zhao, 2021; Alaa et al., 2023; Kiyani et al., 2024) . However, such partitioning based on the calibration set often leads to overly large prediction regions (Bian & Barber, 2023; Plassier et al., 2024) .  \nAn alternative approach weights the empirical cumulative distribution function with a “localizer” function that quantifies the similarity between calibration points and the test sample (Guan, 2023) . Although this method improves the localization of predictions, it has significant limitations, especially in high-dimensional covariate spaces.  \nFinally, several methods focus on the transformation of conformity scores (Han et al., 2022; Dey et al., 2022; Izbicki et al., 2022; Deutschmann et al., 2023; Dheur et al., 2024; Colombo, 2024) . These techniques adjust conformity scores to better approximate the conditional coverage. However, they usually require e","cbCaitE7iz2Oq5LR","https://ap.wps.com/l/cbCaitE7iz2Oq5LR","pdf",1085570,1,34,"English","en",105,"# Introduction\n## Conditional vs marginal validity\n## Prior relaxations of exact conditional coverage\n## Localization and weighting approaches\n## Conformity score transformations\n# Background\n## Regression setup and notation","[{\"question\":\"What does the theoretical analysis quantify?\",\"answer\":\"The analysis provides a bound relating approximate conditional validity to the approximation error from estimating the conditional quantile of conformity scores. \"}]","Rectifying Conformity Scores for Better Conditional Coverage | PDF",1785899160,86,{"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":78,"head_meta":80,"extra_data":82,"updated_unix":28},"rectifying-conformity-scores-for-better-conditional-coverage","",{"@graph":36,"@context":77},[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/rectifying-conformity-scores-for-better-conditional-coverage/125466/",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":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71],{"name":72,"@type":73,"acceptedAnswer":74},"What does the theoretical analysis quantify?","Question",{"text":75,"@type":76},"The analysis provides a bound relating approximate conditional validity to the approximation error from estimating the conditional quantile of conformity scores.","Answer","https://schema.org",{"og:url":52,"og:type":79,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":81,"canonical":52},"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":46,"category_name":86,"show_sort_weight":87,"slug":88},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":90,"show_sort_weight":91,"slug":92},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Exam",70,"exam",{"id":98,"doc_module":4,"doc_module_name":46,"category_name":99,"show_sort_weight":100,"slug":101},5,"Comic",60,"comic",{"id":103,"doc_module":4,"doc_module_name":46,"category_name":104,"show_sort_weight":105,"slug":106},6,"Technology",50,"technology",{"id":108,"doc_module":4,"doc_module_name":46,"category_name":109,"show_sort_weight":110,"slug":111},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":113,"slug":114},30,"research-report",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":46,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":124,"slug":126},10,"Lifestyle","lifestyle",{"id":128,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":98,"slug":130},19,"General","general"]