[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-122172-en":3,"doc-seo-122172-105":30,"detail-sidebar-cat-0-en-105":84},{"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},122172,7971461740886,"Theodore","https://ap-avatar.wpscdn.com/davatar_3d24733baf745e90a7e4bdd5f77d97b2",8,"Research & Report","On the Learnability of Out-of-distribution Detection - Learnability Study","Supervised learning assumes training and test data follow the same distribution, yet real-world deployment often violates this through out-of-distribution (OOD) inputs with unseen labels. This paper studies generalization for OOD detection using Probably Approximately Correct (PAC) learning, matching common evaluation metrics such as risk and AUC. It derives a necessary condition for learnability, proves impossibility theorems under certain scenarios, then identifies practical conditions that can avoid these barriers and provides theoretical support for representative OOD methods.","On the Learnability of Out-of-distribution Detection  \nZhen Fang  \nAustralian Arti􀀌cial Intelligence Institute University of Technology Sydney  \n61 Broadway, Ultimo NSW 2007, Australia  \nYixuan Li  \nDepartment of Computer Sciences The University of Wisconsin Madison  \n1210 W Dayton St, Madison, WI 53706, USA Feng Liu 􀀀  \nSchool of Computing and Information Systems The University of Melbourne  \n700 Swanston Street, Carlton VIC 3053, Australia  \nBo Han  \nDepartment of Computer Science Hong Kong Baptist University  \nKowloon Tong, Hong Kong SAR Jie Lu 􀀀  \nAustralian Arti􀀌cial Intelligence Institute University of Technology Sydney  \n61 Broadway, Ultimo NSW 2007, Australia  \n[zhen.fang@uts.edu.au](zhen.fang@uts.edu.au)  \n[sharonli@cs.wisc.edu](sharonli@cs.wisc.edu)  \n[feng.liu1@unimelb.edu.au](feng.liu1@unimelb.edu.au)  \n[bhanml@comp.hkbu.edu.hk](bhanml@comp.hkbu.edu.hk)  \n[jie.lu@uts.edu.au](jie.lu@uts.edu.au)  \nEditor: Amos Storkey  \nAbstract  \nSupervised learning aims to train a classi􀀌er under the assumption that training and test data are from the same distribution. To ease the above assumption, researchers have studied a more realistic setting: out-of-distribution (OOD) detection, where test data may come from classes that are unknown during training (i.e., OOD data) . Due to the unavailability and diversity of OOD data, good generalization ability is crucial for e􀀋ective OOD detection algorithms, and corresponding learning theory is still an open problem. To study the generalization of OOD detection, this paper investigates the probably approximately correct (PAC) learning theory of OOD detection that 􀀌ts the commonly used evaluation metrics in the literature. First, we 􀀌nd a necessary condition for the learnability of OOD detection. Then, using this condition, we prove several impossibility theorems for the learnability of OOD detection under some scenarios. Although the impossibility theorems are frustrating, we 􀀌nd that some conditions of these impossibility theorems may not hold in some practical scenarios. Based on this observation, we next give several necessary and su􀀎cient conditions to characterize the learnability of OOD detection in some practical scenarios. Lastly, we o􀀋er theoretical support for representative OOD detection works based on our OOD theory.  \nKeywords: out-of-distribution detection, weakly supervised learning, learnability  \n©2024 Zhen Fang, Yixuan Li, Feng Liu, Bo Han, Jie Lu.  \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  \nprovided at [http://jmlr.org/papers/v25/23-1257.html](http://jmlr.org/papers/v25/23-1257.html).  \nFang, Li, Liu, Han, Lu  \n1. Introduction  \nThe success of supervised learning is established on an in-distribution (ID) assumption that training and test data share the same distribution (Dosovitskiy et al., 2021; Huang et al., 2017; Hsu et al., 2020; Yang et al., 2021) . However, in many real-world scenarios, the distribution of test data violates the assumption and, instead, contains out-of-distribution (OOD) data whose labels have not been seen during the training process (Bendale and Boult, 2016; Chen et al., 2021a) . To mitigate the risk brought by OOD data, a more practical learning scenario is considered in the machine learning 􀀌eld: OOD detection, which determines whether an input is ID/OOD, while classifying the ID data into respective classes.  \nOOD detection can signi􀀌cantly increase the reliability of machine learning models when deploying them in the real world. Many seminar algorithms have been developed to empirically address the OOD detection problem (Hendrycks and Gimpel, 2017; Liang et al., 2018; Lee et al., 2018; Zong et al., 2018; Pidhorskyi et al., 2018; Nalisnick et al., 2019; Hendryckset al., 2019; Ren et al., 2019; Lin et al., 2021; Salehi et al., 2021; Sun et al., 2021) . A common sol","cbCaiq3ibn0xT7HU","https://ap.wps.com/l/cbCaiq3ibn0xT7HU","pdf",801398,1,83,"English","en",105,"# Introduction\n## Learning scenario: from in-distribution to OOD detection\n## Motivation and research question: PAC learnability under risk and AUC\n## Paper structure: domain space and function space framework","[{\"question\":\"How do the authors reconcile impossibility results with practical scenarios?\",\"answer\":\"They show that some conditions required for the impossibility theorems may not hold in real-world applications. Based on this observation, they derive alternative conditions under which learnability can still be achieved.\"}]","On the Learnability of Out-of-distribution Detection - Learnability Study | PDF",1785809178,209,{"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":79,"head_meta":81,"extra_data":83,"updated_unix":28},"on-the-learnability-of-out-of-distribution-detection-learnability-study","",{"@graph":36,"@context":78},[37,54,69],{"@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/on-the-learnability-of-out-of-distribution-detection-learnability-study/122172/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"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","2026-08-05","2026-08-04",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72],{"name":73,"@type":74,"acceptedAnswer":75},"How do the authors reconcile impossibility results with practical scenarios?","Question",{"text":76,"@type":77},"They show that some conditions required for the impossibility theorems may not hold in real-world applications. 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