[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-125614-en":3,"doc-seo-125614-105":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},125614,549758146520,"Patrick","https://ap-avatar.wpscdn.com/avatar/80002397d8c0411e94?_k=1775819394049821470",8,"Research & Report","Rank-based Decomposable Losses in Machine Learning - A Survey","Recent works show a key paradigm for designing loss functions that relate individual losses to aggregate losses. Individual loss evaluates model quality on each sample, while aggregate loss combines per-sample losses or scores through an aggregation procedure. Ranking order captures the fundamental relation among individual values, and decomposability allows a loss to be written as an ensemble of individual terms. This survey reviews rank-based decomposable losses, proposes a taxonomy based on aggregate versus individual perspectives, derives general formulas, connects to prior research, and outlines future directions.","arXiv :2207 .08768v 3 [ cs .LG] 14 Jul 2023  \nRank-based Decomposable Losses in Machine  \nLearning: A Survey  \nShu Hu􀀃 , Xin Wang, Senior Member, IEEE, Siwei Lyu, Fellow, IEEE  \nAbstract—Recent works have revealed an essential paradigm in designing loss functions that differentiate individual losses vs. aggregate losses. The individual loss measures the quality of the model on a sample, while the aggregate loss combines individual losses/scores over each training sample. Both have a common procedure that aggregates a set of individual values to a single numerical value. The ranking order reflects the most fundamental relation among individual values in designing losses. In addition, decomposability, in which a loss can be decomposed into an ensemble of individual terms, becomes a significant property of organizing losses/scores. This survey provides a systematic and comprehensive review of rank-based decomposable losses in machine learning. Specifically, we provide a new taxonomy of loss functions that follows the perspectives of aggregate loss and individual loss. We identify the aggregator to form such losses, which are examples of set functions. We organize the rank-based decomposable losses into eight categories. Following these categories, we review the literature on rank-based aggregate losses and rank-based individual losses. We describe general formulas for these losses and connect them with existing research topics. We also suggest future research directions spanning unexplored, remaining, and emerging issues in rank-based decomposable losses.  \nIndex Terms—Loss Function, Aggregate Loss, Individual Loss, Rank-based Loss, Robust Learning, Machine Learning, Deep Learning  \n1 INTRODUCTION  \nMACHINE learning is instrumental to recent advances  \nin artificial intelligence and big data analysis. They have been used in almost every area of computer science and many fields of natural sciences, engineering, and social sciences. Practical applications of machine learning algorithms are also abundant – it is not an exaggeration to say that without efficient and effective machine learning algorithms, many industries, such as internet advertisement, automatic driving, and social network mining, would not have flourished. Most machine learning models are trained by minimizing a learning objective over a set of training samples. The learning objective comprises the learning loss corresponding to the errors on the training set, regularizers that control the model complexity, and constraints that incorporate conditions on the model parameters.  \nIn forming the learning objective, training loss is a critical component. The loss function is often constructed by aggregating a set of individual values into a single numerical value. The loss measures the quality of the model on a single training sample and is referred to as the individual loss. For example, in binary classification, the individual loss usually quantifies the discrepancy between the prediction score and the label. On the other hand, the loss that works overall training data is referred to as the aggregate loss, which combines individual losses or scores (prediction scores from  \n􀀏 Shu Hu is with the Department of Computer Information and Graphics Technology, Purdue School of Engineering and Technology at Indiana University-Purdue University Indianapolis, IN, 46202, USA and the Heinz College of Information Systems and Public Policy, Carnegie Mellon University, Pittsburgh, PA, 15213, USA. e-mail:([shuhu@cmu.edu](shuhu@cmu.edu))  \n􀀏 Xin Wang, and Siwei Lyu are with the Department of Computer Science and Engineering, University at Buffalo, SUNY, Buffalo, NY 14260, USA. e-mail:(fxwang264, [siweilyu](siweilyug@buffalo.edu)[g](siweilyug@buffalo.edu)[@buffalo.edu](siweilyug@buffalo.edu))  \n􀀏 This work was supported by NSF IIS-2008532.  \n􀀃 Shu Hu is the corresponding author.  \nF ~~ ~~  \na model on samples) of a learning model over each training sample. For example, to evaluate the empirical ","cbCaieZWBBHNbGHk","https://ap.wps.com/l/cbCaieZWBBHNbGHk","pdf",4118944,1,20,"English","en",105,"# Introduction\n## Individual loss vs. aggregate loss\n## Decomposable vs. non-decomposable losses\n# Taxonomy and classification\n## Set functions as aggregators\n## Eight categories of rank-based decomposable losses\n# Review and formulas\n## Rank-based aggregate losses\n## Rank-based individual losses\n# Future research directions","[{\"question\":\"What is the main focus of this survey on loss functions?\",\"answer\":\"The survey systematically reviews rank-based decomposable losses, emphasizing how ranking order and decomposability shape loss design. It distinguishes losses formed from aggregate versus individual perspectives and unifies them through a new taxonomy.\"},{\"question\":\"How do individual loss and aggregate loss differ?\",\"answer\":\"Individual loss measures model quality on a single training sample, while aggregate loss combines individual losses or scores across all training samples using an aggregation procedure.\"},{\"question\":\"What does “decomposable” mean in the context of these losses?\",\"answer\":\"A decomposable loss can be expressed as an ensemble of individual terms, typically linked to per-sample contributions. This property is used to organize both aggregate and individual rank-based losses in the survey.\"}]","Rank-based Decomposable Losses in Machine Learning - A Survey | PDF",1785900229,50,{"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},"rank-based-decomposable-losses-in-machine-learning-a-survey","",{"@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/rank-based-decomposable-losses-in-machine-learning-a-survey/125614/",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 is the main focus of this survey on loss functions?","Question",{"text":75,"@type":76},"The survey systematically reviews rank-based decomposable losses, emphasizing how ranking order and decomposability shape loss design. It distinguishes losses formed from aggregate versus individual perspectives and unifies them through a new taxonomy.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How do individual loss and aggregate loss differ?",{"text":80,"@type":76},"Individual loss measures model quality on a single training sample, while aggregate loss combines individual losses or scores across all training samples using an aggregation procedure.",{"name":82,"@type":73,"acceptedAnswer":83},"What does “decomposable” mean in the context of these losses?",{"text":84,"@type":76},"A decomposable loss can be expressed as an ensemble of individual terms, typically linked to per-sample contributions. This property is used to organize both aggregate and individual rank-based losses in the survey.","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},[93,97,101,105,110,114,119,122,126,129,133],{"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":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":29,"slug":113},6,"Technology","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":21,"slug":125},9,"Religion & Spirituality","religion-spirituality",{"id":21,"doc_module":4,"doc_module_name":46,"category_name":127,"show_sort_weight":21,"slug":128},"World Cup","world-cup",{"id":130,"doc_module":4,"doc_module_name":46,"category_name":131,"show_sort_weight":130,"slug":132},10,"Lifestyle","lifestyle",{"id":134,"doc_module":4,"doc_module_name":46,"category_name":135,"show_sort_weight":106,"slug":136},19,"General","general"]