[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-123139-en":3,"doc-seo-123139-105":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},123139,7971461740886,"Theodore","https://ap-avatar.wpscdn.com/davatar_3d24733baf745e90a7e4bdd5f77d97b2",8,"Research & Report","Comparing machine learning algorithms by union-free generic depth","We propose a framework to descriptively analyze samples of partial orders using depth functions. While depth has been intensively studied for linear and metric spaces, it remains largely unexplored for non-standard data types such as partial orders. The paper introduces the union-free generic (ufg) depth via an adaptation of simplicial depth on the space of all partial orders. Using ufg depth with multidimensional performance measures, it enables classifier comparisons on standard benchmark datasets, highlighting differences from existing benchmarking approaches.","International Journal of Approximate Reasoning 169 (2024) 109166  \nContents lists available at ScienceDirect  \nInternational Journal of Approximate Reasoning  \njournal [homepage: www.elsevier.com/locate/ijar](homepage: www.elsevier.com/locate/ijar)  \n| Comparing machine learning algorithms by union-free generic depth |  |  |  |\n| --- | --- | --- | --- |\n| Hannah Blocher ∗ , Georg Schollmeyer, Malte Nalenz, Christoph Jansen Department of Statistics, LMU Munich, Ludwigstr. 33, Munich, 80539, Bavaria, Germany |  |  |  |\n| A R T I C L E I N F O |  | A B S T R A C T |  |\n| Keywords:\u003Cbr>Partial orders\u003Cbr>Data depth Benchmarking Algorithm comparison Outlier detection Non-standard data |  | We propose a framework for descriptively analyzing sets of partial orders based on the concept of depth functions. Despite intensive studies in linear and metric spaces, there is very little discussion on depth functions for non-standard data types such as partial orders. We introduce an adaptation of the well-known simplicial depth to the set of all partial orders, the union-free generic (ufg) depth. Moreover, we utilize our ufg depth for a comparison of machine learning algorithms based on multidimensional performance measures. Concretely, we provide two examples of classifier comparisons on samples of standard benchmark data sets. Our results demonstrate promisingly the wide variety of different analysis approaches based on ufg methods. Furthermore, the examples outline that our approach differs substantially from existing benchmarking approaches, and thus adds a new perspective to the vivid debate on classifier comparison.1 |  |\n\n1. Introduction and related literature  \nWe begin with the general motivation for this paper and an overview of the contributions of our paper to the comparison of machine learning algorithms. We also provide references to related literature.  \n1.1. Motivation  \nPartial orders – and the systematic incomparabilities of objects encoded in them – occur naturally in a variety of problems in a wide range of scientific disciplines. Examples range from decision theory, where the agents under consideration might be unable to arrange the consequences of their actions into total orders (see, e.g., [52,35]) or have partial cardinal preferences (see, e.g., [31,29]), over social choice theory, where a fair aggregate order might only be possible by incorporating systematic incomparabilities (see, e.g., [43,32]), to finance, where risky assets do not always have to be comparable (see, e.g., [37,13]). Of course, many other relevant examples exist.  \nIn the specific context of statistics and machine learning, the incompleteness of the considered orders often originates from the fact that the objects to be ordered are compared with respect to several criteria and/or on several instances simultaneously: only if there is unanimous dominance of one object over another, this order is included in the corresponding relation. Quite a number of  \n* Corresponding author.  \n[E-mail address:](E-mail address: hannah.blocher@stat.uni-muenchen.de)[ hannah.blocher@stat.uni-muenchen.de](E-mail address: hannah.blocher@stat.uni-muenchen.de) (H. Blocher).  \n1 Open Science: Reproducible implementation and data analysis are available at: [https://github.com/hannahblo/Comparing_Algorithms_Using_UFG_Depth](https://github.com/hannahblo/Comparing_Algorithms_Using_UFG_Depth).  \n[https://doi.org/10.1016/j.ijar.2024.109166](https://doi.org/10.1016/j.ijar.2024.109166)  \nReceived 8 December 2023; Received in revised form 14 February 2024; Accepted 4 March 2024  \nAvailable online 7 March 2024  \n0888-613X/© 2024 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY-NC license ([http://creativecommons.org/licenses/by-nc/4.0/](http://creativecommons.org/licenses/by-nc/4.0/)).  \nH. Blocher, G. Schollmeyer, M. Nalenz et al. International Journal of Approximate Reasoning 169 (2024) 109166  \nresearch papers recently have been devoted to such compar","cbCaiuHd6nWe0Ci2","https://ap.wps.com/l/cbCaiuHd6nWe0Ci2","pdf",1469840,1,23,"English","en",105,"# Abstract\n# Keywords\n# 1. Introduction and related literature\n## 1.1. Motivation","[{\"question\":\"What problem does the paper address for classifier comparison?\",\"answer\":\"It addresses how to compare classifiers when performance is represented through partial orders with systematic incomparabilities rather than a single total ranking.\"},{\"question\":\"What is the proposed union-free generic (ufg) depth?\",\"answer\":\"It is an adaptation of simplicial depth to the set of all partial orders, providing a depth function tailored to poset-valued data.\"},{\"question\":\"How is ufg depth used in the paper?\",\"answer\":\"The paper applies ufg depth to compare machine learning algorithms using multidimensional performance measures, illustrated through two examples on standard benchmark datasets.\"}]","Comparing machine learning algorithms by union-free generic depth | PDF",1785814826,58,{"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},"comparing-machine-learning-algorithms-by-union-free-generic-depth","",{"@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/comparing-machine-learning-algorithms-by-union-free-generic-depth/123139/",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","2026-08-04",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 the paper address for classifier comparison?","Question",{"text":75,"@type":76},"It addresses how to compare classifiers when performance is represented through partial orders with systematic incomparabilities rather than a single total ranking.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What is the proposed union-free generic (ufg) depth?",{"text":80,"@type":76},"It is an adaptation of simplicial depth to the set of all partial orders, providing a depth function tailored to poset-valued data.",{"name":82,"@type":73,"acceptedAnswer":83},"How is ufg depth used in the paper?",{"text":84,"@type":76},"The paper applies ufg depth to compare machine learning algorithms using multidimensional performance measures, illustrated through two examples on standard benchmark datasets.","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},[93,97,101,105,110,115,120,123,128,131,135],{"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":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]