[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-122944-en":3,"doc-seo-122944-105":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},122944,4398048950312,"Violet","https://ap-avatar.wpscdn.com/avatar/400002538284de19e3c?_k=1778320343897328908",8,"Research & Report","Comparing Machine Learning Algorithms by Union-Free Generic Depth - New benchmarking depth framework","A framework is proposed to descriptively analyze sets of partial orders using depth functions. While depth and related concepts are well studied for linear and metric spaces, depth for nonstandard data types such as partial orders remains limited. The work adapts simplicial depth to the set of all partial orders, introducing the union-free generic (ufg) depth. The ufg depth then supports multidimensional performance comparisons of machine learning algorithms, illustrated via two classifier comparison examples on standard benchmark datasets.","arXiv :2312 . 12839v3 [ cs .LG] 21 Feb 2024  \nHighlights  \nComparing Machine Learning Algorithms by Union-Free Generic Depth  \nHannah Blocher, Georg Schollmeyer, Malte Nalenz, Christoph Jansen  \n• Introducing a depth function on the set of partial orders.  \n• Analyzing the empirical distribution of a sample of partial orders.  \n• Developing multidimensional performance comparison.  \n• Introducing a new benchmarking approach for machine learning algorithms.  \n• Providing two concrete multidimensional evaluations of classification algorithms.  \nComparing Machine Learning Algorithms by Union-Free Generic Depth  \nHannah Blochera,∗, Georg Schollmeyera , Malte Nalenza , Christoph Jansena  \na Department of Statistics, LMU Munich, Ludwigstr.  \n33, Munich, 80539, Bavaria, Germany  \nAbstract  \nWe 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 nonstandard 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  \nKeywords: partial orders, data depth, benchmarking, algorithm comparison, outlier detection, non-standard data  \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.  \n∗ Corresponding author  \nEmail address: [hannah.blocher@stat.uni-muenchen.de](hannah.blocher@stat.uni-muenchen.de) (Hannah 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)  \nPreprint submitted to International Journal of Approximate Reasoning February 22, 2024  \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., Seidenfeld et al. (1995); Kikuti et al. (2011)) or have partial cardinal preferences (see, e.g., Jansen et al. (2018a, 2022)), over social choice theory, where a fair aggregate order might only be possible by incorporating systematic incomparabilities (see, e.g., Pini et al. (2011); Jansen et al. (2018b)), to finance, where risky assets do not always have tobe comparable (see, e.g., Levy and Levy (1984); Chang et al. (2015)) . 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 research papers recently have been devoted to such comparison in the specific context of classification algorithms, either with respect to multiple quality metrics (e.g., Eugster et al. (2012); Jansen et al. (2023a)) or across multiple data ","cbCaicEKHrUQVIxS","https://ap.wps.com/l/cbCaicEKHrUQVIxS","pdf",1145712,1,57,"English","en",105,"# Highlights\n# Abstract\n# Keywords\n# Introduction and Related Literature\n## Motivation","[{\"question\":\"What problem does the paper address in machine learning algorithm comparison?\",\"answer\":\"It addresses how to compare classifiers when performance can be represented as partial orders with systematic incomparabilities, rather than a single total ranking.\"},{\"question\":\"What is the main methodological contribution?\",\"answer\":\"The paper introduces the union-free generic (ufg) depth, adapting simplicial depth to analyze the set of all partial orders.\"},{\"question\":\"How is the proposed ufg depth used in the paper?\",\"answer\":\"It is used to perform multidimensional comparisons of machine learning algorithms, demonstrated through two classifier comparison examples on standard benchmark datasets.\"}]","Comparing Machine Learning Algorithms by Union-Free Generic Depth - 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