[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-127038-en":3,"doc-seo-127038-105":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},127038,962084928904,"Asher","https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d",8,"Research & Report","Ranking the Importance of Variables in a Nonparametric Frontier Analysis Using Unsupervised Machine Learning Techniques","The paper develops and compares methodologies to rank variable importance in productive processes, using an adaptation of One-Class Support Vector Machines. Two machine-learning-inspired strategies are proposed: one based on random shuffling of a variable’s values and another leveraging the dual formulation’s objective value. The work also motivates suitability for production settings and evaluates performance through computational experiments. Results show the shuffling-based approach yields superior ranking accuracy across multiple scenarios, including cases with one relevant and one irrelevant input.","mathematics  \nArticle  \nRanking the Importance of Variables in a Nonparametric Frontier Analysis Using Unsupervised Machine Learning Techniques  \nRaul Moragues 1,2, Juan Aparicio 1,3, * and Miriam Esteve 1  \nCitation: Moragues, R.; Aparicio, J.; Esteve, M. Ranking the Importance of Variables in a Nonparametric Frontier Analysis Using Unsupervised Machine Learning Techniques. Mathematics 2023, 11, 2590. [https://](https://)[ ](https://)[doi.org/10.3390/math11112590](doi.org/10.3390/math11112590)  \nAcademic Editor: Andrea Scozzari  \nReceived: 17 May 2023  \nRevised: 31 May 2023  \nAccepted: 1 June 2023  \nPublished: 5 June 2023  \nCopyright: © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ([https://](https://)[ ](https://)[creativecommons.org/licenses/by/](creativecommons.org/licenses/by/)[ ](creativecommons.org/licenses/by/)[4.0/](4.0/)) .  \n1 Center of Operations Research (CIO), Miguel Hernandez University of Elche (UMH), 03202 Elche, Spain; rmoragues@umh.es (R.M.)  \n2 Ph.D. Program in Economics (DEcIDE), Miguel Hernandez University of Elche (UMH), 03202 Elche, Spain  \n3 Joint Research Unit, Valencian Graduate School and Research Network of Artificial Intelligence (valgrAI), 46022 Valencia, Spain  \n* Correspondence: j.aparicio@umh.es  \nAbstract: In this paper, we propose and compare new methodologies for ranking the importance of variables in productive processes via an adaptation of OneClass Support Vector Machines. In particular, we adapt two methodologies inspired by the machine learning literature: one involving the random shuffling of values of a variable and another one using the objective value of the dual formulation of the model. Additionally, we motivate the use of these type of algorithms in the production context and compare their performance via a computational experiment. We observe that the methodology based on shuffling the values of a variable outperforms the methodology based on the dual formulation. We observe that the shuffling-based methodology correctly ranks the variables in 94% of the scenarios with one relevant input and one irrelevant input. Moreover, it correctly ranks each variable in at least 65% of replications of a scenario with three relevant inputs and one irrelevant input.  \nKeywords: data envelopment analysis; feature ranking; model specification; unsupervised machine learning; technical efficiency; overfitting  \nMSC: 90C08  \n1. Introduction  \nA topic which has attracted large amounts of interest from the machine learning and statistical communities is the importance which certain variables have when building models to predict or explain a response variable. This can be encountered in a large variety of fields, such as the measurement of the technical efficiency of a set of homogeneous entities (companies, public organizations, etc.), related to microeconomics and operations research. Some of the early contributions in this area of study can be traced back to the work by Cobb and Douglas [1], who empirically estimated a production function. Later, Koopmans proposed a formal definition of technical efficiency [2], and Debreu and Farrell introduced a way to measure it, following an input-oriented or output-oriented radial direction in [3,4], respectively. A link between the measures of efficiency and production technologies was introduced by Shephard in [5] . Building on these foundations, a variety of approaches have been proposed, which are usually split in the literature into parametric and nonparametric methodologies. Representative examples of each approach, which are two of the most well-known techniques, are the Data Envelopment Analysis (DEA) in thenonparametric family [6,7], and the Stochastic Frontier Analysis (SFA) in the parametric one [8,9] .  \nIn this article, we focus on the nonparametric approach due to some of its characteristics, such as its flexibi","cbCaiazGpA21uhwm","https://ap.wps.com/l/cbCaiazGpA21uhwm","pdf",492935,1,24,"English","en",105,"# Introduction\n## Background on technical efficiency and frontier methods\n## From parametric to nonparametric approaches\n## Motivation for variable importance ranking\n# Methodology (proposed approaches)\n## One-Class Support Vector Machines adaptation\n## Variable-value shuffling strategy\n## Dual-objective-based strategy\n# Computational experiment and results\n## Ranking performance and accuracy\n## Comparison of methodologies","[{\"question\":\"What is the main goal of the proposed study?\",\"answer\":\"To rank the importance of variables in productive processes using an adaptation of One-Class Support Vector Machines.\"},{\"question\":\"How do the two proposed ranking methodologies differ?\",\"answer\":\"One randomly shuffles values of a variable, while the other uses the objective value from the dual formulation of the model.\"},{\"question\":\"Which methodology performs better in the computational experiments?\",\"answer\":\"The shuffling-based methodology outperforms the dual formulation-based methodology, achieving high correct ranking rates in tested scenarios.\"}]","Ranking the Importance of Variables in a Nonparametric Frontier Analysis Using Unsupervised Machine Learning Techniques | PDF",1785936493,60,{"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},"ranking-the-importance-of-variables-in-a-nonparametric-frontier-analysis-using-unsupervised-machine-learning-techniques","",{"@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/ranking-the-importance-of-variables-in-a-nonparametric-frontier-analysis-using-unsupervised-machine-learning-techniques/127038/",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 goal of the proposed study?","Question",{"text":75,"@type":76},"To rank the importance of variables in productive processes using an adaptation of One-Class Support Vector Machines.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How do the two proposed ranking methodologies differ?",{"text":80,"@type":76},"One randomly shuffles values of a variable, while the other uses the objective value from the dual formulation of the model.",{"name":82,"@type":73,"acceptedAnswer":83},"Which methodology performs better in the computational experiments?",{"text":84,"@type":76},"The shuffling-based methodology outperforms the dual formulation-based methodology, achieving high correct ranking rates in tested scenarios.","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},[93,97,101,105,109,114,119,122,127,130,134],{"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":29,"slug":108},5,"Comic","comic",{"id":110,"doc_module":4,"doc_module_name":46,"category_name":111,"show_sort_weight":112,"slug":113},6,"Technology",50,"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":125,"slug":126},9,"Religion & Spirituality",20,"religion-spirituality",{"id":125,"doc_module":4,"doc_module_name":46,"category_name":128,"show_sort_weight":125,"slug":129},"World Cup","world-cup",{"id":131,"doc_module":4,"doc_module_name":46,"category_name":132,"show_sort_weight":131,"slug":133},10,"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":46,"category_name":136,"show_sort_weight":106,"slug":137},19,"General","general"]