BenchMetrics Prob: Benchmarking of probabilistic error/loss performance evaluation instruments for binary-classification problems

BenchMetrics Prob: Benchmarking of probabilistic error/loss performance evaluation instruments for binary-classification problems | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article BenchMetrics Prob: Benchmarking of probabilistic error/loss performance evaluation instruments for binary-classification problems Gürol Canbek This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-1356087/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Performance evaluation is key to building, training, validating, testing, comparing, and publishing classifier models for machine-learning-based classification problems. Two categories of performance instruments are confusion-matrix-derived metrics such as accuracy, true positive rate, and F1 and graphical-based metrics such as area-under-receiver-operating-characteristic-curve. Probabilistic-based performance instruments that are originally used for regression and time series forecasting are also applied in some binary-class or multi-class classifiers, such as artificial neural networks. Besides widely-known probabilistic instruments such as Mean Squared Error ( MSE ), Root Mean Square Error ( RMSE ), and LogLoss , there are many instruments. However, it is not identified that any of those is proper to use specifically in binary-classification performance evaluation. This study proposes BenchMetrics Prob, a qualitative and quantitative benchmarking method, to systematically evaluate probabilistic instruments via five criteria and fourteen simulation cases based on hypothetical classifiers on synthetic datasets. These criteria and cases give more insights to select a proper instrument in a binary-classification performance evaluation. The method was tested on over 31 instruments/instrument variants and the results have distinguished that three instruments are the most robust for binary-classification performance evaluation, namely Sum Squared Error ( SSE ), MSE with RMSE variant, and Mean Absolute Error ( MAE ). The results also showed that instrument variants with summarization functions other than mean ( e.g. , median and geometric mean) and the instrument subtypes proposed later to improve performance evaluation in regression such as relative/percentage/symmetric-percentage error instruments are not robust. Researchers should be aware of using those instruments in selecting or reporting performance in binary classification problems. Artificial Intelligence and Machine Learning binary classification performance evaluation performance metrics performance measures probabilistic performance evaluation benchmarking Full Text Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-1356087","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":83508026,"identity":"34319ee5-d322-41b1-8642-1914a9cf78ce","order_by":0,"name":"Gürol Canbek","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAsElEQVRIiWNgGAWjYLCCBxVAQoKBmQQtCWdI1pLYRooW+Yjchw8S59nJm0s3HzZgqLGJJqjF8Ea6sUHitmTDnXOOJScwHEvLbSCoZUYam0TitgOMG27kGB9gbDhMrJY5B+w33Mj/TJwWeQmQloYDiUBbmBOI0mLA84zZIOFYcvKGO8eMgQwi/CLfnsb44EONne2G282PJT7U2BBhywFkXgIh5WBbCBo6CkbBKBgFowAAaTI/hIpbvcQAAAAASUVORK5CYII=","orcid":"https://orcid.org/0000-0002-9337-097X","institution":"","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Gürol","middleName":"","lastName":"Canbek","suffix":""}],"badges":[],"createdAt":"2022-02-13 19:07:49","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":true,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false,"coiExplicitlySet":false},"doi":"10.21203/rs.3.rs-1356087/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-1356087/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":18208520,"identity":"28ec7aa8-d3c6-4bc0-a13b-7519c222fefc","added_by":"auto","created_at":"2022-02-14 19:40:55","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3984602,"visible":true,"origin":"","legend":"","description":"","filename":"BenchMetricsProbGCanbek.pdf","url":"https://assets-eu.researchsquare.com/files/rs-1356087/v1_covered.pdf"}],"financialInterests":"","formattedTitle":"\u003cp\u003eBenchMetrics Prob: Benchmarking of probabilistic error/loss performance evaluation instruments for binary-classification problems\u003c/p\u003e","fulltext":[{"header":"Full Text","content":"This preprint is available for \u003ca href='/article/rs-1356087/latest.pdf' target='_blank'\u003edownload as a PDF\u003c/a\u003e."}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"binary classification, performance evaluation, performance metrics, performance measures, probabilistic performance evaluation, benchmarking","lastPublishedDoi":"10.21203/rs.3.rs-1356087/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-1356087/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003ePerformance evaluation is key to building, training, validating, testing, comparing, and publishing classifier models for machine-learning-based classification problems. Two categories of performance instruments are confusion-matrix-derived metrics such as accuracy, true positive rate, and \u003cem\u003eF1\u003c/em\u003e and graphical-based metrics such as area-under-receiver-operating-characteristic-curve. Probabilistic-based performance instruments that are originally used for regression and time series forecasting are also applied in some binary-class or multi-class classifiers, such as artificial neural networks. Besides widely-known probabilistic instruments such as Mean Squared Error (\u003cem\u003eMSE\u003c/em\u003e), Root Mean Square Error (\u003cem\u003eRMSE\u003c/em\u003e), and \u003cem\u003eLogLoss\u003c/em\u003e, there are many instruments. However, it is not identified that any of those is proper to use specifically in binary-classification performance evaluation. This study proposes BenchMetrics Prob, a qualitative and quantitative benchmarking method, to systematically evaluate probabilistic instruments via five criteria and fourteen simulation cases based on hypothetical classifiers on synthetic datasets. These criteria and cases give more insights to select a proper instrument in a binary-classification performance evaluation. The method was tested on over 31 instruments/instrument variants and the results have distinguished that three instruments are the most robust for binary-classification performance evaluation, namely Sum Squared Error (\u003cem\u003eSSE\u003c/em\u003e), \u003cem\u003eMSE\u003c/em\u003e with \u003cem\u003eRMSE\u003c/em\u003e variant, and Mean Absolute Error (\u003cem\u003eMAE\u003c/em\u003e). The results also showed that instrument variants with summarization functions other than mean (\u003cem\u003ee.g.\u003c/em\u003e, median and geometric mean) and the instrument subtypes proposed later to improve performance evaluation in regression such as relative/percentage/symmetric-percentage error instruments are not robust. 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