{"id":"https://openalex.org/W4414601064","doi":"https://doi.org/10.1007/s13748-025-00404-w","title":"Multinomial Classification Certainty: a new uncertainty metric for multinomial outcome prediction","display_name":"Multinomial Classification Certainty: a new uncertainty metric for multinomial outcome prediction","publication_year":2025,"publication_date":"2025-09-29","ids":{"openalex":"https://openalex.org/W4414601064","doi":"https://doi.org/10.1007/s13748-025-00404-w","pmid":"https://pubmed.ncbi.nlm.nih.gov/42369577"},"language":"en","primary_location":{"id":"doi:10.1007/s13748-025-00404-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s13748-025-00404-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s13748-025-00404-w.pdf","source":{"id":"https://openalex.org/S2480581173","display_name":"Progress in Artificial Intelligence","issn_l":"2192-6352","issn":["2192-6352","2192-6360"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Progress in Artificial Intelligence","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s13748-025-00404-w.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5075346171","display_name":"Florian van Daalen","orcid":"https://orcid.org/0000-0002-2229-8587"},"institutions":[{"id":"https://openalex.org/I2800191616","display_name":"Maastricht University Medical Centre","ror":"https://ror.org/02d9ce178","country_code":"NL","type":"funder","lineage":["https://openalex.org/I2800191616"]},{"id":"https://openalex.org/I4210114239","display_name":"Department of Health","ror":"https://ror.org/0225asj53","country_code":"TW","type":"government","lineage":["https://openalex.org/I4210114239"]},{"id":"https://openalex.org/I4210161616","display_name":"Maastro Clinic","ror":"https://ror.org/059wkzj26","country_code":"NL","type":"healthcare","lineage":["https://openalex.org/I4210161616"]}],"countries":["NL","TW"],"is_corresponding":true,"raw_author_name":"Florian van Daalen","raw_affiliation_strings":["Department of Health Promotion, Care and Public Health Research Institute (CAPHRI), University Maastricht Medical Centre+, Maastricht, Netherlands","Department of Radiation Oncology (Maastro), GROW Research Institute for Oncology and Reproduction, University Maastricht Medical Centre+, Maastricht, Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Health Promotion, Care and Public Health Research Institute (CAPHRI), University Maastricht Medical Centre+, Maastricht, Netherlands","institution_ids":["https://openalex.org/I2800191616","https://openalex.org/I4210114239"]},{"raw_affiliation_string":"Department of Radiation Oncology (Maastro), GROW Research Institute for Oncology and Reproduction, University Maastricht Medical Centre+, Maastricht, Netherlands","institution_ids":["https://openalex.org/I4210161616"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077645218","display_name":"Ralph Brecheisen","orcid":"https://orcid.org/0000-0001-9937-2602"},"institutions":[{"id":"https://openalex.org/I4210161616","display_name":"Maastro Clinic","ror":"https://ror.org/059wkzj26","country_code":"NL","type":"healthcare","lineage":["https://openalex.org/I4210161616"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Ralph Brecheisen","raw_affiliation_strings":["Department of Radiation Oncology (Maastro), GROW Research Institute for Oncology and Reproduction, University Maastricht Medical Centre+, Maastricht, Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Radiation Oncology (Maastro), GROW Research Institute for Oncology and Reproduction, University Maastricht Medical Centre+, Maastricht, Netherlands","institution_ids":["https://openalex.org/I4210161616"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004688031","display_name":"Leonard Wee","orcid":"https://orcid.org/0000-0003-1612-9055"},"institutions":[{"id":"https://openalex.org/I4210161616","display_name":"Maastro Clinic","ror":"https://ror.org/059wkzj26","country_code":"NL","type":"healthcare","lineage":["https://openalex.org/I4210161616"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Leonard Wee","raw_affiliation_strings":["Department of Radiation Oncology (Maastro), GROW Research Institute for Oncology and Reproduction, University Maastricht Medical Centre+, Maastricht, Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Radiation Oncology (Maastro), GROW Research Institute for Oncology and Reproduction, University Maastricht Medical Centre+, Maastricht, Netherlands","institution_ids":["https://openalex.org/I4210161616"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102442933","display_name":"Andr\u00e9 Dekker","orcid":null},"institutions":[{"id":"https://openalex.org/I4210161616","display_name":"Maastro Clinic","ror":"https://ror.org/059wkzj26","country_code":"NL","type":"healthcare","lineage":["https://openalex.org/I4210161616"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Andre Dekker","raw_affiliation_strings":["Department of Radiation Oncology (Maastro), GROW Research Institute for Oncology and Reproduction, University Maastricht Medical Centre+, Maastricht, Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Radiation Oncology (Maastro), GROW Research Institute for Oncology and Reproduction, University Maastricht Medical Centre+, Maastricht, Netherlands","institution_ids":["https://openalex.org/I4210161616"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058533373","display_name":"I\u00f1igo Bermejo","orcid":"https://orcid.org/0000-0001-9105-8088"},"institutions":[{"id":"https://openalex.org/I4210161616","display_name":"Maastro Clinic","ror":"https://ror.org/059wkzj26","country_code":"NL","type":"healthcare","lineage":["https://openalex.org/I4210161616"]},{"id":"https://openalex.org/I878454856","display_name":"Hasselt University","ror":"https://ror.org/04nbhqj75","country_code":"BE","type":"education","lineage":["https://openalex.org/I878454856"]}],"countries":["BE","NL"],"is_corresponding":false,"raw_author_name":"Inigo Bermejo","raw_affiliation_strings":["Data Science Institute, Hasselt University, Hasselt, Belgium","Department of Radiation Oncology (Maastro), GROW Research Institute for Oncology and Reproduction, University Maastricht Medical Centre+, Maastricht, Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Data Science Institute, Hasselt University, Hasselt, Belgium","institution_ids":["https://openalex.org/I878454856"]},{"raw_affiliation_string":"Department of Radiation Oncology (Maastro), GROW Research Institute for Oncology and Reproduction, University Maastricht Medical Centre+, Maastricht, Netherlands","institution_ids":["https://openalex.org/I4210161616"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5075346171"],"corresponding_institution_ids":["https://openalex.org/I2800191616","https://openalex.org/I4210114239","https://openalex.org/I4210161616"],"apc_list":{"value":2780,"currency":"USD","value_usd":2780},"apc_paid":{"value":2780,"currency":"USD","value_usd":2780},"fwci":2.8447,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.91942096,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":98},"biblio":{"volume":"15","issue":"2","first_page":"259","last_page":"271"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.9162999987602234,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.9162999987602234,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/multinomial-distribution","display_name":"Multinomial distribution","score":0.7305999994277954},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.6782000064849854},{"id":"https://openalex.org/keywords/certainty","display_name":"Certainty","score":0.641700029373169},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.4814000129699707},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.4738999903202057},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4690999984741211},{"id":"https://openalex.org/keywords/outcome","display_name":"Outcome (game theory)","score":0.4318000078201294},{"id":"https://openalex.org/keywords/multinomial-logistic-regression","display_name":"Multinomial logistic regression","score":0.3400000035762787}],"concepts":[{"id":"https://openalex.org/C192065140","wikidata":"https://www.wikidata.org/wiki/Q1147928","display_name":"Multinomial distribution","level":2,"score":0.7305999994277954},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.6782000064849854},{"id":"https://openalex.org/C7493553","wikidata":"https://www.wikidata.org/wiki/Q1520777","display_name":"Certainty","level":2,"score":0.641700029373169},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6039999723434448},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5985000133514404},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.5501999855041504},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.4814000129699707},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.4738999903202057},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4690999984741211},{"id":"https://openalex.org/C148220186","wikidata":"https://www.wikidata.org/wiki/Q7111912","display_name":"Outcome (game theory)","level":2,"score":0.4318000078201294},{"id":"https://openalex.org/C117568660","wikidata":"https://www.wikidata.org/wiki/Q1650843","display_name":"Multinomial logistic regression","level":2,"score":0.3400000035762787},{"id":"https://openalex.org/C2780876879","wikidata":"https://www.wikidata.org/wiki/Q3054749","display_name":"Meaning (existential)","level":2,"score":0.3366999924182892},{"id":"https://openalex.org/C177769412","wikidata":"https://www.wikidata.org/wiki/Q278090","display_name":"Prior probability","level":3,"score":0.30649998784065247},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.30410000681877136},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2976999878883362},{"id":"https://openalex.org/C2780898871","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Performance metric","level":2,"score":0.2897999882698059},{"id":"https://openalex.org/C139502532","wikidata":"https://www.wikidata.org/wiki/Q1122090","display_name":"Computational intelligence","level":2,"score":0.2888000011444092},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.2728999853134155},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.2655999958515167},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.26409998536109924},{"id":"https://openalex.org/C2778334786","wikidata":"https://www.wikidata.org/wiki/Q1586270","display_name":"Variation (astronomy)","level":2,"score":0.263700008392334},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.2599000036716461},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2581999897956848}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s13748-025-00404-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s13748-025-00404-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s13748-025-00404-w.pdf","source":{"id":"https://openalex.org/S2480581173","display_name":"Progress in Artificial Intelligence","issn_l":"2192-6352","issn":["2192-6352","2192-6360"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Progress in Artificial Intelligence","raw_type":"journal-article"},{"id":"pmid:42369577","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/42369577","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Progress in artificial intelligence","raw_type":null},{"id":"pmh:oai:cris.maastrichtuniversity.nl:openaire/c458e9d7-5ec2-47ef-b3a8-07f97cf660de","is_oa":true,"landing_page_url":"https://cris.maastrichtuniversity.nl/en/publications/c458e9d7-5ec2-47ef-b3a8-07f97cf660de","pdf_url":null,"source":{"id":"https://openalex.org/S4306402616","display_name":"Research Publications (Maastricht University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I34352273","host_organization_name":"Maastricht University","host_organization_lineage":["https://openalex.org/I34352273"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"van Daalen, F, Brecheisen, R, Wee, L, Dekker, A & Bermejo, I 2026, 'Multinomial Classification Certainty : a new uncertainty metric for multinomial outcome prediction', Progress in Artificial Intelligence, vol. 15, no. 2, pp. 259-271. https://doi.org/10.1007/s13748-025-00404-w","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:documentserver.uhasselt.be:1942/47527","is_oa":true,"landing_page_url":"http://hdl.handle.net/1942/47527","pdf_url":"https://documentserver.uhasselt.be//bitstream/1942/47527/1/Multinomial%20Classification%20Certainty_%20a%20new%20uncertainty%20metric%20for%20multinomial%20outcome%20prediction.pdf","source":{"id":"https://openalex.org/S4306401926","display_name":"Document Server@UHasselt (UHasselt)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I878454856","host_organization_name":"Hasselt University","host_organization_lineage":["https://openalex.org/I878454856"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:pubmedcentral.nih.gov:13308692","is_oa":true,"landing_page_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC13308692/","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Prog Artif Intell","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1007/s13748-025-00404-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s13748-025-00404-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s13748-025-00404-w.pdf","source":{"id":"https://openalex.org/S2480581173","display_name":"Progress in Artificial Intelligence","issn_l":"2192-6352","issn":["2192-6352","2192-6360"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Progress in Artificial Intelligence","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8094170266","display_name":"CARRIER - Coronary ARtery disease: Risk estimations and Interventions for prevention and EaRly detection \u2013 a Personal Health Train project","funder_award_id":"628.011.212","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"}],"funders":[{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4414601064.pdf","grobid_xml":"https://content.openalex.org/works/W4414601064.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W1580375566","https://openalex.org/W2021956654","https://openalex.org/W2046107991","https://openalex.org/W2066593954","https://openalex.org/W2089571936","https://openalex.org/W2125231355","https://openalex.org/W2126022166","https://openalex.org/W2142047467","https://openalex.org/W2539910027","https://openalex.org/W2585399080","https://openalex.org/W2622427151","https://openalex.org/W2736661778","https://openalex.org/W2767191022","https://openalex.org/W2789234756","https://openalex.org/W2899311772","https://openalex.org/W2944858146","https://openalex.org/W2966241529","https://openalex.org/W2978725006","https://openalex.org/W3011100113","https://openalex.org/W3014596384","https://openalex.org/W3025819524","https://openalex.org/W3035622304","https://openalex.org/W3104422614","https://openalex.org/W3113568521","https://openalex.org/W3134774296"],"related_works":[],"abstract_inverted_index":{"Certainty":[0],"of":[1,12,28,57,77,91,94,102,160,172],"classifications":[2],"is":[3,35,47,56,87,122,125,135],"crucial":[4],"when":[5,32,118],"it":[6,46],"comes":[7],"to":[8,50,129,156],"the":[9,25,54,78,81,92,100,105,114,158,177],"practical":[10,39],"application":[11],"machine":[13],"learning":[14],"models.":[15],"Model":[16],"performance":[17,27],"measures":[18],"such":[19,41],"as":[20,42],"accuracy":[21],"are":[22],"focused":[23],"on":[24],"average":[26,65],"a":[29,33,38,43,58,72,119,132,139,147],"model.":[30],"However,":[31],"model":[34,55,161],"used":[36],"in":[37,99],"setting,":[40],"medical":[44],"clinic,":[45],"more":[48,136],"important":[49,181],"know":[51],"how":[52],"certain":[53,137],"given":[59],"prediction":[60],"or":[61],"classification":[62,74,134],"than":[63,113,138],"its":[64],"performance.":[66],"Unfortunately,":[67],"often":[68],"models":[69],"only":[70,110],"provide":[71],"final":[73],"label,":[75],"usually":[76],"class":[79],"with":[80],"highest":[82,106],"probability.":[83],"This":[84],"output,":[85],"however,":[86],"not":[88],"sufficiently":[89],"informative":[90],"certainty":[93,159,173],"this":[95,143,170,184],"particular":[96,133],"classification,":[97],"especially":[98],"presence":[101],"multiple":[103],"classes:":[104],"probability":[107,120],"might":[108],"be":[109],"barely":[111],"higher":[112],"second":[115],"highest.":[116],"Even":[117],"distribution":[121],"provided,":[123],"there":[124],"no":[126],"established":[127],"metric":[128,149],"determine":[130],"if":[131],"different":[140],"one.":[141],"In":[142],"article":[144],"we":[145,150,175],"propose":[146],"novel":[148],"have":[151],"termed":[152],"Multinomial":[153],"Classification":[154],"Certainty,":[155],"represent":[157,169],"predictions.":[162],"We":[163],"discuss":[164],"why":[165],"existing":[166],"methods":[167],"cannot":[168],"type":[171],"and":[174],"show":[176],"mathematical":[178],"meaning":[179],"behind":[180],"thresholds":[182],"for":[183],"new":[185],"measure.":[186]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
