{"id":"https://openalex.org/W1835766057","doi":"https://doi.org/10.1186/s13637-015-0028-3","title":"On optimal Bayesian classification and risk estimation under multiple classes","display_name":"On optimal Bayesian classification and risk estimation under multiple classes","publication_year":2015,"publication_date":"2015-10-24","ids":{"openalex":"https://openalex.org/W1835766057","doi":"https://doi.org/10.1186/s13637-015-0028-3","mag":"1835766057","pmid":"https://pubmed.ncbi.nlm.nih.gov/26523135"},"language":"en","primary_location":{"id":"doi:10.1186/s13637-015-0028-3","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s13637-015-0028-3","pdf_url":"https://bsb-eurasipjournals.springeropen.com/counter/pdf/10.1186/s13637-015-0028-3","source":{"id":"https://openalex.org/S22696228","display_name":"EURASIP Journal on Bioinformatics and Systems Biology","issn_l":"1687-4145","issn":["1687-4145","1687-4153"],"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":"EURASIP Journal on Bioinformatics and Systems Biology","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://bsb-eurasipjournals.springeropen.com/counter/pdf/10.1186/s13637-015-0028-3","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037999551","display_name":"Lori A. Dalton","orcid":"https://orcid.org/0000-0001-8715-5723"},"institutions":[{"id":"https://openalex.org/I52357470","display_name":"The Ohio State University","ror":"https://ror.org/00rs6vg23","country_code":"US","type":"education","lineage":["https://openalex.org/I52357470"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Lori A. Dalton","raw_affiliation_strings":["Department of Electrical and Computer Engineering, The Ohio State University, Columbus, 43210 OH USA ; Department of Biomedical Informatics, The Ohio State University, Columbus, 43210 OH USA","Department of Biomedical Informatics, The Ohio State University, Columbus, USA","Department of Electrical and Computer Engineering, The Ohio State University, Columbus, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, The Ohio State University, Columbus, 43210 OH USA ; Department of Biomedical Informatics, The Ohio State University, Columbus, 43210 OH USA","institution_ids":[]},{"raw_affiliation_string":"Department of Biomedical Informatics, The Ohio State University, Columbus, USA","institution_ids":["https://openalex.org/I52357470"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, The Ohio State University, Columbus, USA","institution_ids":["https://openalex.org/I52357470"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111733816","display_name":"Mohammadmahdi R. Yousefi","orcid":null},"institutions":[{"id":"https://openalex.org/I52357470","display_name":"The Ohio State University","ror":"https://ror.org/00rs6vg23","country_code":"US","type":"education","lineage":["https://openalex.org/I52357470"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mohammadmahdi R. Yousefi","raw_affiliation_strings":["Department of Electrical and Computer Engineering, The Ohio State University, Columbus, 43210 OH USA","Department of Electrical and Computer Engineering, The Ohio State University, Columbus, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, The Ohio State University, Columbus, 43210 OH USA","institution_ids":[]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, The Ohio State University, Columbus, USA","institution_ids":["https://openalex.org/I52357470"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5037999551"],"corresponding_institution_ids":["https://openalex.org/I52357470"],"apc_list":null,"apc_paid":null,"fwci":0.7545,"has_fulltext":true,"cited_by_count":12,"citation_normalized_percentile":{"value":0.7127605,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"2015","issue":"1","first_page":"8","last_page":"8"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10885","display_name":"Gene expression and cancer classification","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T10885","display_name":"Gene expression and cancer classification","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.9932000041007996,"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"}},{"id":"https://openalex.org/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9803000092506409,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.7244059443473816},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.591549277305603},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.5723334550857544},{"id":"https://openalex.org/keywords/mean-squared-error","display_name":"Mean squared error","score":0.5665785670280457},{"id":"https://openalex.org/keywords/bayes-theorem","display_name":"Bayes' theorem","score":0.5606901049613953},{"id":"https://openalex.org/keywords/homoscedasticity","display_name":"Homoscedasticity","score":0.5121746063232422},{"id":"https://openalex.org/keywords/binary-classification","display_name":"Binary classification","score":0.4979827404022217},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4840911626815796},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.46343737840652466},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.3875083327293396},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.37523484230041504},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.35211649537086487},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.33862388134002686},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.3340662717819214},{"id":"https://openalex.org/keywords/support-vector-machine","display_name":"Support vector machine","score":0.15256252884864807},{"id":"https://openalex.org/keywords/heteroscedasticity","display_name":"Heteroscedasticity","score":0.10209915041923523}],"concepts":[{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.7244059443473816},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.591549277305603},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.5723334550857544},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.5665785670280457},{"id":"https://openalex.org/C207201462","wikidata":"https://www.wikidata.org/wiki/Q182505","display_name":"Bayes' theorem","level":3,"score":0.5606901049613953},{"id":"https://openalex.org/C104409967","wikidata":"https://www.wikidata.org/wiki/Q1054836","display_name":"Homoscedasticity","level":3,"score":0.5121746063232422},{"id":"https://openalex.org/C66905080","wikidata":"https://www.wikidata.org/wiki/Q17005494","display_name":"Binary classification","level":3,"score":0.4979827404022217},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4840911626815796},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.46343737840652466},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3875083327293396},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.37523484230041504},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35211649537086487},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.33862388134002686},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.3340662717819214},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.15256252884864807},{"id":"https://openalex.org/C101104100","wikidata":"https://www.wikidata.org/wiki/Q1063540","display_name":"Heteroscedasticity","level":2,"score":0.10209915041923523},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1186/s13637-015-0028-3","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s13637-015-0028-3","pdf_url":"https://bsb-eurasipjournals.springeropen.com/counter/pdf/10.1186/s13637-015-0028-3","source":{"id":"https://openalex.org/S22696228","display_name":"EURASIP Journal on Bioinformatics and Systems Biology","issn_l":"1687-4145","issn":["1687-4145","1687-4153"],"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":"EURASIP Journal on Bioinformatics and Systems Biology","raw_type":"journal-article"},{"id":"pmid:26523135","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/26523135","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":"EURASIP journal on bioinformatics & systems biology","raw_type":null},{"id":"pmh:oai:pubmedcentral.nih.gov:4619473","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/4619473","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"EURASIP J Bioinform Syst Biol","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1186/s13637-015-0028-3","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s13637-015-0028-3","pdf_url":"https://bsb-eurasipjournals.springeropen.com/counter/pdf/10.1186/s13637-015-0028-3","source":{"id":"https://openalex.org/S22696228","display_name":"EURASIP Journal on Bioinformatics and Systems Biology","issn_l":"1687-4145","issn":["1687-4145","1687-4153"],"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":"EURASIP Journal on Bioinformatics and Systems Biology","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.6000000238418579,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G1179801774","display_name":null,"funder_award_id":"1453563","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2344427966","display_name":null,"funder_award_id":"CCF-1422631","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3583663229","display_name":null,"funder_award_id":"CCF-1422631 and CCF-1453563","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6364702372","display_name":null,"funder_award_id":"1422631","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7400560131","display_name":null,"funder_award_id":"CCF-1453563","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320337348","display_name":"National Human Genome Research Institute","ror":"https://ror.org/00baak391"},{"id":"https://openalex.org/F4320337351","display_name":"National Cancer Institute","ror":"https://ror.org/040gcmg81"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1835766057.pdf","grobid_xml":"https://content.openalex.org/works/W1835766057.grobid-xml"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W230097570","https://openalex.org/W1564947197","https://openalex.org/W1579925870","https://openalex.org/W1663973292","https://openalex.org/W1964496517","https://openalex.org/W1972909920","https://openalex.org/W1985495956","https://openalex.org/W1991567646","https://openalex.org/W1995945562","https://openalex.org/W2035038062","https://openalex.org/W2040615655","https://openalex.org/W2057658881","https://openalex.org/W2085538190","https://openalex.org/W2087347434","https://openalex.org/W2096552892","https://openalex.org/W2104092906","https://openalex.org/W2110298216","https://openalex.org/W2112207178","https://openalex.org/W2117897510","https://openalex.org/W2119821739","https://openalex.org/W2119985557","https://openalex.org/W2122814955","https://openalex.org/W2134258050","https://openalex.org/W2134717973","https://openalex.org/W2138449831","https://openalex.org/W2153417333","https://openalex.org/W2153635508","https://openalex.org/W2158111773","https://openalex.org/W2160450758","https://openalex.org/W2165875224","https://openalex.org/W2166122445","https://openalex.org/W2166162270","https://openalex.org/W2322523654","https://openalex.org/W2331432542","https://openalex.org/W2528252365","https://openalex.org/W2797563284","https://openalex.org/W4248681815"],"related_works":["https://openalex.org/W2388528498","https://openalex.org/W2262753808","https://openalex.org/W956967588","https://openalex.org/W2119309329","https://openalex.org/W3094460295","https://openalex.org/W2894129938","https://openalex.org/W2380616114","https://openalex.org/W3202682398","https://openalex.org/W1869351066","https://openalex.org/W2117545158"],"abstract_inverted_index":{"A":[0],"recently":[1],"proposed":[2],"optimal":[3,8,16,18,42,79],"Bayesian":[4,60,80],"classification":[5],"paradigm":[6],"addresses":[7],"error":[9,19,22,69],"rate":[10],"analysis":[11,24],"for":[12,88,121],"small-sample":[13],"discrimination,":[14],"including":[15],"classifiers,":[17,66,77],"estimators,":[20],"and":[21,41,78,94,97,106],"estimation":[23],"tools":[25,90],"with":[26,45,127],"respect":[27,46],"to":[28,47,102],"the":[29,67,104,122],"probability":[30],"of":[31,71],"misclassification":[32],"under":[33,64,75,91,124],"binary":[34,135],"classes.":[35],"Here,":[36],"we":[37,117],"address":[38],"multi-class":[39],"problems":[40],"expected":[43],"risk":[44,50,61,73,81],"a":[48,99],"given":[49],"function,":[51],"which":[52,130],"are":[53,111,131],"common":[54],"settings":[55],"in":[56,134],"bioinformatics.":[57],"We":[58,84],"present":[59,98,118],"estimators":[62,74],"(BRE)":[63],"arbitrary":[65,72,76],"mean-square":[68],"(MSE)":[70],"classifiers":[82],"(OBRC).":[83],"provide":[85],"analytic":[86,109,119],"expressions":[87,110],"these":[89],"several":[92],"discrete":[93],"Gaussian":[95,125],"models":[96,126],"new":[100,132],"methodology":[101],"approximate":[103],"BRE":[105],"MSE":[107,123],"when":[108],"not":[112],"available.":[113],"Of":[114],"particular":[115],"note,":[116],"forms":[120],"homoscedastic":[128],"covariances,":[129],"even":[133],"classification.":[136]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}