{"id":"https://openalex.org/W2584597132","doi":"https://doi.org/10.1007/s10994-016-5616-2","title":"High-probability minimax probability machines","display_name":"High-probability minimax probability machines","publication_year":2017,"publication_date":"2017-02-02","ids":{"openalex":"https://openalex.org/W2584597132","doi":"https://doi.org/10.1007/s10994-016-5616-2","mag":"2584597132"},"language":"en","primary_location":{"id":"doi:10.1007/s10994-016-5616-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10994-016-5616-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10994-016-5616-2.pdf","source":{"id":"https://openalex.org/S62148650","display_name":"Machine Learning","issn_l":"0885-6125","issn":["0885-6125","1573-0565"],"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":"Machine Learning","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10994-016-5616-2.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002745661","display_name":"Simon Cousins","orcid":"https://orcid.org/0000-0002-5855-4896"},"institutions":[{"id":"https://openalex.org/I45129253","display_name":"University College London","ror":"https://ror.org/02jx3x895","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I45129253"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Simon Cousins","raw_affiliation_strings":["Department of Computer Science, University College London, Gower Street, London, WC1E 6BT, UK"],"raw_orcid":"https://orcid.org/0000-0002-5855-4896","affiliations":[{"raw_affiliation_string":"Department of Computer Science, University College London, Gower Street, London, WC1E 6BT, UK","institution_ids":["https://openalex.org/I45129253"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047980012","display_name":"John Shawe\u2010Taylor","orcid":"https://orcid.org/0000-0002-2030-0073"},"institutions":[{"id":"https://openalex.org/I45129253","display_name":"University College London","ror":"https://ror.org/02jx3x895","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I45129253"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"John Shawe-Taylor","raw_affiliation_strings":["Department of Computer Science, University College London, Gower Street, London, WC1E 6BT, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University College London, Gower Street, London, WC1E 6BT, UK","institution_ids":["https://openalex.org/I45129253"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5002745661"],"corresponding_institution_ids":["https://openalex.org/I45129253"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":{"value":2990,"currency":"USD","value_usd":2990},"fwci":1.3581,"has_fulltext":true,"cited_by_count":11,"citation_normalized_percentile":{"value":0.85673356,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"106","issue":"6","first_page":"863","last_page":"886"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.9998000264167786,"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"}},{"id":"https://openalex.org/T11652","display_name":"Imbalanced Data Classification Techniques","score":0.9991000294685364,"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"}},{"id":"https://openalex.org/T12535","display_name":"Machine Learning and Data Classification","score":0.9984999895095825,"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/minimax","display_name":"Minimax","score":0.8792644739151001},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6368391513824463},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6190561652183533},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.5801485776901245},{"id":"https://openalex.org/keywords/covariance-matrix","display_name":"Covariance matrix","score":0.5678659081459045},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.5674188733100891},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.45402413606643677},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.42976754903793335},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.335890531539917},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2845362424850464}],"concepts":[{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.8792644739151001},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6368391513824463},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6190561652183533},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.5801485776901245},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.5678659081459045},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.5674188733100891},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.45402413606643677},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.42976754903793335},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.335890531539917},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2845362424850464},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10994-016-5616-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10994-016-5616-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10994-016-5616-2.pdf","source":{"id":"https://openalex.org/S62148650","display_name":"Machine Learning","issn_l":"0885-6125","issn":["0885-6125","1573-0565"],"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":"Machine Learning","raw_type":"journal-article"},{"id":"pmh:oai:eprints.ucl.ac.uk.OAI2:1542973","is_oa":false,"landing_page_url":"https://discovery.ucl.ac.uk/id/eprint/1542973/","pdf_url":null,"source":{"id":"https://openalex.org/S4306400024","display_name":"UCL Discovery (University College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45129253","host_organization_name":"University College London","host_organization_lineage":["https://openalex.org/I45129253"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Machine Learning , 106 (6) pp. 863-886. (2017)","raw_type":"Article"}],"best_oa_location":{"id":"doi:10.1007/s10994-016-5616-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10994-016-5616-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10994-016-5616-2.pdf","source":{"id":"https://openalex.org/S62148650","display_name":"Machine Learning","issn_l":"0885-6125","issn":["0885-6125","1573-0565"],"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":"Machine Learning","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.5199999809265137,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320320286","display_name":"University College London","ror":"https://ror.org/02jx3x895"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2584597132.pdf","grobid_xml":"https://content.openalex.org/works/W2584597132.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W582641449","https://openalex.org/W1491621334","https://openalex.org/W1510073064","https://openalex.org/W1972284617","https://openalex.org/W2001619934","https://openalex.org/W2017753243","https://openalex.org/W2029538739","https://openalex.org/W2061293389","https://openalex.org/W2087347434","https://openalex.org/W2108067579","https://openalex.org/W2112284223","https://openalex.org/W2119320253","https://openalex.org/W2119821739","https://openalex.org/W2148603752","https://openalex.org/W2156909104","https://openalex.org/W2158897665","https://openalex.org/W2170708028","https://openalex.org/W2198331616","https://openalex.org/W2260382512","https://openalex.org/W4238284510","https://openalex.org/W4285719527","https://openalex.org/W6616943978","https://openalex.org/W6650842192","https://openalex.org/W6676301758","https://openalex.org/W6677291549","https://openalex.org/W6677891154","https://openalex.org/W6684997022","https://openalex.org/W6821113053","https://openalex.org/W7024225124"],"related_works":["https://openalex.org/W2938527049","https://openalex.org/W2005988940","https://openalex.org/W2046316070","https://openalex.org/W2045245841","https://openalex.org/W2977813918","https://openalex.org/W2162093541","https://openalex.org/W3172067426","https://openalex.org/W2624714000","https://openalex.org/W2150394675","https://openalex.org/W3008285301"],"abstract_inverted_index":{"In":[0,137],"this":[1,100,138,142,191],"paper":[2,139],"we":[3,140,183],"focus":[4],"on":[5,12,20,55,86,124,159,173],"constructing":[6],"binary":[7],"classifiers":[8],"that":[9,64,89,148,197,235],"are":[10,95],"built":[11],"the":[13,30,34,56,87,90,104,125,132,146,151,153,160,165,174,186,195,199,214,224,233,237,244,252],"premise":[14],"of":[15,70,82,134,162,226,239,246,254],"minimising":[16],"an":[17,52],"upper":[18,53,122,171],"bound":[19,54],"their":[21,109,180],"future":[22,57,126],"misclassification":[23,58,127,203],"rate.":[24,204],"We":[25],"pay":[26],"particular":[27],"attention":[28],"to":[29,113,131,189,223,251],"approach":[31],"taken":[32],"by":[33],"minimax":[35,166,187],"probability":[36],"machine":[37],"(Lanckriet":[38],"et":[39],"al.":[40],"in":[41,60,97,106,120,150,221,236],"J":[42],"Mach":[43],"Learn":[44],"Res":[45],"3:555\u2013582,":[46],"2003":[47],"),":[48],"which":[49],"directly":[50],"minimises":[51,198],"rate":[59,128],"a":[61,74,209],"worst-case":[62,202],"setting:":[63],"is,":[65],"under":[66,164],"all":[67],"possible":[68],"choices":[69],"class-conditional":[71],"distributions":[72],"with":[73,240],"given":[75],"mean":[76,154],"and":[77,92,108,129,144,155,179,193],"covariance":[78,93,156],"matrix.":[79],"The":[80,205],"validity":[81],"these":[83],"bounds":[84,123,172],"rests":[85],"assumption":[88],"means":[91],"matrices":[94],"known":[96],"advance,":[98],"however":[99],"is":[101,219],"not":[102],"always":[103],"case":[105,238],"practice":[107],"empirical":[110,181],"counterparts":[111],"have":[112],"be":[114],"used":[115],"instead.":[116],"This":[117],"can":[118,184,249],"result":[119],"erroneous":[121],"lead":[130,250],"formulation":[133],"sub-optimal":[135],"predictors.":[136,256],"address":[141],"oversight":[143],"study":[145],"influence":[147],"uncertainty":[149,192,207,248],"moments,":[152],"matrix,":[157],"has":[158],"construction":[161],"predictors":[163],"principle.":[167],"By":[168],"using":[169],"high-probability":[170,200],"deviation":[175],"between":[176],"true":[177],"moments":[178],"counterparts,":[182],"re-formulate":[185],"optimisation":[188],"incorporate":[190],"find":[194],"predictor":[196],",":[201],"moment":[206,227,247],"introduces":[208],"natural":[210],"regularisation":[211],"component":[212],"into":[213],"optimisation,":[215],"where":[216],"each":[217],"class":[218],"regularised":[220],"proportion":[222],"degree":[225],"uncertainty.":[228],"Experimental":[229],"results":[230],"would":[231],"support":[232],"view":[234],"limited":[241],"data":[242],"availability,":[243],"incorporation":[245],"formation":[253],"better":[255]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":2}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}