{"id":"https://openalex.org/W2029279587","doi":"https://doi.org/10.1162/089976602753633411","title":"Bayesian Framework for Least-Squares Support Vector Machine Classifiers, Gaussian Processes, and Kernel Fisher Discriminant Analysis","display_name":"Bayesian Framework for Least-Squares Support Vector Machine Classifiers, Gaussian Processes, and Kernel Fisher Discriminant Analysis","publication_year":2002,"publication_date":"2002-05-01","ids":{"openalex":"https://openalex.org/W2029279587","doi":"https://doi.org/10.1162/089976602753633411","mag":"2029279587","pmid":"https://pubmed.ncbi.nlm.nih.gov/11972910"},"language":"en","primary_location":{"id":"doi:10.1162/089976602753633411","is_oa":false,"landing_page_url":"https://doi.org/10.1162/089976602753633411","pdf_url":null,"source":{"id":"https://openalex.org/S207023548","display_name":"Neural Computation","issn_l":"0899-7667","issn":["0899-7667","1530-888X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057239297","display_name":"Tony Van Gestel","orcid":null},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":true,"raw_author_name":"T. Van Gestel","raw_affiliation_strings":["Katholieke Universiteit Leuven, Department of Electrical Engineering ESAT-SISTA, B-3001 Leuven, Belgium","Katholieke Universiteit Leuven, Department of Electrical Engineering ESAT-SISTA, B-3001 Leuven, Belgium#TAB#"],"affiliations":[{"raw_affiliation_string":"Katholieke Universiteit Leuven, Department of Electrical Engineering ESAT-SISTA, B-3001 Leuven, Belgium","institution_ids":["https://openalex.org/I99464096"]},{"raw_affiliation_string":"Katholieke Universiteit Leuven, Department of Electrical Engineering ESAT-SISTA, B-3001 Leuven, Belgium#TAB#","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078854904","display_name":"Johan A. K. Suykens","orcid":"https://orcid.org/0000-0002-8846-6352"},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"J. A. K. Suykens","raw_affiliation_strings":["Katholieke Universiteit Leuven, Department of Electrical Engineering ESAT-SISTA, B-3001 Leuven, Belgium","Katholieke Universiteit Leuven, Department of Electrical Engineering ESAT-SISTA, B-3001 Leuven, Belgium#TAB#"],"affiliations":[{"raw_affiliation_string":"Katholieke Universiteit Leuven, Department of Electrical Engineering ESAT-SISTA, B-3001 Leuven, Belgium","institution_ids":["https://openalex.org/I99464096"]},{"raw_affiliation_string":"Katholieke Universiteit Leuven, Department of Electrical Engineering ESAT-SISTA, B-3001 Leuven, Belgium#TAB#","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003709708","display_name":"Gert Lanckriet","orcid":null},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"G. Lanckriet","raw_affiliation_strings":["Katholieke Universiteit Leuven, Department of Electrical Engineering ESAT-SISTA, B-3001 Leuven, Belgium","Katholieke Universiteit Leuven, Department of Electrical Engineering ESAT-SISTA, B-3001 Leuven, Belgium#TAB#"],"affiliations":[{"raw_affiliation_string":"Katholieke Universiteit Leuven, Department of Electrical Engineering ESAT-SISTA, B-3001 Leuven, Belgium","institution_ids":["https://openalex.org/I99464096"]},{"raw_affiliation_string":"Katholieke Universiteit Leuven, Department of Electrical Engineering ESAT-SISTA, B-3001 Leuven, Belgium#TAB#","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046878128","display_name":"Adriaan Lambrechts","orcid":"https://orcid.org/0000-0001-9533-0712"},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"A. Lambrechts","raw_affiliation_strings":["Katholieke Universiteit Leuven, Department of Electrical Engineering ESAT-SISTA, B-3001 Leuven, Belgium","Katholieke Universiteit Leuven, Department of Electrical Engineering ESAT-SISTA, B-3001 Leuven, Belgium#TAB#"],"affiliations":[{"raw_affiliation_string":"Katholieke Universiteit Leuven, Department of Electrical Engineering ESAT-SISTA, B-3001 Leuven, Belgium","institution_ids":["https://openalex.org/I99464096"]},{"raw_affiliation_string":"Katholieke Universiteit Leuven, Department of Electrical Engineering ESAT-SISTA, B-3001 Leuven, Belgium#TAB#","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018814006","display_name":"Bart De Moor","orcid":"https://orcid.org/0000-0002-1154-5028"},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"B. De Moor","raw_affiliation_strings":["Katholieke Universiteit Leuven, Department of Electrical Engineering ESAT-SISTA, B-3001 Leuven, Belgium","Katholieke Universiteit Leuven, Department of Electrical Engineering ESAT-SISTA, B-3001 Leuven, Belgium#TAB#"],"affiliations":[{"raw_affiliation_string":"Katholieke Universiteit Leuven, Department of Electrical Engineering ESAT-SISTA, B-3001 Leuven, Belgium","institution_ids":["https://openalex.org/I99464096"]},{"raw_affiliation_string":"Katholieke Universiteit Leuven, Department of Electrical Engineering ESAT-SISTA, B-3001 Leuven, Belgium#TAB#","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022355148","display_name":"Joos Vandewalle","orcid":"https://orcid.org/0000-0001-7716-2460"},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"J. Vandewalle","raw_affiliation_strings":["Katholieke Universiteit Leuven, Department of Electrical Engineering ESAT-SISTA, B-3001 Leuven, Belgium","Katholieke Universiteit Leuven, Department of Electrical Engineering ESAT-SISTA, B-3001 Leuven, Belgium#TAB#"],"affiliations":[{"raw_affiliation_string":"Katholieke Universiteit Leuven, Department of Electrical Engineering ESAT-SISTA, B-3001 Leuven, Belgium","institution_ids":["https://openalex.org/I99464096"]},{"raw_affiliation_string":"Katholieke Universiteit Leuven, Department of Electrical Engineering ESAT-SISTA, B-3001 Leuven, Belgium#TAB#","institution_ids":["https://openalex.org/I99464096"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5057239297"],"corresponding_institution_ids":["https://openalex.org/I99464096"],"apc_list":null,"apc_paid":null,"fwci":13.0013,"has_fulltext":false,"cited_by_count":293,"citation_normalized_percentile":{"value":0.99743677,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"14","issue":"5","first_page":"1115","last_page":"1147"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10640","display_name":"Spectroscopy and Chemometric Analyses","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1602","display_name":"Analytical Chemistry"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10640","display_name":"Spectroscopy and Chemometric Analyses","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1602","display_name":"Analytical Chemistry"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9958999752998352,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T11871","display_name":"Advanced Statistical Methods and Models","score":0.9918000102043152,"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/least-squares-support-vector-machine","display_name":"Least squares support vector machine","score":0.6550315618515015},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6430585384368896},{"id":"https://openalex.org/keywords/support-vector-machine","display_name":"Support vector machine","score":0.6284850835800171},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.5492411255836487},{"id":"https://openalex.org/keywords/kernel-method","display_name":"Kernel method","score":0.524696946144104},{"id":"https://openalex.org/keywords/radial-basis-function-kernel","display_name":"Radial basis function kernel","score":0.5116298794746399},{"id":"https://openalex.org/keywords/perceptron","display_name":"Perceptron","score":0.49398094415664673},{"id":"https://openalex.org/keywords/decision-boundary","display_name":"Decision boundary","score":0.4775981903076172},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.46866095066070557},{"id":"https://openalex.org/keywords/kernel-fisher-discriminant-analysis","display_name":"Kernel Fisher discriminant analysis","score":0.4666253328323364},{"id":"https://openalex.org/keywords/feature-vector","display_name":"Feature vector","score":0.44504591822624207},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.37760522961616516},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.37335047125816345},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.273624449968338},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.2111307680606842}],"concepts":[{"id":"https://openalex.org/C145828037","wikidata":"https://www.wikidata.org/wiki/Q17086219","display_name":"Least squares support vector machine","level":3,"score":0.6550315618515015},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6430585384368896},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.6284850835800171},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5492411255836487},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.524696946144104},{"id":"https://openalex.org/C75866337","wikidata":"https://www.wikidata.org/wiki/Q7280263","display_name":"Radial basis function kernel","level":4,"score":0.5116298794746399},{"id":"https://openalex.org/C60908668","wikidata":"https://www.wikidata.org/wiki/Q690207","display_name":"Perceptron","level":3,"score":0.49398094415664673},{"id":"https://openalex.org/C42023084","wikidata":"https://www.wikidata.org/wiki/Q5249231","display_name":"Decision boundary","level":3,"score":0.4775981903076172},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.46866095066070557},{"id":"https://openalex.org/C181367576","wikidata":"https://www.wikidata.org/wiki/Q6394184","display_name":"Kernel Fisher discriminant analysis","level":4,"score":0.4666253328323364},{"id":"https://openalex.org/C83665646","wikidata":"https://www.wikidata.org/wiki/Q42139305","display_name":"Feature vector","level":2,"score":0.44504591822624207},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37760522961616516},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.37335047125816345},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.273624449968338},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.2111307680606842}],"mesh":[{"descriptor_ui":"D001185","descriptor_name":"Artificial Intelligence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D001185","descriptor_name":"Artificial Intelligence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D001185","descriptor_name":"Artificial Intelligence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D001499","descriptor_name":"Bayes Theorem","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D001499","descriptor_name":"Bayes Theorem","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D001499","descriptor_name":"Bayes Theorem","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016011","descriptor_name":"Normal Distribution","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016011","descriptor_name":"Normal Distribution","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016011","descriptor_name":"Normal Distribution","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016018","descriptor_name":"Least-Squares Analysis","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016018","descriptor_name":"Least-Squares Analysis","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016018","descriptor_name":"Least-Squares Analysis","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true}],"locations_count":4,"locations":[{"id":"doi:10.1162/089976602753633411","is_oa":false,"landing_page_url":"https://doi.org/10.1162/089976602753633411","pdf_url":null,"source":{"id":"https://openalex.org/S207023548","display_name":"Neural Computation","issn_l":"0899-7667","issn":["0899-7667","1530-888X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Computation","raw_type":"journal-article"},{"id":"pmid:11972910","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/11972910","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":"Neural computation","raw_type":null},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.139.6025","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.139.6025","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://iesk.et.uni-magdeburg.de/ko/papers/kfd/kernel_fisher_discriminant_analysis_gestel.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.17.7450","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.17.7450","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.kernel-machines.org/papers/upload_19627_NCvangestel2281.ps","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.6600000262260437}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W99903558","https://openalex.org/W187881133","https://openalex.org/W1488435683","https://openalex.org/W1504315696","https://openalex.org/W1524706172","https://openalex.org/W1550570395","https://openalex.org/W1554663460","https://openalex.org/W1563088657","https://openalex.org/W1596717185","https://openalex.org/W1601740268","https://openalex.org/W1618905105","https://openalex.org/W1654787807","https://openalex.org/W1657213141","https://openalex.org/W1755117326","https://openalex.org/W2007154098","https://openalex.org/W2014803657","https://openalex.org/W2020329269","https://openalex.org/W2041387425","https://openalex.org/W2041657594","https://openalex.org/W2084812512","https://openalex.org/W2088538739","https://openalex.org/W2101728970","https://openalex.org/W2104287253","https://openalex.org/W2105210673","https://openalex.org/W2111440106","https://openalex.org/W2115438515","https://openalex.org/W2116723448","https://openalex.org/W2117063635","https://openalex.org/W2117812871","https://openalex.org/W2118113396","https://openalex.org/W2120879667","https://openalex.org/W2132890143","https://openalex.org/W2139701068","https://openalex.org/W2140095548","https://openalex.org/W2147993235","https://openalex.org/W2148603752","https://openalex.org/W2156909104","https://openalex.org/W2159935273","https://openalex.org/W2165058613","https://openalex.org/W2413535096","https://openalex.org/W2798909945","https://openalex.org/W3017143921","https://openalex.org/W4244577065"],"related_works":["https://openalex.org/W4248019443","https://openalex.org/W1971073335","https://openalex.org/W2129407254","https://openalex.org/W2220937770","https://openalex.org/W2005263400","https://openalex.org/W1536156198","https://openalex.org/W2903240209","https://openalex.org/W2372906999","https://openalex.org/W1533418482","https://openalex.org/W2009083069"],"abstract_inverted_index":{"The":[0,162,190],"Bayesian":[1,174,224,253,284],"evidence":[2,175,225,285],"framework":[3,226,286],"has":[4,166,193],"been":[5,214],"successfully":[6],"applied":[7],"to":[8,69,149,157,179],"the":[9,16,21,29,34,37,61,89,95,100,114,133,141,145,180,199,209,223,230,236,245,249,264,278,283],"design":[10],"of":[11,18,23,36,39,94,129,252],"multilayer":[12],"perceptrons":[13],"(MLPs)":[14],"in":[15,65,75,88,92,140,172,177,186,244],"work":[17],"MacKay.":[19],"Nevertheless,":[20],"training":[22],"MLPs":[24],"suffers":[25],"from":[26,103,136,235],"drawbacks":[27],"like":[28],"nonconvex":[30],"optimization":[31],"problem":[32,116],"and":[33,99,126,132,153,197],"choice":[35],"number":[38],"hidden":[40],"units.":[41],"In":[42,110,220],"support":[43],"vector":[44,63],"machines":[45],"(SVMs)":[46],"for":[47,168,184,218],"classification,":[48],"as":[49,212],"introduced":[50],"by":[51,59,120,261],"Vapnik,":[52],"a":[53,66,70,77,104,122,137,150,173,205],"nonlinear":[54,67],"decision":[55],"boundary":[56],"is":[57,82,118,154,227],"obtained":[58,215,243,260,269],"mapping":[60],"input":[62],"first":[64],"way":[68],"high-dimensional":[71],"kernel-induced":[72],"feature":[73,237],"space":[74,91,238,247],"which":[76],"linear":[78,138],"large":[79],"margin":[80],"classifier":[81,232,280],"constructed.":[83],"Practical":[84],"expressions":[85,171,211,241],"are":[86,242,259],"formulated":[87],"dual":[90,142,246],"terms":[93],"related":[96,156],"kernel":[97,158],"function,":[98],"solution":[101,134],"follows":[102,135],"(convex)":[105],"quadratic":[106],"programming":[107],"(QP)":[108],"problem.":[109],"least-squares":[111,123,146,163],"SVMs":[112],"(LS-SVMs),":[113],"SVM":[115],"formulation":[117,147,152,165,192],"modified":[119],"introducing":[121],"cost":[124],"function":[125],"equality":[127],"instead":[128],"inequality":[130],"constraints,":[131],"system":[139],"space.":[143],"Implicitly,":[144],"corresponds":[148],"regression":[151,164],"also":[155],"Fisher":[159],"discriminant":[160],"analysis.":[161],"advantages":[167],"deriving":[169],"analytic":[170,240],"framework,":[176],"contrast":[178],"classification":[181],"formulations":[182],"used,":[183],"example,":[185],"gaussian":[187],"processes":[188],"(GPs).":[189],"LS-SVM":[191,231,279],"clear":[194],"primal-dual":[195],"interpretations,":[196],"without":[198],"bias":[200],"term,":[201],"one":[202],"explicitly":[203],"constructs":[204],"model":[206,265],"that":[207,277],"yields":[208,288],"same":[210],"have":[213],"with":[216,229],"GPs":[217],"regression.":[219],"this":[221],"article,":[222],"combined":[228],"formulation.":[233],"Starting":[234],"formulation,":[239],"on":[248,270],"different":[250],"levels":[251],"inference,":[254],"while":[255],"posterior":[256],"class":[257],"probabilities":[258],"marginalizing":[262],"over":[263],"parameters.":[266],"Empirical":[267],"results":[268],"10":[271],"public":[272],"domain":[273],"data":[274],"sets":[275],"show":[276],"designed":[281],"within":[282],"consistently":[287],"good":[289],"generalization":[290],"performances.":[291]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":12},{"year":2019,"cited_by_count":10},{"year":2018,"cited_by_count":17},{"year":2017,"cited_by_count":18},{"year":2016,"cited_by_count":14},{"year":2015,"cited_by_count":9},{"year":2014,"cited_by_count":13},{"year":2013,"cited_by_count":13},{"year":2012,"cited_by_count":8}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}