{"id":"https://openalex.org/W2274052023","doi":"https://doi.org/10.1162/neco_a_00817","title":"Online Pairwise Learning Algorithms","display_name":"Online Pairwise Learning Algorithms","publication_year":2016,"publication_date":"2016-02-19","ids":{"openalex":"https://openalex.org/W2274052023","doi":"https://doi.org/10.1162/neco_a_00817","mag":"2274052023","pmid":"https://pubmed.ncbi.nlm.nih.gov/26890352"},"language":"en","primary_location":{"id":"doi:10.1162/neco_a_00817","is_oa":false,"landing_page_url":"https://doi.org/10.1162/neco_a_00817","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","https://openalex.org/P4310316440"],"host_organization_lineage_names":["The MIT Press","Massachusetts Institute of Technology"],"type":"journal"},"license":null,"license_id":null,"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/A5048960543","display_name":"Yiming Ying","orcid":null},"institutions":[{"id":"https://openalex.org/I392282","display_name":"University at Albany, State University of New York","ror":"https://ror.org/012zs8222","country_code":"US","type":"education","lineage":["https://openalex.org/I392282"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Yiming Ying","raw_affiliation_strings":["Department of Mathematics and Statistics, State University of New York at Albany, Albany, NY 12222, U.S.A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, State University of New York at Albany, Albany, NY 12222, U.S.A","institution_ids":["https://openalex.org/I392282"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006802589","display_name":"Ding\u2010Xuan Zhou","orcid":"https://orcid.org/0000-0003-0224-9216"},"institutions":[{"id":"https://openalex.org/I168719708","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23","country_code":"HK","type":"education","lineage":["https://openalex.org/I168719708"]}],"countries":["HK"],"is_corresponding":true,"raw_author_name":"Ding-Xuan Zhou","raw_affiliation_strings":["Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong, China","institution_ids":["https://openalex.org/I168719708"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5006802589","https://openalex.org/A5048960543"],"corresponding_institution_ids":["https://openalex.org/I168719708","https://openalex.org/I392282"],"apc_list":null,"apc_paid":null,"fwci":10.2656,"has_fulltext":false,"cited_by_count":46,"citation_normalized_percentile":{"value":0.97795851,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"28","issue":"4","first_page":"743","last_page":"777"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.996399998664856,"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":0.996399998664856,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9915000200271606,"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/T12101","display_name":"Advanced Bandit Algorithms Research","score":0.987500011920929,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/reproducing-kernel-hilbert-space","display_name":"Reproducing kernel Hilbert space","score":0.8086910247802734},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6964761018753052},{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.6695612668991089},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.475247859954834},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.45497676730155945},{"id":"https://openalex.org/keywords/hinge-loss","display_name":"Hinge loss","score":0.45464783906936646},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.44172146916389465},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.4333469569683075},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.3795713186264038},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3646235466003418},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.36064472794532776},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.29876863956451416},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2774546146392822},{"id":"https://openalex.org/keywords/support-vector-machine","display_name":"Support vector machine","score":0.17196819186210632},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.11153334379196167}],"concepts":[{"id":"https://openalex.org/C80884492","wikidata":"https://www.wikidata.org/wiki/Q3345678","display_name":"Reproducing kernel Hilbert space","level":3,"score":0.8086910247802734},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6964761018753052},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.6695612668991089},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.475247859954834},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45497676730155945},{"id":"https://openalex.org/C39891107","wikidata":"https://www.wikidata.org/wiki/Q5767098","display_name":"Hinge loss","level":3,"score":0.45464783906936646},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.44172146916389465},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.4333469569683075},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.3795713186264038},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3646235466003418},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.36064472794532776},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.29876863956451416},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2774546146392822},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.17196819186210632},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.11153334379196167},{"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:10.1162/neco_a_00817","is_oa":false,"landing_page_url":"https://doi.org/10.1162/neco_a_00817","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","https://openalex.org/P4310316440"],"host_organization_lineage_names":["The MIT Press","Massachusetts Institute of Technology"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Computation","raw_type":"journal-article"},{"id":"pmid:26890352","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/26890352","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":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":55,"referenced_works":["https://openalex.org/W93885277","https://openalex.org/W560409768","https://openalex.org/W597932189","https://openalex.org/W1490654344","https://openalex.org/W1516903196","https://openalex.org/W1532499126","https://openalex.org/W1572386387","https://openalex.org/W1578240932","https://openalex.org/W1698155719","https://openalex.org/W1808718325","https://openalex.org/W1970781863","https://openalex.org/W1978810924","https://openalex.org/W1986280275","https://openalex.org/W1992208280","https://openalex.org/W1994616650","https://openalex.org/W1996652862","https://openalex.org/W2002658919","https://openalex.org/W2017332415","https://openalex.org/W2022829242","https://openalex.org/W2025199224","https://openalex.org/W2033855314","https://openalex.org/W2034978228","https://openalex.org/W2047221353","https://openalex.org/W2047278710","https://openalex.org/W2059571389","https://openalex.org/W2087789467","https://openalex.org/W2097462699","https://openalex.org/W2099210314","https://openalex.org/W2106053110","https://openalex.org/W2109339818","https://openalex.org/W2110654099","https://openalex.org/W2113651538","https://openalex.org/W2121038136","https://openalex.org/W2136691247","https://openalex.org/W2144064004","https://openalex.org/W2149433471","https://openalex.org/W2154558852","https://openalex.org/W2158781299","https://openalex.org/W2159930037","https://openalex.org/W2166903773","https://openalex.org/W2188523697","https://openalex.org/W2279956800","https://openalex.org/W2401415512","https://openalex.org/W2579923771","https://openalex.org/W2604272474","https://openalex.org/W2913243980","https://openalex.org/W2950740915","https://openalex.org/W2990138404","https://openalex.org/W3140704799","https://openalex.org/W3141455185","https://openalex.org/W4245558064","https://openalex.org/W4251115686","https://openalex.org/W4253840677","https://openalex.org/W4285719527","https://openalex.org/W4299828299"],"related_works":["https://openalex.org/W2942806827","https://openalex.org/W2124216369","https://openalex.org/W2607502190","https://openalex.org/W2103195393","https://openalex.org/W2013380735","https://openalex.org/W4234882900","https://openalex.org/W4387349426","https://openalex.org/W4294294773","https://openalex.org/W1724002428","https://openalex.org/W2274052023"],"abstract_inverted_index":{"Pairwise":[0,66],"learning":[1,6,42,181],"usually":[2],"refers":[3],"to":[4,62,72,96],"a":[5,10,44,53,97,111,128,170,213],"task":[7],"that":[8,59,91,131],"involves":[9],"loss":[11,46,102],"function":[12,47,103,115,120],"depending":[13],"on":[14,146,194],"pairs":[15],"of":[16,52,141,158,172,179,197],"examples,":[17],"among":[18],"which":[19,89],"the":[20,64,92,101,118,133,138,147,156,177,184,195],"most":[21],"notable":[22],"ones":[23],"are":[24,94,153],"bipartite":[25],"ranking,":[26],"metric":[27],"learning,":[28],"and":[29,116,182,204],"AUC":[30],"maximization.":[31],"In":[32,70],"this":[33],"letter":[34],"we":[35,60,126],"study":[36],"an":[37,49,122,166],"online":[38],"algorithm":[39],"for":[40,137,169,207],"pairwise":[41,180],"with":[43,110,210],"least-square":[45],"in":[48,121,176,212],"unconstrained":[50,123],"setting":[51,178],"reproducing":[54],"kernel":[55],"Hilbert":[56,214],"space":[57],"(RKHS)":[58],"refer":[61],"as":[63],"Online":[65],"lEaRning":[67],"Algorithm":[68],"(OPERA).":[69],"contrast":[71],"existing":[73],"works":[74],"(Kar,":[75],"Sriperumbudur,":[76],"Jain,":[77],"&":[78,85],"Karnick,":[79],"2013":[80],";":[81],"Wang,":[82],"Khardon,":[83],"Pechyony,":[84],"Jones,":[86],"2012":[87],"),":[88],"require":[90],"iterates":[93],"restricted":[95],"bounded":[98],"domain":[99],"or":[100],"is":[104,108],"strongly":[105],"convex,":[106],"OPERA":[107,142],"associated":[109,201],"non-strongly":[112],"convex":[113],"objective":[114],"learns":[117],"target":[119],"RKHS.":[124],"Specifically,":[125],"establish":[127,165],"general":[129],"theorem":[130],"guarantees":[132],"almost":[134],"sure":[135],"convergence":[136,151,185],"last":[139],"iterate":[140],"without":[143],"any":[144],"assumptions":[145],"underlying":[148],"distribution.":[149],"Explicit":[150],"rates":[152],"derived":[154],"under":[155],"condition":[157],"polynomially":[159],"decaying":[160],"step":[161],"sizes.":[162],"We":[163],"also":[164],"interesting":[167],"property":[168],"family":[171],"widely":[173],"used":[174],"kernels":[175],"illustrate":[183],"results":[186],"using":[187,199],"such":[188],"kernels.":[189],"Our":[190],"methodology":[191],"mainly":[192],"depends":[193],"characterization":[196],"RKHSs":[198],"its":[200],"integral":[202],"operators":[203],"probability":[205],"inequalities":[206],"random":[208],"variables":[209],"values":[211],"space.":[215]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":10},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}
