{"id":"https://openalex.org/W4416649981","doi":"https://doi.org/10.1109/tpami.2025.3637063","title":"Closing the Approximation Gap of Partial AUC Optimization: A Tale of Two Formulations","display_name":"Closing the Approximation Gap of Partial AUC Optimization: A Tale of Two Formulations","publication_year":2025,"publication_date":"2025-11-25","ids":{"openalex":"https://openalex.org/W4416649981","doi":"https://doi.org/10.1109/tpami.2025.3637063","pmid":"https://pubmed.ncbi.nlm.nih.gov/41289125"},"language":"en","primary_location":{"id":"doi:10.1109/tpami.2025.3637063","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2025.3637063","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2512.01213","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5053213796","display_name":"Yangbangyan Jiang","orcid":"https://orcid.org/0000-0002-0148-8306"},"institutions":[{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yangbangyan Jiang","raw_affiliation_strings":["School of Computer Science and Technology, University of Chinese Academy of Sciences, Beijing, China"],"affiliations":[{"raw_affiliation_string":"School of Computer Science and Technology, University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210165038"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089092566","display_name":"Qianqian Xu","orcid":"https://orcid.org/0000-0002-3512-7277"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210090176","display_name":"Institute of Computing Technology","ror":"https://ror.org/0090r4d87","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210090176"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qianqian Xu","raw_affiliation_strings":["Key Laboratory of Intelligent Information Processing, Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Key Laboratory of Intelligent Information Processing, Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210090176","https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071552563","display_name":"Huiyang Shao","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Huiyang Shao","raw_affiliation_strings":["ByteDance Inc., Beijing, China"],"affiliations":[{"raw_affiliation_string":"ByteDance Inc., Beijing, China","institution_ids":[]}]},{"author_position":"middle","author":{"id":null,"display_name":"Zhiyong Yang","orcid":"https://orcid.org/0000-0002-4409-4999"},"institutions":[{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhiyong Yang","raw_affiliation_strings":["School of Computer Science and Technology, University of Chinese Academy of Sciences, Beijing, China"],"affiliations":[{"raw_affiliation_string":"School of Computer Science and Technology, University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210165038"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079963720","display_name":"Shilong Bao","orcid":"https://orcid.org/0000-0002-4336-8900"},"institutions":[{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shilong Bao","raw_affiliation_strings":["School of Computer Science and Technology, University of Chinese Academy of Sciences, Beijing, China"],"affiliations":[{"raw_affiliation_string":"School of Computer Science and Technology, University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210165038"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068837264","display_name":"Xiaochun Cao","orcid":"https://orcid.org/0000-0001-7141-708X"},"institutions":[{"id":"https://openalex.org/I157773358","display_name":"Sun Yat-sen University","ror":"https://ror.org/0064kty71","country_code":"CN","type":"education","lineage":["https://openalex.org/I157773358"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaochun Cao","raw_affiliation_strings":["School of Cyber Science and Technology, Shenzhen Campus of Sun Yat-sen University, Shenzhen, China"],"affiliations":[{"raw_affiliation_string":"School of Cyber Science and Technology, Shenzhen Campus of Sun Yat-sen University, Shenzhen, China","institution_ids":["https://openalex.org/I157773358"]}]},{"author_position":"last","author":{"id":null,"display_name":"Qingming Huang","orcid":"https://orcid.org/0000-0001-7542-296X"},"institutions":[{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qingming Huang","raw_affiliation_strings":["School of Computer Science and Technology, University of Chinese Academy of Sciences, Beijing, China"],"affiliations":[{"raw_affiliation_string":"School of Computer Science and Technology, University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210165038"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":7,"corresponding_author_ids":["https://openalex.org/A5053213796"],"corresponding_institution_ids":["https://openalex.org/I4210165038"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.18826967,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"48","issue":"3","first_page":"3482","last_page":"3498"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11652","display_name":"Imbalanced Data Classification Techniques","score":0.8672000169754028,"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/T11652","display_name":"Imbalanced Data Classification Techniques","score":0.8672000169754028,"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/T12026","display_name":"Explainable Artificial Intelligence (XAI)","score":0.017100000753998756,"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/T11653","display_name":"Financial Distress and Bankruptcy Prediction","score":0.017000000923871994,"subfield":{"id":"https://openalex.org/subfields/1402","display_name":"Accounting"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.7401000261306763},{"id":"https://openalex.org/keywords/minimax","display_name":"Minimax","score":0.7233999967575073},{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.6466000080108643},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.6036999821662903},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5900999903678894},{"id":"https://openalex.org/keywords/closing","display_name":"Closing (real estate)","score":0.5493999719619751},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.5397999882698059},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5055000185966492},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4372999966144562},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.429500013589859}],"concepts":[{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.7401000261306763},{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.7233999967575073},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.6466000080108643},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6248000264167786},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.6036999821662903},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5900999903678894},{"id":"https://openalex.org/C2778775528","wikidata":"https://www.wikidata.org/wiki/Q5135432","display_name":"Closing (real estate)","level":2,"score":0.5493999719619751},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.5397999882698059},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5095999836921692},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5055000185966492},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48339998722076416},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4372999966144562},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.429500013589859},{"id":"https://openalex.org/C129848803","wikidata":"https://www.wikidata.org/wiki/Q2564360","display_name":"Sample size determination","level":2,"score":0.3874000012874603},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.35580000281333923},{"id":"https://openalex.org/C117148685","wikidata":"https://www.wikidata.org/wiki/Q6865376","display_name":"Minimax approximation algorithm","level":2,"score":0.35429999232292175},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.3400000035762787},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33180001378059387},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.3301999866962433},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.32030001282691956},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.3165000081062317},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.3091999888420105},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.30570000410079956},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.3046000003814697},{"id":"https://openalex.org/C160824197","wikidata":"https://www.wikidata.org/wiki/Q2071054","display_name":"Linear approximation","level":3,"score":0.3025999963283539},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.29679998755455017},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2815000116825104},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.2734000086784363},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.2696000039577484},{"id":"https://openalex.org/C87007009","wikidata":"https://www.wikidata.org/wiki/Q210832","display_name":"Statistical hypothesis testing","level":2,"score":0.2689000070095062},{"id":"https://openalex.org/C145242015","wikidata":"https://www.wikidata.org/wiki/Q774123","display_name":"Approximation theory","level":2,"score":0.2669999897480011},{"id":"https://openalex.org/C93959086","wikidata":"https://www.wikidata.org/wiki/Q6888345","display_name":"Model selection","level":2,"score":0.2662999927997589}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tpami.2025.3637063","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2025.3637063","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},{"id":"pmid:41289125","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/41289125","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":"IEEE transactions on pattern analysis and machine intelligence","raw_type":null},{"id":"pmh:oai:arXiv.org:2512.01213","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2512.01213","pdf_url":"https://arxiv.org/pdf/2512.01213","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2512.01213","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2512.01213","pdf_url":"https://arxiv.org/pdf/2512.01213","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1023919524","display_name":null,"funder_award_id":", Grant","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1121271761","display_name":null,"funder_award_id":"Program","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1231421488","display_name":null,"funder_award_id":"under","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1342017981","display_name":null,"funder_award_id":"62471013","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1895809455","display_name":null,"funder_award_id":"2025M771492","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G2025660881","display_name":null,"funder_award_id":"E4EQ1101","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G2082826544","display_name":null,"funder_award_id":"Postdoctoral","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2376276132","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G2732183982","display_name":null,"funder_award_id":"U23B2051","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G37568934","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3840657713","display_name":null,"funder_award_id":"62441232","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G391238517","display_name":null,"funder_award_id":", and","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4039563609","display_name":null,"funder_award_id":"XDB06","funder_id":"https://openalex.org/F4320321133","funder_display_name":"Chinese Academy of Sciences"},{"id":"https://openalex.org/G4199693610","display_name":null,"funder_award_id":"62236008","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4414281452","display_name":null,"funder_award_id":"62025604","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4734482802","display_name":null,"funder_award_id":"2023M743441","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G5030940285","display_name":null,"funder_award_id":"2023M","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6212863906","display_name":null,"funder_award_id":"U21B2038","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6258415954","display_name":null,"funder_award_id":"Chinese","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7475320587","display_name":null,"funder_award_id":"62406305","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7726157001","display_name":null,"funder_award_id":"Grant No.","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8531886777","display_name":null,"funder_award_id":"62525212","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G854551255","display_name":null,"funder_award_id":"202407","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G8951484681","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G89782005","display_name":null,"funder_award_id":"62476068","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321133","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35"},{"id":"https://openalex.org/F4320321543","display_name":"China Postdoctoral Science Foundation","ror":"https://ror.org/0426zh255"},{"id":"https://openalex.org/F4320322847","display_name":"Youth Innovation Promotion Association of the Chinese Academy of Sciences","ror":"https://ror.org/031141b54"},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null},{"id":"https://openalex.org/F4320335892","display_name":"Youth Innovation Promotion Association","ror":null}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4416649981.pdf"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"As":[0],"a":[1,17,36,93,177,187,202,226],"variant":[2],"of":[3,20,110,134,190,206,216,229,245],"the":[4,7,11,31,72,79,98,107,126,129,132,150,154,173,183,214,217,222,243],"Area":[5],"Under":[6],"ROC":[8,32],"Curve":[9],"(AUC),":[10],"partial":[12],"AUC":[13],"(PAUC)":[14],"focuses":[15],"on":[16,221,238],"specific":[18],"range":[19],"false":[21],"positive":[22,27],"rate":[23,28,189],"(FPR)":[24],"and/or":[25],"true":[26],"(TPR)":[29],"in":[30,40,75],"curve.":[33],"It":[34],"is":[35,60,140],"pivotal":[37],"evaluation":[38],"metric":[39],"real-world":[41],"scenarios":[42],"with":[43,121,128,169],"both":[44],"class":[45],"imbalance":[46],"and":[47,62,162,186,196,224],"decision":[48],"constraints.":[49],"However,":[50],"selecting":[51],"instances":[52],"within":[53],"these":[54],"constrained":[55],"intervals":[56],"during":[57],"its":[58],"calculation":[59],"NP-hard,":[61],"thus":[63],"typically":[64],"requires":[65],"approximation":[66,90,108],"techniques":[67],"for":[68,193],"practical":[69],"resolution.":[70],"Despite":[71],"progress":[73],"made":[74],"PAUC":[76,100,111],"optimization":[77,112],"over":[78],"last":[80],"few":[81],"years,":[82],"most":[83],"existing":[84],"methods":[85],"still":[86],"suffer":[87],"from":[88],"uncontrollable":[89],"errors":[91],"or":[92],"limited":[94],"scalability":[95],"when":[96],"optimizing":[97],"approximate":[99],"objectives.":[101],"In":[102],"this":[103],"paper,":[104],"we":[105,200],"close":[106],"gap":[109],"by":[113,159],"presenting":[114],"two":[115],"simple":[116],"instance-wise":[117,146],"minimax":[118,208],"reformulations:":[119],"one":[120],"an":[122,144,170],"asymptotically":[123],"vanishing":[124],"gap,":[125],"other":[127],"unbiasedness":[130],"at":[131],"cost":[133],"more":[135],"variables.":[136],"Our":[137],"key":[138],"idea":[139],"to":[141,148],"first":[142],"establish":[143],"equivalent":[145],"problem":[147],"lower":[149],"time":[151],"complexity,":[152],"simplify":[153],"complicated":[155],"sample":[156,184],"selection":[157],"procedure":[158],"threshold":[160],"learning,":[161],"then":[163],"apply":[164],"different":[165],"smoothing":[166],"techniques.":[167],"Equipped":[168],"efficient":[171],"solver,":[172],"resulting":[174],"algorithms":[175],"enjoy":[176],"linear":[178],"per-iteration":[179],"computational":[180],"complexity":[181],"w.r.t.":[182],"size":[185],"convergence":[188],"$O(\\epsilon":[191],"^{-1/3})$O(\u03b5-1/3)":[192],"typical":[194],"one-way":[195],"two-way":[197],"PAUCs.":[198],"Moreover,":[199],"provide":[201],"tight":[203],"generalization":[204,223],"bound":[205],"our":[207,246],"reformulations.":[209],"The":[210],"result":[211],"explicitly":[212],"demonstrates":[213],"impact":[215],"TPR/FPR":[218],"constraints":[219],"$\\alpha$\u03b1/$\\beta$\u03b2":[220],"exhibits":[225],"sharp":[227],"order":[228],"$\\tilde{O}(\\alpha":[230],"^{-1}n_+^{-1}":[231],"+":[232],"\\beta":[233],"^{-1}n_-^{-1})$O\u02dc(\u03b1-1n+-1+\u03b2-1n--1).":[234],"Finally,":[235],"extensive":[236],"experiments":[237],"several":[239],"benchmark":[240],"datasets":[241],"validate":[242],"strength":[244],"proposed":[247],"methods.":[248]},"counts_by_year":[],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2025-11-25T00:00:00"}