{"id":"https://openalex.org/W7152006380","doi":"https://doi.org/10.48550/arxiv.2604.05669","title":"Efficient machine unlearning with minimax optimality","display_name":"Efficient machine unlearning with minimax optimality","publication_year":2026,"publication_date":"2026-04-07","ids":{"openalex":"https://openalex.org/W7152006380","doi":"https://doi.org/10.48550/arxiv.2604.05669"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.05669","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.05669","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.05669","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5133153208","display_name":"Jingyi Xie","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xie, Jingyi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133181828","display_name":"Linjun Zhang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Linjun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5133216662","display_name":"Sai Li","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Sai","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12535","display_name":"Machine Learning and Data Classification","score":0.19249999523162842,"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/T12535","display_name":"Machine Learning and Data Classification","score":0.19249999523162842,"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":0.08020000159740448,"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/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.07890000194311142,"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":0.8305000066757202},{"id":"https://openalex.org/keywords/oracle","display_name":"Oracle","score":0.6162999868392944},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.4332999885082245},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.43140000104904175},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.38929998874664307},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.38429999351501465},{"id":"https://openalex.org/keywords/statistical-inference","display_name":"Statistical inference","score":0.33809998631477356}],"concepts":[{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.8305000066757202},{"id":"https://openalex.org/C55166926","wikidata":"https://www.wikidata.org/wiki/Q2892946","display_name":"Oracle","level":2,"score":0.6162999868392944},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5864999890327454},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4763000011444092},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.4332999885082245},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.43140000104904175},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.38929998874664307},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.38429999351501465},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3521000146865845},{"id":"https://openalex.org/C134261354","wikidata":"https://www.wikidata.org/wiki/Q938438","display_name":"Statistical inference","level":2,"score":0.33809998631477356},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.33329999446868896},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.32030001282691956},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.31859999895095825},{"id":"https://openalex.org/C67186912","wikidata":"https://www.wikidata.org/wiki/Q367664","display_name":"Data modeling","level":2,"score":0.2962999939918518},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2808000147342682},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.2784000039100647},{"id":"https://openalex.org/C114289077","wikidata":"https://www.wikidata.org/wiki/Q3284399","display_name":"Statistical model","level":2,"score":0.2766000032424927},{"id":"https://openalex.org/C2778712577","wikidata":"https://www.wikidata.org/wiki/Q3505966","display_name":"Retraining","level":2,"score":0.259799987077713},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.2540999948978424},{"id":"https://openalex.org/C160920958","wikidata":"https://www.wikidata.org/wiki/Q7662746","display_name":"Synthetic data","level":2,"score":0.25060001015663147}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.05669","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.05669","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.05669","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.05669","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[{"score":0.6931737661361694,"display_name":"Decent work and economic growth","id":"https://metadata.un.org/sdg/8"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"There":[0],"is":[1],"a":[2,55,100],"growing":[3],"demand":[4],"for":[5,58,84],"efficient":[6],"data":[7,42,91,106,165],"removal":[8],"to":[9,17,36,159],"comply":[10],"with":[11,61],"regulations":[12],"like":[13],"the":[14,19,29,38,45,86,94,104,113,127,131,153],"GDPR":[15],"and":[16,65,79,99,121,130,148],"mitigate":[18],"influence":[20,39],"of":[21,31,40,47,89,103],"biased":[22],"or":[23],"corrupted":[24],"data.":[25],"This":[26],"has":[27],"motivated":[28],"field":[30],"machine":[32,59],"unlearning,":[33],"which":[34],"aims":[35],"eliminate":[37],"specific":[41],"subsets":[43],"without":[44,142],"cost":[46,124],"full":[48,144],"retraining.":[49,145],"In":[50],"this":[51],"work,":[52],"we":[53,73],"propose":[54],"statistical":[56],"framework":[57],"unlearning":[60,123],"generic":[62],"loss":[63],"functions":[64],"establish":[66,80,137],"theoretical":[67],"guarantees.":[68],"For":[69],"squared":[70],"loss,":[71],"especially,":[72],"develop":[74],"Unlearning":[75],"Least":[76],"Squares":[77],"(ULS)":[78],"its":[81],"minimax":[82],"optimality":[83],"estimating":[85],"model":[87,133],"parameter":[88],"remaining":[90,105],"when":[92],"only":[93],"pre-trained":[95],"estimator,":[96],"forget":[97,128,132],"samples,":[98],"small":[101],"subsample":[102],"are":[107],"available.":[108],"Our":[109],"results":[110],"reveal":[111],"that":[112,152],"estimation":[114],"error":[115],"decomposes":[116],"into":[117],"an":[118,122],"oracle":[119],"term":[120],"determined":[125],"by":[126],"proportion":[129],"bias.":[134],"We":[135],"further":[136],"asymptotically":[138],"valid":[139],"inference":[140],"procedures":[141],"requiring":[143,162],"Numerical":[146],"experiments":[147],"real-data":[149],"applications":[150],"demonstrate":[151],"proposed":[154],"method":[155],"achieves":[156],"performance":[157],"close":[158],"retraining":[160],"while":[161],"substantially":[163],"less":[164],"access.":[166]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-04-09T00:00:00"}
