{"id":"https://openalex.org/W7165916906","doi":"https://doi.org/10.48550/arxiv.2606.25743","title":"Black-Box Assisted Regression: Phase Transitions and Minimax Optimality","display_name":"Black-Box Assisted Regression: Phase Transitions and Minimax Optimality","publication_year":2026,"publication_date":"2026-06-24","ids":{"openalex":"https://openalex.org/W7165916906","doi":"https://doi.org/10.48550/arxiv.2606.25743"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.25743","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.25743","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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.2606.25743","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5139349348","display_name":"Yan Zhou","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Zhou, Yan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5139349348"],"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/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.4178999960422516,"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/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.4178999960422516,"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":0.3912000060081482,"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/T10764","display_name":"Privacy-Preserving Technologies in Data","score":0.03009999915957451,"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":0.8192999958992004},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.7272999882698059},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.6096000075340271},{"id":"https://openalex.org/keywords/regression","display_name":"Regression","score":0.5422000288963318},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.5192999839782715},{"id":"https://openalex.org/keywords/nonparametric-statistics","display_name":"Nonparametric statistics","score":0.4706000089645386},{"id":"https://openalex.org/keywords/selection","display_name":"Selection (genetic algorithm)","score":0.4514999985694885},{"id":"https://openalex.org/keywords/nonparametric-regression","display_name":"Nonparametric regression","score":0.4505999982357025},{"id":"https://openalex.org/keywords/regression-analysis","display_name":"Regression analysis","score":0.414900004863739}],"concepts":[{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.8192999958992004},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.7272999882698059},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6096000075340271},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5669999718666077},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.5422000288963318},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.5192999839782715},{"id":"https://openalex.org/C102366305","wikidata":"https://www.wikidata.org/wiki/Q1097688","display_name":"Nonparametric statistics","level":2,"score":0.4706000089645386},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.4514999985694885},{"id":"https://openalex.org/C74127309","wikidata":"https://www.wikidata.org/wiki/Q3455886","display_name":"Nonparametric regression","level":3,"score":0.4505999982357025},{"id":"https://openalex.org/C152877465","wikidata":"https://www.wikidata.org/wiki/Q208042","display_name":"Regression analysis","level":2,"score":0.414900004863739},{"id":"https://openalex.org/C93959086","wikidata":"https://www.wikidata.org/wiki/Q6888345","display_name":"Model selection","level":2,"score":0.3896999955177307},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.38670000433921814},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37860000133514404},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3758000135421753},{"id":"https://openalex.org/C133939421","wikidata":"https://www.wikidata.org/wiki/Q6865379","display_name":"Minimax estimator","level":4,"score":0.3481000065803528},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.3409000039100647},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3393999934196472},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.33070001006126404},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.32670000195503235},{"id":"https://openalex.org/C149288129","wikidata":"https://www.wikidata.org/wiki/Q185357","display_name":"Phase transition","level":2,"score":0.3255000114440918},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.31380000710487366},{"id":"https://openalex.org/C48921125","wikidata":"https://www.wikidata.org/wiki/Q10861030","display_name":"Linear regression","level":2,"score":0.3093999922275543},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.28380000591278076},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2816999852657318},{"id":"https://openalex.org/C19619285","wikidata":"https://www.wikidata.org/wiki/Q196372","display_name":"Observational error","level":2,"score":0.2712000012397766},{"id":"https://openalex.org/C774472","wikidata":"https://www.wikidata.org/wiki/Q6760393","display_name":"Margin (machine learning)","level":2,"score":0.26649999618530273},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.2623000144958496},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.25920000672340393},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.2535000145435333}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.25743","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.25743","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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.2606.25743","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.25743","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Foundation":[0],"models":[1],"are":[2],"often":[3],"used":[4],"as":[5],"fixed":[6,45],"black-box":[7,32,137],"predictors":[8],"for":[9],"downstream":[10],"tasks":[11],"with":[12,78,163,168],"limited":[13],"labeled":[14,39],"data,":[15],"but":[16],"their":[17],"predictions":[18],"may":[19],"be":[20],"biased":[21],"and":[22,41,108,165],"unsafe":[23],"to":[24,54,59,112,114,148],"trust":[25],"blindly.":[26],"We":[27,64,83],"study":[28],"this":[29],"setting":[30],"through":[31],"assisted":[33],"nonparametric":[34],"regression:":[35],"a":[36,44,66,71,86,92],"learner":[37],"observes":[38],"samples":[40],"can":[42],"query":[43],"predictor":[46,105,138],"$f_0$,":[47,95,107],"while":[48,161],"the":[49,97,103,117,136,143,157,174,181],"target":[50],"$f^*$":[51],"is":[52,120,178],"close":[53],"$f_0$":[55,115],"in":[56],"$L_2(P_X)$":[57],"up":[58,147],"an":[60,149],"unknown":[61],"radius":[62],"$\u03b4$.":[63],"give":[65],"finite-sample":[67],"minimax":[68,145],"characterization":[69],"showing":[70],"phase":[72,159],"transition":[73],"at":[74,100],"$\u03b4_c(n)":[75],"\\asymp":[76],"n^{-\u03b2/(2\u03b2+d)}$,":[77],"leading":[79,144],"risk":[80],"$\\min\\{\u03b4^2,":[81],"n^{-2\u03b2/(2\u03b2+d)}\\}$.":[82],"then":[84],"analyze":[85],"Safe":[87],"Residual":[88],"Estimator:":[89],"it":[90],"learns":[91],"correction":[93,119],"around":[94],"initializes":[96],"residual":[98],"head":[99],"zero":[101],"so":[102],"initial":[104],"equals":[106],"uses":[109],"holdout":[110],"selection":[111],"revert":[113],"when":[116],"learned":[118],"not":[121],"supported":[122],"by":[123],"validation":[124],"data.":[125],"Here,":[126],"\"safe\"":[127],"means":[128],"avoiding":[129],"negative":[130],"transfer,":[131],"i.e.,":[132],"performing":[133],"worse":[134],"than":[135],"alone.":[139],"The":[140],"estimator":[141],"matches":[142],"term":[146],"additive":[150],"validation-selection":[151],"cost.":[152],"Synthetic":[153],"regression":[154,184],"experiments":[155],"verify":[156],"predicted":[158],"transition,":[160],"CIFAR-100":[162],"CLIP":[164],"AG":[166],"News":[167],"Qwen3-8B":[169],"provide":[170],"practice-facing":[171],"evidence":[172],"that":[173],"same":[175],"residual-correction":[176],"tradeoff":[177],"useful":[179],"beyond":[180],"formal":[182],"squared-loss":[183],"setting.":[185]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-06-26T00:00:00"}
