{"id":"https://openalex.org/W7148997502","doi":"https://doi.org/10.48550/arxiv.2604.01502","title":"Conformal Risk Control under Non-Monotone Losses: Theory and Finite-Sample Guarantees","display_name":"Conformal Risk Control under Non-Monotone Losses: Theory and Finite-Sample Guarantees","publication_year":2026,"publication_date":"2026-04-02","ids":{"openalex":"https://openalex.org/W7148997502","doi":"https://doi.org/10.48550/arxiv.2604.01502"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.01502","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.01502","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":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.01502","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5132909248","display_name":"Tareq Aldirawi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Aldirawi, Tareq","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5132865406","display_name":"Yun Li","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Yun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5132872978","display_name":"Wenge Guo","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Guo, Wenge","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"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/T10136","display_name":"Statistical Methods and Inference","score":0.17440000176429749,"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"}},"topics":[{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.17440000176429749,"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"}},{"id":"https://openalex.org/T12879","display_name":"Distributed Sensor Networks and Detection Algorithms","score":0.15710000693798065,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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":0.09669999778270721,"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/monotonic-function","display_name":"Monotonic function","score":0.6254000067710876},{"id":"https://openalex.org/keywords/minimax","display_name":"Minimax","score":0.5874999761581421},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5309000015258789},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.5095999836921692},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5085999965667725},{"id":"https://openalex.org/keywords/sample-size-determination","display_name":"Sample size determination","score":0.4943999946117401},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.4471000134944916},{"id":"https://openalex.org/keywords/resampling","display_name":"Resampling","score":0.4447000026702881}],"concepts":[{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.6254000067710876},{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.5874999761581421},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5309000015258789},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.5095999836921692},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5085999965667725},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5041999816894531},{"id":"https://openalex.org/C129848803","wikidata":"https://www.wikidata.org/wiki/Q2564360","display_name":"Sample size determination","level":2,"score":0.4943999946117401},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.4471000134944916},{"id":"https://openalex.org/C150921843","wikidata":"https://www.wikidata.org/wiki/Q1170431","display_name":"Resampling","level":2,"score":0.4447000026702881},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.43700000643730164},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.4113999903202057},{"id":"https://openalex.org/C165838908","wikidata":"https://www.wikidata.org/wiki/Q736777","display_name":"Calibration","level":2,"score":0.41029998660087585},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.40639999508857727},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.4020000100135803},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.3939000070095062},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36649999022483826},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3578999936580658},{"id":"https://openalex.org/C2776836416","wikidata":"https://www.wikidata.org/wiki/Q1364844","display_name":"False alarm","level":2,"score":0.32190001010894775},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.30390000343322754},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.2962000072002411},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.29019999504089355},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.2856000065803528},{"id":"https://openalex.org/C107321475","wikidata":"https://www.wikidata.org/wiki/Q5374254","display_name":"Empirical risk minimization","level":2,"score":0.27810001373291016},{"id":"https://openalex.org/C191178318","wikidata":"https://www.wikidata.org/wiki/Q2256906","display_name":"Thresholding","level":3,"score":0.2770000100135803},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.26339998841285706}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.01502","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.01502","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":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.01502","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.01502","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":"article"},"sustainable_development_goals":[{"score":0.6041114330291748,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Conformal":[0],"risk":[1,119,155,238],"control":[2,120,239],"(CRC)":[3],"provides":[4],"distribution-free":[5],"guarantees":[6,189],"for":[7,142,232],"controlling":[8],"the":[9,21,31,34,70,96,105,108,113,126,134,153,157,163,170,201,223],"expected":[10],"loss":[11,22,67],"at":[12],"a":[13,26,76,79,90,139,146],"user-specified":[14],"level.":[15],"Existing":[16],"theory":[17],"typically":[18],"assumes":[19],"that":[20,29,95,152,179,229],"decreases":[23],"monotonically":[24],"with":[25,205],"tuning":[27,71],"parameter":[28,72],"governs":[30],"size":[32,111,149],"of":[33,98,148,165,226],"prediction":[35,249],"set.":[36],"However,":[37],"this":[38,60,180],"assumption":[39],"is":[40,73,129,169,182],"often":[41],"violated":[42],"in":[43,83],"practice,":[44],"where":[45,167],"losses":[46,144],"may":[47],"behave":[48],"non-monotonically":[49],"due":[50],"to":[51,133,203],"competing":[52],"objectives":[53],"such":[54],"as":[55],"coverage":[56],"and":[57,85,112,197,199,217],"efficiency.":[58],"In":[59,116],"paper,":[61],"we":[62,93],"study":[63],"CRC":[64,99],"under":[65,190],"non-monotone":[66],"functions":[68],"when":[69,125],"selected":[74],"from":[75],"finite":[77],"grid,":[78],"setting":[80],"commonly":[81],"arising":[82],"thresholding":[84],"discretized":[86],"decision":[87],"rules.":[88],"Revisiting":[89],"known":[91],"counterexample,":[92],"show":[94],"validity":[97],"without":[100],"monotonicity":[101,244],"depends":[102],"critically":[103],"on":[104,162,213,243],"relationship":[106],"between":[107],"calibration":[109,127,171],"sample":[110,128,172],"grid":[114,135,147],"resolution.":[115],"particular,":[117],"reliable":[118],"can":[121],"still":[122],"be":[123],"achieved":[124],"sufficiently":[130],"large":[131],"relative":[132],"size.":[136,173],"We":[137,185],"establish":[138],"finite-sample":[140,233],"guarantee":[141],"bounded":[143],"over":[145],"$m$,":[150],"showing":[151],"excess":[154],"above":[156],"target":[158],"level":[159],"$\u03b1$":[160],"scales":[161],"order":[164],"$\\sqrt{\\log(m)/n}$,":[166],"$n$":[168],"A":[174],"matching":[175],"lower":[176],"bound":[177],"demonstrates":[178],"rate":[181],"minimax":[183],"optimal.":[184],"also":[186],"derive":[187],"refined":[188],"additional":[191],"structural":[192],"conditions,":[193],"including":[194],"Lipschitz":[195],"continuity":[196],"monotonicity,":[198],"extend":[200],"analysis":[202],"settings":[204],"distribution":[206],"shift":[207],"via":[208],"importance":[209],"weighting.":[210],"Numerical":[211],"experiments":[212],"synthetic":[214],"multilabel":[215],"classification":[216],"real":[218],"object":[219],"detection":[220],"data":[221],"illustrate":[222],"practical":[224],"implications":[225],"non-monotonicity.":[227],"Methods":[228],"explicitly":[230],"account":[231],"uncertainty":[234],"achieve":[235],"more":[236],"stable":[237],"than":[240],"approaches":[241],"based":[242],"transformations,":[245],"while":[246],"maintaining":[247],"competitive":[248],"set":[250],"sizes.":[251]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-04-04T00:00:00"}
