{"id":"https://openalex.org/W7204916264","doi":"https://doi.org/10.48550/arxiv.2608.29789","title":"A Unified Perspective on Conformal Prediction and Wasserstein Distributionally Robust Optimization for Uncertainty Quantification","display_name":"A Unified Perspective on Conformal Prediction and Wasserstein Distributionally Robust Optimization for Uncertainty Quantification","publication_year":2026,"publication_date":"2026-08-30","ids":{"openalex":"https://openalex.org/W7204916264","doi":"https://doi.org/10.48550/arxiv.2608.29789"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.29789","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.29789","pdf_url":"https://arxiv.org/pdf/2608.29789","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,"listed_in":[],"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.29789","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039522805","display_name":"Kehan Long","orcid":"https://orcid.org/0000-0003-2839-7188","observed_orcids":["https://orcid.org/0000-0003-2839-7188"]},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Long, Kehan","raw_affiliation_strings":["Contextual Robotics Institute , University of California San Diego , La Jolla , CA , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Contextual Robotics Institute , University of California San Diego , La Jolla , CA , USA","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102026945","display_name":"Yiqi Zhao","orcid":"https://orcid.org/0000-0002-8799-8023","observed_orcids":["https://orcid.org/0000-0002-8799-8023"]},"institutions":[{"id":"https://openalex.org/I1174212","display_name":"University of Southern California","ror":"https://ror.org/03taz7m60","country_code":"US","type":"education","lineage":["https://openalex.org/I1174212"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zhao, Yiqi","raw_affiliation_strings":["Thomas Lord Department of Computer Science , University of Southern California , Los Angeles , CA , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Thomas Lord Department of Computer Science , University of Southern California , Los Angeles , CA , USA","institution_ids":["https://openalex.org/I1174212"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071034766","display_name":"Pol Mestres","orcid":"https://orcid.org/0000-0002-6409-8903","observed_orcids":["https://orcid.org/0000-0002-6409-8903"]},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mestres, Pol","raw_affiliation_strings":["Department of Mechanical and Civil Engineering , California Institute of Technology , Pasadena , CA , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical and Civil Engineering , California Institute of Technology , Pasadena , CA , USA","institution_ids":["https://openalex.org/I122411786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027184150","display_name":"Lars Lindemann","orcid":"https://orcid.org/0000-0003-3430-6625","observed_orcids":["https://orcid.org/0000-0003-3430-6625"]},"institutions":[{"id":"https://openalex.org/I1174212","display_name":"University of Southern California","ror":"https://ror.org/03taz7m60","country_code":"US","type":"education","lineage":["https://openalex.org/I1174212"]},{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]},{"id":"https://openalex.org/I4405255889","display_name":"Automatic Control Laboratory","ror":"https://ror.org/03hjcs512","country_code":"CH","type":"facility","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088","https://openalex.org/I4405255889"]}],"countries":["CH","US"],"is_corresponding":false,"raw_author_name":"Lindemann, Lars","raw_affiliation_strings":["Automatic Control Laboratory , ETH Z\u00fcrich , Z\u00fcrich , Switzerland","Thomas Lord Department of Computer Science , University of Southern California , Los Angeles , CA , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Automatic Control Laboratory , ETH Z\u00fcrich , Z\u00fcrich , Switzerland","institution_ids":["https://openalex.org/I35440088","https://openalex.org/I4405255889"]},{"raw_affiliation_string":"Thomas Lord Department of Computer Science , University of Southern California , Los Angeles , CA , USA","institution_ids":["https://openalex.org/I1174212"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066400889","display_name":"Nikolay Atanasov","orcid":"https://orcid.org/0000-0003-0272-7580","observed_orcids":["https://orcid.org/0000-0003-0272-7580"]},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Atanasov, Nikolay","raw_affiliation_strings":["Contextual Robotics Institute , University of California San Diego , La Jolla , CA , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Contextual Robotics Institute , University of California San Diego , La Jolla , CA , USA","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5122862646","display_name":"Jorge Cort\u00e9s","orcid":"https://orcid.org/0000-0001-9582-5184","observed_orcids":["https://orcid.org/0000-0001-9582-5184"]},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Cort\u00e9s, Jorge","raw_affiliation_strings":["Contextual Robotics Institute , University of California San Diego , La Jolla , CA , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Contextual Robotics Institute , University of California San Diego , La Jolla , CA , USA","institution_ids":["https://openalex.org/I36258959"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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/T11413","display_name":"Risk and Portfolio Optimization","score":0.4343000054359436,"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"}},"topics":[{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.4343000054359436,"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"}},{"id":"https://openalex.org/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.24459999799728394,"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/T12535","display_name":"Machine Learning and Data Classification","score":0.027899999171495438,"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/conformal-prediction","display_name":"conformal prediction","score":1.0},{"id":"https://openalex.org/keywords/distributionally-robust-optimization","display_name":"distributionally robust optimization","score":0.9829999804496765},{"id":"https://openalex.org/keywords/wasserstein-ambiguity-set","display_name":"Wasserstein ambiguity set","score":0.8479999899864197},{"id":"https://openalex.org/keywords/uncertainty-quantification","display_name":"uncertainty quantification","score":0.9980000257492065},{"id":"https://openalex.org/keywords/finite-sample-validity","display_name":"finite-sample validity","score":0.746999979019165},{"id":"https://openalex.org/keywords/quantile-estimation","display_name":"quantile estimation","score":0.7929999828338623},{"id":"https://openalex.org/keywords/prediction-sets","display_name":"prediction sets","score":0.5099999904632568},{"id":"https://openalex.org/keywords/exchangeability","display_name":"exchangeability","score":0.5580000281333923}],"concepts":[{"id":"https://openalex.org/C118671147","wikidata":"https://www.wikidata.org/wiki/Q578714","display_name":"Quantile","level":2,"score":0.8840000033378601},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6312000155448914},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6262999773025513},{"id":"https://openalex.org/C165838908","wikidata":"https://www.wikidata.org/wiki/Q736777","display_name":"Calibration","level":2,"score":0.5516999959945679},{"id":"https://openalex.org/C2780522230","wikidata":"https://www.wikidata.org/wiki/Q1140419","display_name":"Ambiguity","level":2,"score":0.4903999865055084},{"id":"https://openalex.org/C193254401","wikidata":"https://www.wikidata.org/wiki/Q2160088","display_name":"Robust optimization","level":2,"score":0.4781999886035919},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4779999852180481},{"id":"https://openalex.org/C2781117939","wikidata":"https://www.wikidata.org/wiki/Q5374245","display_name":"Empirical likelihood","level":3,"score":0.47620001435279846},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.46720001101493835},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.4494999945163727},{"id":"https://openalex.org/C32230216","wikidata":"https://www.wikidata.org/wiki/Q7882499","display_name":"Uncertainty quantification","level":2,"score":0.43220001459121704},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.41019999980926514},{"id":"https://openalex.org/C98385598","wikidata":"https://www.wikidata.org/wiki/Q1339385","display_name":"Empirical distribution function","level":2,"score":0.38760000467300415},{"id":"https://openalex.org/C137209882","wikidata":"https://www.wikidata.org/wiki/Q1403517","display_name":"Measurement uncertainty","level":2,"score":0.3734000027179718},{"id":"https://openalex.org/C12713177","wikidata":"https://www.wikidata.org/wiki/Q1900281","display_name":"Perspective (graphical)","level":2,"score":0.3571000099182129},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.3325999975204468},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.32659998536109924},{"id":"https://openalex.org/C2776292839","wikidata":"https://www.wikidata.org/wiki/Q5179217","display_name":"Coverage probability","level":3,"score":0.31139999628067017},{"id":"https://openalex.org/C49344536","wikidata":"https://www.wikidata.org/wiki/Q726441","display_name":"Cauchy distribution","level":2,"score":0.3025999963283539},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.2827000021934509},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2786000072956085},{"id":"https://openalex.org/C44082924","wikidata":"https://www.wikidata.org/wiki/Q1767128","display_name":"Order statistic","level":2,"score":0.2770000100135803},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.2680000066757202},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2651999890804291},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2630999982357025},{"id":"https://openalex.org/C141513077","wikidata":"https://www.wikidata.org/wiki/Q378542","display_name":"Independent and identically distributed random variables","level":3,"score":0.2621999979019165},{"id":"https://openalex.org/C67226441","wikidata":"https://www.wikidata.org/wiki/Q1665389","display_name":"Robust statistics","level":3,"score":0.26109999418258667},{"id":"https://openalex.org/C63817138","wikidata":"https://www.wikidata.org/wiki/Q3455889","display_name":"Quantile regression","level":2,"score":0.25999999046325684},{"id":"https://openalex.org/C2776836416","wikidata":"https://www.wikidata.org/wiki/Q1364844","display_name":"False alarm","level":2,"score":0.250900000333786}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.29789","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.29789","pdf_url":"https://arxiv.org/pdf/2608.29789","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,"listed_in":[],"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.29789","doi":"https://doi.org/10.48550/arxiv.2608.29789","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.29789","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,"listed_in":[],"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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.29789","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.29789","pdf_url":"https://arxiv.org/pdf/2608.29789","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,"listed_in":[],"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204916264.pdf","grobid_xml":"https://content.openalex.org/works/W7204916264.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W3127102228","https://openalex.org/W4378942327","https://openalex.org/W4391801072","https://openalex.org/W4402354095","https://openalex.org/W4404571268","https://openalex.org/W4405655184","https://openalex.org/W7140075586","https://openalex.org/W7203888414"],"related_works":["https://openalex.org/W7077577378","https://openalex.org/W7213495885","https://openalex.org/W7212242122","https://openalex.org/W4403995381","https://openalex.org/W7140351646","https://openalex.org/W7106228543","https://openalex.org/W4414199188","https://openalex.org/W7203888414","https://openalex.org/W4391409075","https://openalex.org/W4396782091"],"abstract_inverted_index":{"Uncertainty":[0],"quantification":[1],"from":[2],"finite":[3,79],"data":[4,81],"is":[5],"central":[6],"to":[7,77,145],"machine":[8],"learning,":[9],"optimization,":[10],"and":[11,22,29,70,100,181,243],"automation":[12],"systems,":[13],"where":[14],"decisions":[15],"must":[16],"remain":[17],"reliable":[18],"under":[19,47],"limited":[20],"samples":[21,221],"test-time":[23],"distribution":[24,180],"shift.":[25],"Conformal":[26],"prediction":[27,41],"(CP)":[28],"distributionally":[30],"robust":[31],"optimization":[32],"(DRO)":[33],"offer":[34],"two":[35,107],"complementary":[36],"approaches:":[37],"CP":[38,69,99,115,158,201],"constructs":[39],"data-dependent":[40,84],"sets":[42],"with":[43,93,147],"distribution-free":[44,162],"finite-sample":[45],"validity":[46],"exchangeability,":[48],"while":[49,165],"DRO":[50,71,101,121,166,237],"optimizes":[51],"worst-case":[52],"performance":[53],"over":[54,150,186],"an":[55,59,127],"ambiguity":[56,128,188],"set":[57],"around":[58],"empirical":[60,104],"distribution.":[61,199],"We":[62],"develop":[63],"a":[64,83,88,160,168,235],"unified":[65],"probabilistic":[66],"perspective":[67],"on":[68,175,203],"by":[72],"viewing":[73],"both":[74],"as":[75],"ways":[76],"turn":[78],"calibration":[80,152,210],"into":[82],"quantile":[85,105,118,124,227],"estimator":[86,218],"that":[87],"test":[89],"score":[90,198],"falls":[91],"below":[92],"high":[94,148],"probability.":[95],"From":[96],"this":[97,246],"perspective,":[98],"correct":[102],"the":[103,110,117,123,133,138,142,151,178,187,194,197,209,217,225],"along":[106],"coordinates":[108],"of":[109,113,177,196,208],"same":[111,134],"family":[112],"estimators:":[114],"inflates":[116],"level,":[119],"whereas":[120,234],"shifts":[122],"value":[125,241],"through":[126],"radius.":[129],"Both":[130],"methods":[131],"provide":[132],"calibration-conditional":[135],"guarantee":[136],"for":[137],"true":[139],"distribution,":[140],"requiring":[141],"target":[143,226],"coverage":[144,184],"hold":[146],"probability":[149],"sample.":[153],"Their":[154],"constructions":[155],"differ,":[156],"however:":[157],"uses":[159,167],"closed-form,":[161],"level":[163,213],"correction,":[164],"value-space":[169],"correction":[170],"whose":[171],"certified":[172],"radius":[173,238],"depends":[174],"properties":[176],"unknown":[179],"additionally":[182],"guarantees":[183],"uniformly":[185],"set.":[189],"This":[190],"distinction":[191],"emerges":[192],"in":[193,240],"tails":[195],"Because":[200],"relies":[202],"sparse":[204],"upper-tail":[205],"order":[206],"statistics":[207],"samples,":[211],"its":[212],"inflation":[214],"barely":[215],"moves":[216],"when":[219,230],"those":[220],"are":[222,232],"dense":[223],"near":[224],"but":[228],"overshoots":[229],"they":[231],"sparse,":[233],"well-chosen":[236],"corrects":[239],"space":[242],"may":[244],"avoid":[245],"overshoot.":[247]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-02T00:00:00"}
