{"id":"https://openalex.org/W7135098523","doi":"https://doi.org/10.48550/arxiv.2603.10452","title":"Brenier Isotonic Regression","display_name":"Brenier Isotonic Regression","publication_year":2026,"publication_date":"2026-03-11","ids":{"openalex":"https://openalex.org/W7135098523","doi":"https://doi.org/10.48550/arxiv.2603.10452"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.10452","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.10452","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":null,"license_id":null,"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.2603.10452","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5128846917","display_name":"Han Bao","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bao, Han","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019041053","display_name":"Amirreza Eshraghi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Eshraghi, Amirreza","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5128858152","display_name":"Yutong Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Yutong","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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.6668999791145325,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.6668999791145325,"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/T10136","display_name":"Statistical Methods and Inference","score":0.07750000059604645,"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","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/isotonic-regression","display_name":"Isotonic regression","score":0.9472000002861023},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.7461000084877014},{"id":"https://openalex.org/keywords/linear-regression","display_name":"Linear regression","score":0.5608999729156494},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.527999997138977},{"id":"https://openalex.org/keywords/leverage","display_name":"Leverage (statistics)","score":0.5131000280380249},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.49779999256134033},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.48649999499320984},{"id":"https://openalex.org/keywords/regression","display_name":"Regression","score":0.4864000082015991},{"id":"https://openalex.org/keywords/regression-analysis","display_name":"Regression analysis","score":0.47530001401901245}],"concepts":[{"id":"https://openalex.org/C17418463","wikidata":"https://www.wikidata.org/wiki/Q3455874","display_name":"Isotonic regression","level":3,"score":0.9472000002861023},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7731000185012817},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.7461000084877014},{"id":"https://openalex.org/C48921125","wikidata":"https://www.wikidata.org/wiki/Q10861030","display_name":"Linear regression","level":2,"score":0.5608999729156494},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.527999997138977},{"id":"https://openalex.org/C153083717","wikidata":"https://www.wikidata.org/wiki/Q6535263","display_name":"Leverage (statistics)","level":2,"score":0.5131000280380249},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.49779999256134033},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.48649999499320984},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.4864000082015991},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4860999882221222},{"id":"https://openalex.org/C152877465","wikidata":"https://www.wikidata.org/wiki/Q208042","display_name":"Regression analysis","level":2,"score":0.47530001401901245},{"id":"https://openalex.org/C199163554","wikidata":"https://www.wikidata.org/wiki/Q1681619","display_name":"Univariate","level":3,"score":0.4415000081062317},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.4196999967098236},{"id":"https://openalex.org/C165838908","wikidata":"https://www.wikidata.org/wiki/Q736777","display_name":"Calibration","level":2,"score":0.41819998621940613},{"id":"https://openalex.org/C66690126","wikidata":"https://www.wikidata.org/wiki/Q2914302","display_name":"Concave function","level":3,"score":0.3856000006198883},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.38530001044273376},{"id":"https://openalex.org/C64946054","wikidata":"https://www.wikidata.org/wiki/Q4874476","display_name":"Bayesian multivariate linear regression","level":3,"score":0.3779999911785126},{"id":"https://openalex.org/C163175372","wikidata":"https://www.wikidata.org/wiki/Q3339222","display_name":"Linear model","level":2,"score":0.3628000020980835},{"id":"https://openalex.org/C32224588","wikidata":"https://www.wikidata.org/wiki/Q7250175","display_name":"Proper linear model","level":4,"score":0.36160001158714294},{"id":"https://openalex.org/C2988035592","wikidata":"https://www.wikidata.org/wiki/Q208042","display_name":"Regression function","level":3,"score":0.3375000059604645},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.3253999948501587},{"id":"https://openalex.org/C74127309","wikidata":"https://www.wikidata.org/wiki/Q3455886","display_name":"Nonparametric regression","level":3,"score":0.3156999945640564},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.30469998717308044},{"id":"https://openalex.org/C2777634741","wikidata":"https://www.wikidata.org/wiki/Q768993","display_name":"Wasserstein metric","level":2,"score":0.30169999599456787},{"id":"https://openalex.org/C120068334","wikidata":"https://www.wikidata.org/wiki/Q45343","display_name":"Polynomial regression","level":3,"score":0.2775999903678894},{"id":"https://openalex.org/C77056095","wikidata":"https://www.wikidata.org/wiki/Q543183","display_name":"Isotonic","level":2,"score":0.2590000033378601},{"id":"https://openalex.org/C41587187","wikidata":"https://www.wikidata.org/wiki/Q1501882","display_name":"Generalized linear model","level":2,"score":0.25589999556541443}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.10452","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.10452","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.10452","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.10452","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":null,"license_id":null,"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":{"Isotonic":[0],"regression":[1,5,48,52,104],"(IR)":[2],"is":[3,32,39,54,63,74],"shape-constrained":[4],"to":[6,26,101],"maintain":[7],"a":[8,45,51,59,88,103,111],"univariate":[9],"fitting":[10],"curve":[11],"non-decreasing,":[12],"which":[13],"has":[14],"numerous":[15],"applications":[16],"including":[17],"single-index":[18],"models":[19,117],"and":[20,106,118,124,140],"probability":[21,138,152],"calibration.":[22],"When":[23],"it":[24],"comes":[25],"multi-output":[27,47],"regression,":[28],"the":[29,37,64,79,107],"classical":[30],"IR":[31,129,146],"no":[33],"longer":[34],"applicable":[35],"because":[36],"monotonicity":[38,73],"not":[40],"readily":[41],"extendable.":[42],"We":[43,134],"consider":[44],"novel":[46],"problem":[49],"where":[50],"function":[53,62,105,113],"\\emph{cyclically":[55],"monotone}.":[56],"Roughly":[57],"speaking,":[58],"cyclically":[60,89],"monotone":[61,90],"gradient":[65],"of":[66],"some":[67],"convex":[68,108],"potential.":[69],"Whereas":[70],"enforcing":[71],"cyclic":[72],"apparently":[75],"challenging,":[76],"we":[77,126],"leverage":[78],"fact":[80],"that":[81],"Kantorovich's":[82],"optimal":[83,94],"transport":[84],"(OT)":[85],"always":[86],"yields":[87],"coupling":[91],"as":[92,110],"an":[93],"solution.":[95],"This":[96],"perspective":[97],"naturally":[98],"allows":[99],"us":[100],"interpret":[102],"potential":[109,120],"link":[112],"in":[114,121,151],"generalized":[115,141],"linear":[116,142],"Brenier's":[119],"OT,":[122],"respectively,":[123],"hence":[125],"call":[127],"this":[128],"extension":[130],"\\emph{Brenier":[131],"isotonic":[132],"regression}.":[133],"demonstrate":[135],"experiments":[136],"with":[137],"calibration":[139,153],"models.":[143],"In":[144],"particular,":[145],"outperforms":[147],"many":[148],"famous":[149],"baselines":[150],"robustly.":[154]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-03-13T00:00:00"}