{"id":"https://openalex.org/W7222935523","doi":"https://doi.org/10.48550/arxiv.2610.23508","title":"Adaptive conformal prediction on the Grassmannian","display_name":"Adaptive conformal prediction on the Grassmannian","publication_year":2026,"publication_date":"2026-10-16","ids":{"openalex":"https://openalex.org/W7222935523","doi":"https://doi.org/10.48550/arxiv.2610.23508"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.23508","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.23508","pdf_url":"https://arxiv.org/pdf/2610.23508","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/2610.23508","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013517565","display_name":"Dimitrios Loukrezis","orcid":"https://orcid.org/0000-0003-1264-1182","observed_orcids":["https://orcid.org/0000-0003-1264-1182"]},"institutions":[{"id":"https://openalex.org/I1341640284","display_name":"Centrum Wiskunde & Informatica","ror":"https://ror.org/00x7ekv49","country_code":"NL","type":"facility","lineage":["https://openalex.org/I1341640284","https://openalex.org/I2800991832","https://openalex.org/I4405262988"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Loukrezis, Dimitrios","raw_affiliation_strings":["Scientific Computing Group Centrum Wiskunde & Informatica Amsterdam , The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Scientific Computing Group Centrum Wiskunde & Informatica Amsterdam , The Netherlands","institution_ids":["https://openalex.org/I1341640284"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085461931","display_name":"Zachary Grey","orcid":"https://orcid.org/0000-0003-1244-1623","observed_orcids":["https://orcid.org/0000-0003-1244-1623"]},"institutions":[{"id":"https://openalex.org/I1321296531","display_name":"National Institute of Standards and Technology","ror":"https://ror.org/05xpvk416","country_code":"US","type":"government","lineage":["https://openalex.org/I1321296531","https://openalex.org/I1343035065"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Grey, Zachary J.","raw_affiliation_strings":["Applied & Computational Mathematics Division National Institute of Standards & Technology Boulder , CO , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Applied & Computational Mathematics Division National Institute of Standards & Technology Boulder , CO , USA","institution_ids":["https://openalex.org/I1321296531"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5013355128","display_name":"\u0394\u03b7\u03bc\u03ae\u03c4\u03c1\u03b7\u03c2 \u0393. \u0393\u03b9\u03bf\u03b2\u03ac\u03bd\u03b7\u03c2","orcid":"https://orcid.org/0000-0003-2272-2584","observed_orcids":["https://orcid.org/0000-0003-2272-2584"]},"institutions":[{"id":"https://openalex.org/I145311948","display_name":"Johns Hopkins University","ror":"https://ror.org/00za53h95","country_code":"US","type":"education","lineage":["https://openalex.org/I145311948"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Giovanis, Dimitris G.","raw_affiliation_strings":["Dpt. of Civil & Systems Engineering Dpt. of Applied Mathematics and Statistics Johns Hopkins University Baltimore , MD , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dpt. of Civil & Systems Engineering Dpt. of Applied Mathematics and Statistics Johns Hopkins University Baltimore , MD , USA","institution_ids":["https://openalex.org/I145311948"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"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/T11871","display_name":"Advanced Statistical Methods and Models","score":0.14790000021457672,"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/T11871","display_name":"Advanced Statistical Methods and Models","score":0.14790000021457672,"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/T10136","display_name":"Statistical Methods and Inference","score":0.10670000314712524,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.08609999716281891,"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":0.9980000257492065},{"id":"https://openalex.org/keywords/grassmannians","display_name":"Grassmannians","score":0.9049999713897705},{"id":"https://openalex.org/keywords/prediction-regions","display_name":"prediction regions","score":0.7070000171661377},{"id":"https://openalex.org/keywords/metric-balls","display_name":"metric balls","score":0.7749999761581421},{"id":"https://openalex.org/keywords/manifold-geometry","display_name":"manifold geometry","score":0.640999972820282},{"id":"https://openalex.org/keywords/split-conformal-prediction","display_name":"split conformal prediction","score":0.7480000257492065},{"id":"https://openalex.org/keywords/coverage-guarantees","display_name":"coverage guarantees","score":0.6039999723434448},{"id":"https://openalex.org/keywords/heteroscedasticity","display_name":"heteroscedasticity","score":0.8619999885559082},{"id":"https://openalex.org/keywords/airfoil-design","display_name":"airfoil design","score":0.7229999899864197}],"concepts":[{"id":"https://openalex.org/C162929932","wikidata":"https://www.wikidata.org/wiki/Q129638","display_name":"Grassmannian","level":2,"score":0.7114999890327454},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6721000075340271},{"id":"https://openalex.org/C98214594","wikidata":"https://www.wikidata.org/wiki/Q850275","display_name":"Conformal map","level":2,"score":0.6032000184059143},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5751000046730042},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.46619999408721924},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.44200000166893005},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.43790000677108765},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4196000099182129},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.41449999809265137},{"id":"https://openalex.org/C101104100","wikidata":"https://www.wikidata.org/wiki/Q1063540","display_name":"Heteroscedasticity","level":2,"score":0.3833000063896179},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3668999969959259},{"id":"https://openalex.org/C112124176","wikidata":"https://www.wikidata.org/wiki/Q4698744","display_name":"Airfoil","level":2,"score":0.36169999837875366},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3391999900341034},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.31209999322891235},{"id":"https://openalex.org/C152877465","wikidata":"https://www.wikidata.org/wiki/Q208042","display_name":"Regression analysis","level":2,"score":0.2976999878883362},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28839999437332153},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.2858000099658966},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.2752000093460083},{"id":"https://openalex.org/C2778049214","wikidata":"https://www.wikidata.org/wiki/Q7512234","display_name":"Sigma","level":2,"score":0.2734000086784363},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.2694000005722046},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.26420000195503235},{"id":"https://openalex.org/C97931131","wikidata":"https://www.wikidata.org/wiki/Q5282087","display_name":"Discriminative model","level":2,"score":0.2599000036716461}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.23508","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.23508","pdf_url":"https://arxiv.org/pdf/2610.23508","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.2610.23508","doi":"https://doi.org/10.48550/arxiv.2610.23508","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.23508","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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.23508","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.23508","pdf_url":"https://arxiv.org/pdf/2610.23508","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":[{"id":"https://openalex.org/F4320332180","display_name":"Defense Advanced Research Projects Agency","ror":"https://ror.org/02caytj08"},{"id":"https://openalex.org/F4320332815","display_name":"Advanced Research Projects Agency","ror":"https://ror.org/02caytj08"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7222935523.pdf","grobid_xml":"https://content.openalex.org/works/W7222935523.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W3178918997","https://openalex.org/W4406692357","https://openalex.org/W7101847748","https://openalex.org/W7130552811","https://openalex.org/W7172529634","https://openalex.org/W7204749452"],"related_works":["https://openalex.org/W7130552811","https://openalex.org/W7117516689","https://openalex.org/W7090933131","https://openalex.org/W4403048436","https://openalex.org/W7172488701","https://openalex.org/W7172365527","https://openalex.org/W4392606442","https://openalex.org/W2137191505","https://openalex.org/W4389712818","https://openalex.org/W3167215506"],"abstract_inverted_index":{"We":[0,73],"introduce":[1],"a":[2,42],"conformal":[3,69],"prediction":[4,15,44,52,70,110],"framework":[5],"for":[6],"regression":[7],"with":[8],"Grassmann-valued":[9],"responses.":[10],"The":[11,93],"proposed":[12],"method":[13],"constructs":[14],"regions":[16,53],"in":[17,114],"the":[18,25,37,56,62,96,125],"form":[19],"of":[20,67,98],"metric":[21],"balls":[22],"directly":[23],"on":[24,84],"Grassmann":[26],"manifold,":[27],"using":[28],"basis-invariant":[29],"geometric":[30],"distances":[31],"as":[32],"non-conformity":[33,39,100],"measures":[34],"and":[35,79,87],"scaling":[36],"corresponding":[38],"scores":[40],"through":[41],"learned":[43],"difficulty":[45,111],"estimator.":[46],"This":[47],"yields":[48],"locally":[49],"adaptive,":[50],"input-dependent":[51],"that":[54],"respect":[55],"underlying":[57],"manifold":[58],"geometry,":[59],"while":[60,102,123],"retaining":[61],"finite-sample":[63],"marginal":[64],"coverage":[65,107],"guarantee":[66],"split":[68],"under":[71],"exchangeability.":[72],"evaluate":[74],"several":[75],"Grassmannian":[76],"distance":[77],"metrics":[78],"compare":[80],"their":[81],"prediction-region":[82,121],"efficiency":[83],"synthetic":[85],"benchmarks":[86],"an":[88],"airfoil":[89],"inverse":[90],"shape-design":[91],"problem.":[92],"results":[94],"highlight":[95],"advantages":[97],"geometry-aware":[99],"scores,":[101],"local":[103],"adaptation":[104],"improves":[105],"empirical":[106],"uniformity":[108],"across":[109],"levels":[112],"and,":[113],"strongly":[115],"heteroscedastic":[116],"settings,":[117],"can":[118],"substantially":[119],"reduce":[120],"size":[122],"maintaining":[124],"target":[126],"coverage.":[127]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-20T00:00:00"}