{"id":"https://openalex.org/W7220685693","doi":"https://doi.org/10.48550/arxiv.2610.05388","title":"Semi-Supervised Kernel Ridge Fr\u00e9chet Regression","display_name":"Semi-Supervised Kernel Ridge Fr\u00e9chet Regression","publication_year":2026,"publication_date":"2026-10-04","ids":{"openalex":"https://openalex.org/W7220685693","doi":"https://doi.org/10.48550/arxiv.2610.05388"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.05388","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.05388","pdf_url":"https://arxiv.org/pdf/2610.05388","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.05388","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5150649167","display_name":"Jaehee Seo","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I139264467","display_name":"Seoul National University","ror":"https://ror.org/04h9pn542","country_code":"KR","type":"education","lineage":["https://openalex.org/I139264467"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Seo, Jaehee","raw_affiliation_strings":["Dept. of Statistics Seoul National University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dept. of Statistics Seoul National University","institution_ids":["https://openalex.org/I139264467"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5123181512","display_name":"Kwangho Kim","orcid":"https://orcid.org/0000-0001-8846-363X","observed_orcids":["https://orcid.org/0000-0001-8846-363X"]},"institutions":[{"id":"https://openalex.org/I139264467","display_name":"Seoul National University","ror":"https://ror.org/04h9pn542","country_code":"KR","type":"education","lineage":["https://openalex.org/I139264467"]},{"id":"https://openalex.org/I197347611","display_name":"Korea University","ror":"https://ror.org/047dqcg40","country_code":"KR","type":"education","lineage":["https://openalex.org/I197347611"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Kim, Kwangho","raw_affiliation_strings":["Dept. of Statistics Korea University","Dept. of Statistics Seoul National University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dept. of Statistics Korea University","institution_ids":["https://openalex.org/I197347611"]},{"raw_affiliation_string":"Dept. of Statistics Seoul National University","institution_ids":["https://openalex.org/I139264467"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5157681359","display_name":"Jisu Kim","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I139264467","display_name":"Seoul National University","ror":"https://ror.org/04h9pn542","country_code":"KR","type":"education","lineage":["https://openalex.org/I139264467"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Kim, Jisu","raw_affiliation_strings":["Dept. of Statistics Seoul National University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dept. of Statistics Seoul National University","institution_ids":["https://openalex.org/I139264467"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"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":0.6381999850273132,"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":0.6381999850273132,"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":0.11349999904632568,"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":0.0471000000834465,"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/frechet-regression","display_name":"Fr\u00e9chet regression","score":0.9900000095367432},{"id":"https://openalex.org/keywords/semi-supervised-learning","display_name":"semi-supervised learning","score":0.9449999928474426},{"id":"https://openalex.org/keywords/kernel-ridge-regression","display_name":"kernel ridge regression","score":0.9890000224113464},{"id":"https://openalex.org/keywords/prediction-error-bounds","display_name":"prediction error bounds","score":0.8799999952316284},{"id":"https://openalex.org/keywords/convergence-rate","display_name":"convergence rate","score":0.9620000123977661},{"id":"https://openalex.org/keywords/hybrid-stability","display_name":"hybrid stability","score":0.6029999852180481},{"id":"https://openalex.org/keywords/hadamard-spaces","display_name":"Hadamard spaces","score":0.8769999742507935},{"id":"https://openalex.org/keywords/eeg-prediction","display_name":"EEG prediction","score":0.31200000643730164}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7400000095367432},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.6320000290870667},{"id":"https://openalex.org/C120068334","wikidata":"https://www.wikidata.org/wiki/Q45343","display_name":"Polynomial regression","level":3,"score":0.6298999786376953},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.5590999722480774},{"id":"https://openalex.org/C32277403","wikidata":"https://www.wikidata.org/wiki/Q740445","display_name":"Ridge","level":2,"score":0.5245000123977661},{"id":"https://openalex.org/C200695384","wikidata":"https://www.wikidata.org/wiki/Q1739319","display_name":"Kernel regression","level":3,"score":0.4465999901294708},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4465000033378601},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.42800000309944153},{"id":"https://openalex.org/C152877465","wikidata":"https://www.wikidata.org/wiki/Q208042","display_name":"Regression analysis","level":2,"score":0.4194999933242798},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4156000018119812},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.40540000796318054},{"id":"https://openalex.org/C186215838","wikidata":"https://www.wikidata.org/wiki/Q772232","display_name":"Conditional expectation","level":2,"score":0.3774000108242035},{"id":"https://openalex.org/C138777275","wikidata":"https://www.wikidata.org/wiki/Q6884054","display_name":"Mixing (physics)","level":2,"score":0.3684000074863434},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3569999933242798},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.35359999537467957},{"id":"https://openalex.org/C74887250","wikidata":"https://www.wikidata.org/wiki/Q3455892","display_name":"Principal component regression","level":3,"score":0.3467000126838684},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3450999855995178},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.3434999883174896},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33550000190734863},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.33320000767707825},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.32580000162124634},{"id":"https://openalex.org/C48921125","wikidata":"https://www.wikidata.org/wiki/Q10861030","display_name":"Linear regression","level":2,"score":0.3174999952316284},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.30820000171661377},{"id":"https://openalex.org/C160446489","wikidata":"https://www.wikidata.org/wiki/Q7226642","display_name":"Polynomial kernel","level":4,"score":0.30329999327659607},{"id":"https://openalex.org/C119043178","wikidata":"https://www.wikidata.org/wiki/Q320723","display_name":"Covariate","level":2,"score":0.3019999861717224},{"id":"https://openalex.org/C195699287","wikidata":"https://www.wikidata.org/wiki/Q7915722","display_name":"Variable kernel density estimation","level":4,"score":0.28630000352859497},{"id":"https://openalex.org/C60316415","wikidata":"https://www.wikidata.org/wiki/Q6664520","display_name":"Local regression","level":4,"score":0.2773999869823456},{"id":"https://openalex.org/C2988035592","wikidata":"https://www.wikidata.org/wiki/Q208042","display_name":"Regression function","level":3,"score":0.27390000224113464},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.26649999618530273},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2639999985694885},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25940001010894775}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.05388","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.05388","pdf_url":"https://arxiv.org/pdf/2610.05388","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.2610.05388","doi":"https://doi.org/10.48550/arxiv.2610.05388","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.05388","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","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.05388","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.05388","pdf_url":"https://arxiv.org/pdf/2610.05388","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/F4320321292","display_name":"Seoul National University","ror":"https://ror.org/04h9pn542"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220685693.pdf","grobid_xml":"https://content.openalex.org/works/W7220685693.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W6922745830","https://openalex.org/W2114027834","https://openalex.org/W1969146802","https://openalex.org/W2158168589","https://openalex.org/W7163206449","https://openalex.org/W2322825644","https://openalex.org/W3082449787","https://openalex.org/W2616138645","https://openalex.org/W2804368052","https://openalex.org/W6960036738"],"abstract_inverted_index":{"Fr\u00e9chet":[0,22,54,148],"regression":[1,23,149],"provides":[2],"a":[3,86,129,138],"framework":[4],"for":[5,94,133],"predicting":[6],"random":[7],"object-valued":[8],"responses":[9,49],"by":[10,56],"minimizing":[11],"the":[12,52,67,90,96],"conditional":[13,53],"expected":[14],"squared":[15],"distances.":[16],"We":[17,60,98],"propose":[18],"semi-supervised":[19,142],"kernel":[20,37,57,84],"ridge":[21,58],"(SS-KRFR)":[24],"to":[25,50],"exploit":[26],"unlabeled":[27,44,72,114],"covariates":[28],"when":[29],"labeled":[30,42,48,70],"samples":[31],"are":[32],"scarce.":[33],"The":[34],"method":[35],"learns":[36],"spectral":[38],"features":[39],"from":[40,108],"both":[41,107],"and":[43,71,74,112,128,137,144],"covariates,":[45,115],"then":[46],"utilizes":[47],"estimate":[51],"function":[55],"regression.":[59],"derive":[61],"prediction":[62,134],"error":[63],"bounds":[64],"that":[65,102],"distinguish":[66],"roles":[68],"of":[69],"samples,":[73],"establish":[75],"polynomial":[76],"convergence":[77],"rates":[78],"under":[79],"suitable":[80],"conditions.":[81],"Under":[82],"additional":[83],"assumptions,":[85],"sharper":[87],"analysis":[88],"relaxes":[89],"sample":[91],"size":[92],"requirements":[93],"learning":[95],"features.":[97],"also":[99],"develop":[100],"hybrids":[101],"combine":[103],"features,":[104],"predictions,":[105],"or":[106],"models":[109],"fitted":[110],"with":[111],"without":[113],"establishing":[116],"uniform":[117],"stability":[118],"over":[119,146],"mixing":[120],"weights":[121],"in":[122,151],"Hadamard":[123],"spaces":[124],"at":[125],"common":[126],"tuning":[127],"separate":[130],"rate":[131],"guarantee":[132],"mixing.":[135],"Simulations":[136],"real-data":[139],"application":[140],"show":[141],"gains":[143],"improvements":[145],"competing":[147],"methods":[150],"several":[152],"settings.":[153]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-10-07T00:00:00"}