{"id":"https://openalex.org/W2766748337","doi":"https://doi.org/10.1137/18m1199241","title":"Consistency of Lipschitz Learning with Infinite Unlabeled Data and Finite Labeled Data","display_name":"Consistency of Lipschitz Learning with Infinite Unlabeled Data and Finite Labeled Data","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2766748337","doi":"https://doi.org/10.1137/18m1199241","mag":"2766748337"},"language":"en","primary_location":{"id":"doi:10.1137/18m1199241","is_oa":true,"landing_page_url":"https://doi.org/10.1137/18m1199241","pdf_url":null,"source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematics of Data Science","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.1137/18m1199241","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066156899","display_name":"Jeff Calder","orcid":"https://orcid.org/0000-0002-9829-4128"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Jeff Calder","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5066156899"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.954,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.75535532,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"1","issue":"4","first_page":"780","last_page":"812"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.9973000288009644,"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":0.9973000288009644,"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/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9805999994277954,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9695000052452087,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.8950349688529968},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6941007971763611},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.5654346346855164},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5507892966270447},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.54795241355896},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4584483802318573},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.4487874507904053},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.41053470969200134},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4031080901622772},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3616113066673279},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.28141623735427856},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.26088273525238037}],"concepts":[{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.8950349688529968},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6941007971763611},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5654346346855164},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5507892966270447},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.54795241355896},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4584483802318573},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.4487874507904053},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.41053470969200134},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4031080901622772},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3616113066673279},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28141623735427856},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.26088273525238037},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/18m1199241","is_oa":true,"landing_page_url":"https://doi.org/10.1137/18m1199241","pdf_url":null,"source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematics of Data Science","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1710.10364","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1710.10364","pdf_url":"https://arxiv.org/pdf/1710.10364","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:2766748337","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1710.10364","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1710.10364","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1710.10364","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":"article"}],"best_oa_location":{"id":"doi:10.1137/18m1199241","is_oa":true,"landing_page_url":"https://doi.org/10.1137/18m1199241","pdf_url":null,"source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematics of Data Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6277428110","display_name":null,"funder_award_id":"1713691","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1861295442","https://openalex.org/W1969768229","https://openalex.org/W1971148501","https://openalex.org/W1976996455","https://openalex.org/W1979463344","https://openalex.org/W1987642543","https://openalex.org/W2001564373","https://openalex.org/W2066590618","https://openalex.org/W2089296357","https://openalex.org/W2090936839","https://openalex.org/W2091313119","https://openalex.org/W2092046358","https://openalex.org/W2107503465","https://openalex.org/W2111296615","https://openalex.org/W2112796928","https://openalex.org/W2144280422","https://openalex.org/W2154480112","https://openalex.org/W2167768422","https://openalex.org/W2604163838","https://openalex.org/W2738326163","https://openalex.org/W2896696294","https://openalex.org/W2952521183","https://openalex.org/W2962701197","https://openalex.org/W2962826709"],"related_works":["https://openalex.org/W2738326163","https://openalex.org/W2146508075","https://openalex.org/W1984032850","https://openalex.org/W1861295442","https://openalex.org/W3034023082","https://openalex.org/W3195466292","https://openalex.org/W2972280403","https://openalex.org/W3092864612","https://openalex.org/W46108322","https://openalex.org/W2224709232","https://openalex.org/W2736970300","https://openalex.org/W3100105564","https://openalex.org/W2090761569","https://openalex.org/W3172140636","https://openalex.org/W3111733052","https://openalex.org/W2607502190","https://openalex.org/W2000166160","https://openalex.org/W1496467656","https://openalex.org/W2949397613","https://openalex.org/W2952767562"],"abstract_inverted_index":{"We":[0,48],"study":[1],"the":[2,10,36,39,57,92,95,102,111,122,129,138,141],"consistency":[3],"of":[4,12,38,60,94,104,124,132,140],"Lipschitz":[5,25,84],"learning":[6,26,85],"on":[7,72,76],"graphs":[8],"in":[9,29,56,87],"limit":[11],"infinite":[13],"unlabeled":[14,40,96],"data":[15],"and":[16,98,136],"finite":[17],"labeled":[18],"data.":[19],"Previous":[20],"work":[21],"has":[22],"conjectured":[23],"that":[24,51,75,121],"is":[27,33,43,54,86],"well-posed":[28],"this":[30,52],"limit,":[31],"but":[32],"insensitive":[34],"to":[35,73,91,128],"distribution":[37,93],"data,":[41,97],"which":[42],"undesirable":[44],"for":[45],"semi-supervised":[46],"learning.":[47],"first":[49],"prove":[50],"conjecture":[53],"true":[55],"special":[58],"case":[59],"a":[61,77],"random":[62,78],"geometric":[63,79],"graph":[64,80],"model":[65],"with":[66,81],"kernel-based":[67],"weights.":[68,112],"Then":[69],"we":[70,99],"go":[71],"show":[74,100],"self-tuning":[82],"weights,":[83],"fact":[88],"highly":[89],"sensitive":[90],"how":[101],"degree":[103],"sensitivity":[105],"can":[106],"be":[107],"adjusted":[108],"by":[109],"tuning":[110],"In":[113],"both":[114],"cases,":[115],"our":[116],"results":[117],"follow":[118],"from":[119],"showing":[120],"sequence":[123],"learned":[125],"functions":[126],"converges":[127],"viscosity":[130],"solution":[131],"an":[133],"$\\infty$-Laplace-type":[134],"equation":[135],"studying":[137],"structure":[139],"limiting":[142],"equation.":[143]},"counts_by_year":[{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2022-08-20T00:00:00"}
