{"id":"https://openalex.org/W3116360623","doi":"https://doi.org/10.1145/3406325.3451104","title":"VC dimension and distribution-free sample-based testing","display_name":"VC dimension and distribution-free sample-based testing","publication_year":2021,"publication_date":"2021-06-15","ids":{"openalex":"https://openalex.org/W3116360623","doi":"https://doi.org/10.1145/3406325.3451104","mag":"3116360623"},"language":"en","primary_location":{"id":"doi:10.1145/3406325.3451104","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3406325.3451104","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2012.03923","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000042413","display_name":"Eric Blais","orcid":"https://orcid.org/0009-0000-5824-9034"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Eric Blais","raw_affiliation_strings":["University of Waterloo, Canada","University of Waterloo , Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Waterloo, Canada","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"University of Waterloo , Canada","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006264519","display_name":"Renato Ferreira Pinto","orcid":"https://orcid.org/0009-0003-2346-8423"},"institutions":[{"id":"https://openalex.org/I4210148186","display_name":"Google (Canada)","ror":"https://ror.org/04d06q394","country_code":"CA","type":"company","lineage":["https://openalex.org/I1291425158","https://openalex.org/I4210128969","https://openalex.org/I4210148186"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Renato Ferreira Pinto Jr.","raw_affiliation_strings":["Google, Canada","Google Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Google, Canada","institution_ids":["https://openalex.org/I4210148186"]},{"raw_affiliation_string":"Google Canada","institution_ids":["https://openalex.org/I4210148186"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078658717","display_name":"Nathaniel Harms","orcid":"https://orcid.org/0000-0003-0259-9355"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Nathaniel Harms","raw_affiliation_strings":["University of Waterloo, Canada","University of Waterloo , Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Waterloo, Canada","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"University of Waterloo , Canada","institution_ids":["https://openalex.org/I151746483"]}]}],"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":"504","last_page":"517"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":1.0,"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/T12072","display_name":"Machine Learning and Algorithms","score":1.0,"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":0.9976000189781189,"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/T11652","display_name":"Imbalanced Data Classification Techniques","score":0.9922999739646912,"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/dimension","display_name":"Dimension (graph theory)","score":0.7774130702018738},{"id":"https://openalex.org/keywords/property-testing","display_name":"Property testing","score":0.7768721580505371},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.6707950830459595},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.6101281642913818},{"id":"https://openalex.org/keywords/sample","display_name":"Sample (material)","score":0.5751327276229858},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.571746289730072},{"id":"https://openalex.org/keywords/vc-dimension","display_name":"VC dimension","score":0.5395801067352295},{"id":"https://openalex.org/keywords/sample-complexity","display_name":"Sample complexity","score":0.5228817462921143},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.5047298669815063},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4878380596637726},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4436453878879547},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4316253662109375},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4183768630027771},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.41816315054893494},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3862306773662567},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3386702537536621},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10288727283477783},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09791672229766846}],"concepts":[{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.7774130702018738},{"id":"https://openalex.org/C123842658","wikidata":"https://www.wikidata.org/wiki/Q2918980","display_name":"Property testing","level":2,"score":0.7768721580505371},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.6707950830459595},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.6101281642913818},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.5751327276229858},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.571746289730072},{"id":"https://openalex.org/C119322782","wikidata":"https://www.wikidata.org/wiki/Q2662236","display_name":"VC dimension","level":2,"score":0.5395801067352295},{"id":"https://openalex.org/C2778445095","wikidata":"https://www.wikidata.org/wiki/Q18354077","display_name":"Sample complexity","level":2,"score":0.5228817462921143},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.5047298669815063},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4878380596637726},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4436453878879547},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4316253662109375},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4183768630027771},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.41816315054893494},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3862306773662567},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3386702537536621},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10288727283477783},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09791672229766846},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C43617362","wikidata":"https://www.wikidata.org/wiki/Q170050","display_name":"Chromatography","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1145/3406325.3451104","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3406325.3451104","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:2012.03923","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2012.03923","pdf_url":"https://arxiv.org/pdf/2012.03923","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:3116360623","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2012.03923v1","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.2012.03923","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2012.03923","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2012.03923","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2012.03923","pdf_url":"https://arxiv.org/pdf/2012.03923","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.7099999785423279,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3116360623.pdf","grobid_xml":"https://content.openalex.org/works/W3116360623.grobid-xml"},"referenced_works_count":62,"referenced_works":["https://openalex.org/W607505555","https://openalex.org/W1499660792","https://openalex.org/W1517311456","https://openalex.org/W1545614041","https://openalex.org/W1572529050","https://openalex.org/W1573146067","https://openalex.org/W1613749942","https://openalex.org/W1653844607","https://openalex.org/W1964775192","https://openalex.org/W1967689501","https://openalex.org/W1970630090","https://openalex.org/W1982918157","https://openalex.org/W1983415430","https://openalex.org/W1988355994","https://openalex.org/W1997142544","https://openalex.org/W2009813398","https://openalex.org/W2012400640","https://openalex.org/W2019363670","https://openalex.org/W2024095686","https://openalex.org/W2046907549","https://openalex.org/W2059728575","https://openalex.org/W2075328466","https://openalex.org/W2100732817","https://openalex.org/W2127090196","https://openalex.org/W2128717558","https://openalex.org/W2132467825","https://openalex.org/W2150434953","https://openalex.org/W2154952480","https://openalex.org/W2170990775","https://openalex.org/W2179884588","https://openalex.org/W2343833495","https://openalex.org/W2524932090","https://openalex.org/W2568354864","https://openalex.org/W2577805882","https://openalex.org/W2610386774","https://openalex.org/W2767099804","https://openalex.org/W2784208592","https://openalex.org/W2887874679","https://openalex.org/W2888426597","https://openalex.org/W2899114640","https://openalex.org/W2914539165","https://openalex.org/W2945267489","https://openalex.org/W2947780051","https://openalex.org/W2952561116","https://openalex.org/W2962748838","https://openalex.org/W2963017284","https://openalex.org/W2963277597","https://openalex.org/W2963571790","https://openalex.org/W2964190130","https://openalex.org/W2966112855","https://openalex.org/W2966120871","https://openalex.org/W2966223547","https://openalex.org/W2990634459","https://openalex.org/W3003973186","https://openalex.org/W3037911814","https://openalex.org/W3082455050","https://openalex.org/W3099961020","https://openalex.org/W4238893454","https://openalex.org/W4249341414","https://openalex.org/W4254552816","https://openalex.org/W4320933794","https://openalex.org/W6630070655"],"related_works":["https://openalex.org/W3172735654","https://openalex.org/W2185409032","https://openalex.org/W3027494763","https://openalex.org/W157716047","https://openalex.org/W2951316656","https://openalex.org/W2406918565","https://openalex.org/W1496892516","https://openalex.org/W2914377170","https://openalex.org/W1785049690","https://openalex.org/W2951814809","https://openalex.org/W2963650730","https://openalex.org/W1972029750","https://openalex.org/W2014603110","https://openalex.org/W236988976","https://openalex.org/W2186390088","https://openalex.org/W2181972042","https://openalex.org/W2593452835","https://openalex.org/W2996763839","https://openalex.org/W1557692463","https://openalex.org/W2778880769"],"abstract_inverted_index":{"We":[0],"consider":[1],"the":[2,21,28,50],"problem":[3],"of":[4,8,52,59],"determining":[5],"which":[6],"classes":[7],"functions":[9,60],"can":[10,17,65],"be":[11,18,66],"tested":[12],"more":[13],"efficiently":[14],"than":[15],"they":[16],"learned,":[19],"in":[20,61],"distribution-free":[22],"sample-based":[23],"model":[24],"that":[25,37,72],"corresponds":[26],"to":[27,55,80],"standard":[29],"PAC":[30],"learning":[31],"setting.":[32],"Our":[33],"main":[34],"result":[35],"shows":[36],"while":[38],"VC":[39],"dimension":[40,79],"by":[41],"itself":[42],"does":[43],"not":[44],"always":[45],"provide":[46],"tight":[47],"bounds":[48,84],"on":[49,85],"number":[51],"samples":[53],"required":[54],"test":[56],"a":[57,69],"class":[58],"this":[62,86],"model,":[63],"it":[64],"combined":[67],"with":[68],"closely-related":[70],"variant":[71],"we":[73],"call":[74],"\u201clower":[75],"VC\u201d":[76],"(or":[77],"LVC)":[78],"obtain":[81],"strong":[82],"lower":[83],"sample":[87],"complexity.":[88]},"counts_by_year":[],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}