{"id":"https://openalex.org/W4243392806","doi":"https://doi.org/10.1023/a:1026499208981","title":"Rigorous Learning Curve Bounds from Statistical Mechanics","display_name":"Rigorous Learning Curve Bounds from Statistical Mechanics","publication_year":1996,"publication_date":"1996-11-01","ids":{"openalex":"https://openalex.org/W4243392806","doi":"https://doi.org/10.1023/a:1026499208981"},"language":"en","primary_location":{"id":"doi:10.1023/a:1026499208981","is_oa":true,"landing_page_url":"https://doi.org/10.1023/a:1026499208981","pdf_url":"https://link.springer.com/content/pdf/10.1023/A:1026499208981.pdf","source":{"id":"https://openalex.org/S62148650","display_name":"Machine Learning","issn_l":"0885-6125","issn":["0885-6125","1573-0565"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Machine Learning","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1023/A:1026499208981.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090849321","display_name":"David Haussler","orcid":"https://orcid.org/0000-0003-1533-4575"},"institutions":[{"id":"https://openalex.org/I185103710","display_name":"University of California, Santa Cruz","ror":"https://ror.org/03s65by71","country_code":"US","type":"education","lineage":["https://openalex.org/I185103710"]},{"id":"https://openalex.org/I4210150247","display_name":"Santa Cruz County Office of Education","ror":"https://ror.org/05dqak117","country_code":"US","type":"government","lineage":["https://openalex.org/I4210150247"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"David Haussler","raw_affiliation_strings":["U.C. Santa Cruz, Santa Cruz, California"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"U.C. Santa Cruz, Santa Cruz, California","institution_ids":["https://openalex.org/I185103710","https://openalex.org/I4210150247"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Michael Kearns","orcid":null},"institutions":[{"id":"https://openalex.org/I1283103587","display_name":"AT&T (United States)","ror":"https://ror.org/02bbd5539","country_code":"US","type":"company","lineage":["https://openalex.org/I1283103587"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Michael Kearns","raw_affiliation_strings":["AT&T Laboratories Research, Murray Hill, New Jersey"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"AT&T Laboratories Research, Murray Hill, New Jersey","institution_ids":["https://openalex.org/I1283103587"]}]},{"author_position":"middle","author":{"id":null,"display_name":"H. Sebastian Seung","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"H. Sebastian Seung","raw_affiliation_strings":["Bell Laboratories, Lucent Technologies, Murray Hill, New Jersey"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Bell Laboratories, Lucent Technologies, Murray Hill, New Jersey","institution_ids":[]}]},{"author_position":"last","author":{"id":null,"display_name":"Naftali Tishby","orcid":null},"institutions":[{"id":"https://openalex.org/I197251160","display_name":"Hebrew University of Jerusalem","ror":"https://ror.org/03qxff017","country_code":"IL","type":"education","lineage":["https://openalex.org/I197251160"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Naftali Tishby","raw_affiliation_strings":["Hebrew University, Jerusalem, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Hebrew University, Jerusalem, Israel","institution_ids":["https://openalex.org/I197251160"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5090849321"],"corresponding_institution_ids":["https://openalex.org/I185103710","https://openalex.org/I4210150247"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":1.5824,"has_fulltext":true,"cited_by_count":19,"citation_normalized_percentile":{"value":0.83566038,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"25","issue":"2-3","first_page":"195","last_page":"236"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9865000247955322,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9865000247955322,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/statistical-learning-theory","display_name":"Statistical learning theory","score":0.6280819773674011},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.5986994504928589},{"id":"https://openalex.org/keywords/learning-theory","display_name":"Learning theory","score":0.4984142780303955},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4822157621383667},{"id":"https://openalex.org/keywords/statistical-mechanics","display_name":"Statistical mechanics","score":0.4693148136138916},{"id":"https://openalex.org/keywords/probably-approximately-correct-learning","display_name":"Probably approximately correct learning","score":0.45607027411460876},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.43652212619781494},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4334120750427246},{"id":"https://openalex.org/keywords/algorithmic-learning-theory","display_name":"Algorithmic learning theory","score":0.42766886949539185},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3569261431694031},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3315858840942383},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2930823266506195},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.2788904309272766},{"id":"https://openalex.org/keywords/active-learning","display_name":"Active learning (machine learning)","score":0.25481921434402466},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11866530776023865}],"concepts":[{"id":"https://openalex.org/C2779915298","wikidata":"https://www.wikidata.org/wiki/Q7604400","display_name":"Statistical learning theory","level":3,"score":0.6280819773674011},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.5986994504928589},{"id":"https://openalex.org/C92393732","wikidata":"https://www.wikidata.org/wiki/Q1790374","display_name":"Learning theory","level":2,"score":0.4984142780303955},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4822157621383667},{"id":"https://openalex.org/C99874945","wikidata":"https://www.wikidata.org/wiki/Q188715","display_name":"Statistical mechanics","level":2,"score":0.4693148136138916},{"id":"https://openalex.org/C176248197","wikidata":"https://www.wikidata.org/wiki/Q458526","display_name":"Probably approximately correct learning","level":4,"score":0.45607027411460876},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43652212619781494},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4334120750427246},{"id":"https://openalex.org/C32254414","wikidata":"https://www.wikidata.org/wiki/Q4724364","display_name":"Algorithmic learning theory","level":3,"score":0.42766886949539185},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3569261431694031},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3315858840942383},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2930823266506195},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.2788904309272766},{"id":"https://openalex.org/C77967617","wikidata":"https://www.wikidata.org/wiki/Q4677561","display_name":"Active learning (machine learning)","level":2,"score":0.25481921434402466},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11866530776023865},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","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},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.0},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1023/a:1026499208981","is_oa":true,"landing_page_url":"https://doi.org/10.1023/a:1026499208981","pdf_url":"https://link.springer.com/content/pdf/10.1023/A:1026499208981.pdf","source":{"id":"https://openalex.org/S62148650","display_name":"Machine Learning","issn_l":"0885-6125","issn":["0885-6125","1573-0565"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Machine Learning","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1023/a:1026499208981","is_oa":true,"landing_page_url":"https://doi.org/10.1023/a:1026499208981","pdf_url":"https://link.springer.com/content/pdf/10.1023/A:1026499208981.pdf","source":{"id":"https://openalex.org/S62148650","display_name":"Machine Learning","issn_l":"0885-6125","issn":["0885-6125","1573-0565"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Machine Learning","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.8199999928474426,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G729664455","display_name":"Quantitative Analysis of Learning Algorithms","funder_award_id":"9123692","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4243392806.pdf","grobid_xml":"https://content.openalex.org/works/W4243392806.grobid-xml"},"referenced_works_count":39,"referenced_works":["https://openalex.org/W1978923178","https://openalex.org/W1981069195","https://openalex.org/W1984793731","https://openalex.org/W1990124919","https://openalex.org/W1998255116","https://openalex.org/W2003680476","https://openalex.org/W2013362271","https://openalex.org/W2030450972","https://openalex.org/W2042132284","https://openalex.org/W2044442377","https://openalex.org/W2044972994","https://openalex.org/W2045313701","https://openalex.org/W2065842846","https://openalex.org/W2066424095","https://openalex.org/W2066653224","https://openalex.org/W2074416206","https://openalex.org/W2081177492","https://openalex.org/W2084544490","https://openalex.org/W2090559885","https://openalex.org/W2090614046","https://openalex.org/W2094417631","https://openalex.org/W2113924402","https://openalex.org/W2118649542","https://openalex.org/W2133259161","https://openalex.org/W2150872430","https://openalex.org/W2912633461","https://openalex.org/W3011112921","https://openalex.org/W4206718934","https://openalex.org/W4213268973","https://openalex.org/W4232150823","https://openalex.org/W4238284510","https://openalex.org/W4238722143","https://openalex.org/W4244487828","https://openalex.org/W4248349557","https://openalex.org/W4249189474","https://openalex.org/W4292025355","https://openalex.org/W4302591315","https://openalex.org/W6645514819","https://openalex.org/W6657839258"],"related_works":["https://openalex.org/W3144870225","https://openalex.org/W2789122432","https://openalex.org/W2892986808","https://openalex.org/W836619539","https://openalex.org/W2149298154","https://openalex.org/W2016852016","https://openalex.org/W2972514247","https://openalex.org/W2005530305","https://openalex.org/W3108538799","https://openalex.org/W1555424171"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2022-05-12T00:00:00"}