{"id":"https://openalex.org/W1982500696","doi":"https://doi.org/10.1137/0220056","title":"Learning Simple Concepts under Simple Distributions","display_name":"Learning Simple Concepts under Simple Distributions","publication_year":1991,"publication_date":"1991-10-01","ids":{"openalex":"https://openalex.org/W1982500696","doi":"https://doi.org/10.1137/0220056","mag":"1982500696"},"language":"en","primary_location":{"id":"doi:10.1137/0220056","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0220056","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"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 Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100351421","display_name":"Ming Li","orcid":"https://orcid.org/0000-0002-4073-0273"},"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":true,"raw_author_name":"Ming Li","raw_affiliation_strings":["Univ. of Waterloo,Waterloo,Ont.,Canada"],"affiliations":[{"raw_affiliation_string":"Univ. of Waterloo,Waterloo,Ont.,Canada","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029628745","display_name":"Paul Vit\u00e1nyi","orcid":"https://orcid.org/0000-0002-5712-7585"},"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"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Paul M. B. Vit\u00e1nyi","raw_affiliation_strings":["Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands, and Univ. van Amsterdam, Amsterdam, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands, and Univ. van Amsterdam, Amsterdam, The Netherlands","institution_ids":["https://openalex.org/I1341640284"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100351421"],"corresponding_institution_ids":["https://openalex.org/I151746483"],"apc_list":null,"apc_paid":null,"fwci":5.3926,"has_fulltext":false,"cited_by_count":70,"citation_normalized_percentile":{"value":0.95470501,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"20","issue":"5","first_page":"911","last_page":"935"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.9998999834060669,"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":0.9998999834060669,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11269","display_name":"Algorithms and Data Compression","score":0.9955999851226807,"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/simple","display_name":"Simple (philosophy)","score":0.8431472778320312},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5667244791984558},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5638949275016785},{"id":"https://openalex.org/keywords/completeness","display_name":"Completeness (order theory)","score":0.5626519918441772},{"id":"https://openalex.org/keywords/recursively-enumerable-language","display_name":"Recursively enumerable language","score":0.5501799583435059},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.5372194647789001},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.524417519569397},{"id":"https://openalex.org/keywords/concept-class","display_name":"Concept class","score":0.4927881062030792},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4464506506919861},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4270641803741455},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.42327386140823364},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36857080459594727},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.25310975313186646}],"concepts":[{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.8431472778320312},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5667244791984558},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5638949275016785},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.5626519918441772},{"id":"https://openalex.org/C203702658","wikidata":"https://www.wikidata.org/wiki/Q1073063","display_name":"Recursively enumerable language","level":2,"score":0.5501799583435059},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.5372194647789001},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.524417519569397},{"id":"https://openalex.org/C203313322","wikidata":"https://www.wikidata.org/wiki/Q5158394","display_name":"Concept class","level":2,"score":0.4927881062030792},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4464506506919861},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4270641803741455},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.42327386140823364},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36857080459594727},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.25310975313186646},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/0220056","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0220056","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"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 Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.53.7234","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.53.7234","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cwi.nl/~paulv/papers/simple.ps","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/4","score":0.47999998927116394,"display_name":"Quality Education"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1979601782","https://openalex.org/W1990217074","https://openalex.org/W2008438091","https://openalex.org/W2017603160","https://openalex.org/W2018706164","https://openalex.org/W2019363670","https://openalex.org/W2028907144","https://openalex.org/W2029308360","https://openalex.org/W2040924621","https://openalex.org/W2064672629","https://openalex.org/W2066789935","https://openalex.org/W2070695637","https://openalex.org/W2070902649","https://openalex.org/W2076343783","https://openalex.org/W2087445078","https://openalex.org/W2091401625","https://openalex.org/W2092386826","https://openalex.org/W2117049614","https://openalex.org/W2131882306","https://openalex.org/W2135625884","https://openalex.org/W2148454341","https://openalex.org/W2163322487","https://openalex.org/W2428981601","https://openalex.org/W4238893454"],"related_works":["https://openalex.org/W4245749626","https://openalex.org/W1970705056","https://openalex.org/W1887191277","https://openalex.org/W2324635313","https://openalex.org/W2114312528","https://openalex.org/W2334954212","https://openalex.org/W4235288607","https://openalex.org/W2033883636","https://openalex.org/W2032860310","https://openalex.org/W1982500696"],"abstract_inverted_index":{"This":[0,137,163],"paper":[1],"aims":[2],"at":[3],"developing":[4],"a":[5,115,132,148,182,201,221,232,241,249,254,270],"learning":[6,16,61,70,142,154,171,238,297],"theory":[7,268],"where":[8],"\u201csimple\u201d":[9],"concepts":[10,19],"are":[11,52,101,105,109],"easily":[12],"learnable.":[13,54],"In":[14,41],"Valiant\u2019s":[15,194,209],"model,":[17,195],"many":[18],"turn":[20],"out":[21],"to":[22,29,37,50,168,188,245],"be":[23,38,189],"too":[24],"hard":[25],"(like":[26],"NP":[27],"hard)":[28],"learn.":[30],"Relatively":[31],"few":[32],"concept":[33,116,218,225],"classes":[34],"were":[35],"shown":[36],"learnable":[39,119,130,178,192,207,302],"polynomially.":[40],"daily":[42],"life,":[43],"it":[44,64,88,128],"seems":[45],"that":[46,68,100,114,185,204,215],"things":[47],"we":[48],"care":[49],"learn":[51,72],"usually":[53],"To":[55,265],"model":[56],"the":[57,69,112,144,156,160,237,267,288,295,300],"intuitive":[58],"notion":[59],"of":[60,224,235,293],"more":[62],"closely,":[63],"is":[65,85,89,118,129,166,186,205,262,273],"not":[66,190,206,263],"required":[67],"algorithm":[71,239],"(polynomially)":[73],"under":[74,79,120,131,193],"all":[75,80,121],"distributions,":[76,236],"but":[77],"only":[78,126],"simple":[81,86,122,135,260],"distributions.":[82],"A":[83],"distribution":[84,230,261],"if":[87,124,127],"dominated":[90],"by":[91,248],"an":[92],"enumerable":[93],"distribution.":[94,136],"All":[95,277],"distributions":[96,108,123],"with":[97],"computable":[98],"parameters":[99],"used":[102,167],"in":[103,111,143,155,208],"statistics":[104],"simple.":[106],"Simple":[107],"complete":[110],"sense":[113],"class":[117,184,203,219],"and":[125,151,173,200,299],"fixed":[133,243],"\u201cuniversal\u201d":[134,259],"holds":[138],"both":[139],"for":[140,152,216,227,275,280,287],"polynomial":[141,191],"discrete":[145,183,281],"case":[146,158],"(under":[147,159],"modified":[149],"model),":[150],"non-time-restricted":[153],"continuous":[157,202],"usual":[161],"model).":[162],"completeness":[164],"result":[165],"obtain":[169],"new":[170,177,296,301],"algorithms":[172],"several":[174],"quite":[175],"general":[176],"classes.":[179,303],"These":[180],"include":[181],"known":[187],"unless":[196],"RP":[197],"=":[198],"NP,":[199],"model.":[210],"The":[211,258],"results":[212,278],"here":[213],"allow":[214],"each":[217,228],"from":[220,231],"wide":[222,233],"range":[223,234],"classes,":[226],"underlying":[229],"uses":[240],"single":[242,250],"procedure":[244],"draw":[246],"examples":[247],"algorithmic":[251],"process":[252],"using":[253],"random":[255],"number":[256],"generator.":[257],"computable.":[264],"make":[266],"feasible,":[269],"polynomial-time":[271,289],"version":[272],"developed":[274],"it.":[276],"derived":[279],"sample":[282],"spaces":[283],"hold":[284],"mutatis":[285],"mutandis":[286],"versions,":[290],"including":[291],"versions":[292],"completeness,":[294],"algorithms,":[298]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
