{"id":"https://openalex.org/W1985792472","doi":"https://doi.org/10.1137/060670705","title":"Learning Mixtures of Product Distributions over Discrete Domains","display_name":"Learning Mixtures of Product Distributions over Discrete Domains","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W1985792472","doi":"https://doi.org/10.1137/060670705","mag":"1985792472"},"language":"en","primary_location":{"id":"doi:10.1137/060670705","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060670705","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/A5042697545","display_name":"Jon Feldman","orcid":null},"institutions":[{"id":"https://openalex.org/I1291425158","display_name":"Google (United States)","ror":"https://ror.org/00njsd438","country_code":"US","type":"company","lineage":["https://openalex.org/I1291425158","https://openalex.org/I4210128969"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jon Feldman","raw_affiliation_strings":["Google, New York Office, 76 Ninth Avenue, 4th floor, New York, NY 10011"],"affiliations":[{"raw_affiliation_string":"Google, New York Office, 76 Ninth Avenue, 4th floor, New York, NY 10011","institution_ids":["https://openalex.org/I1291425158"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051167298","display_name":"Ryan O\u2019Donnell","orcid":"https://orcid.org/0009-0005-5609-5795"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ryan O'Donnell","raw_affiliation_strings":["School of Computer Science, Carnegie Mellon University, 7121 Wean Hall, Pittsburgh, PA 15213"],"affiliations":[{"raw_affiliation_string":"School of Computer Science, Carnegie Mellon University, 7121 Wean Hall, Pittsburgh, PA 15213","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014866889","display_name":"Rocco A. Servedio","orcid":"https://orcid.org/0000-0003-2407-543X"},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Rocco A. Servedio","raw_affiliation_strings":["Department of Computer Science, Columbia University, 1214 Amsterdam Ave., Mailcode 0401, New York, NY 10027"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Columbia University, 1214 Amsterdam Ave., Mailcode 0401, New York, NY 10027","institution_ids":["https://openalex.org/I78577930"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5051167298"],"corresponding_institution_ids":["https://openalex.org/I74973139"],"apc_list":null,"apc_paid":null,"fwci":5.2792,"has_fulltext":false,"cited_by_count":58,"citation_normalized_percentile":{"value":0.95023687,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"37","issue":"5","first_page":"1536","last_page":"1564"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.9997000098228455,"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":0.9997000098228455,"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/T11269","display_name":"Algorithms and Data Compression","score":0.9977999925613403,"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/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9929999709129333,"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/product","display_name":"Product (mathematics)","score":0.6675279140472412},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6110002994537354},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5648360848426819},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.5134309530258179},{"id":"https://openalex.org/keywords/computational-learning-theory","display_name":"Computational learning theory","score":0.4968624413013458},{"id":"https://openalex.org/keywords/cube","display_name":"Cube (algebra)","score":0.4827117621898651},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4693409204483032},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.46746090054512024},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.45523715019226074},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.44125375151634216},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.434699147939682},{"id":"https://openalex.org/keywords/probably-approximately-correct-learning","display_name":"Probably approximately correct learning","score":0.431287556886673},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3601437211036682},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3118411600589752},{"id":"https://openalex.org/keywords/active-learning","display_name":"Active learning (machine learning)","score":0.13975957036018372},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.12437647581100464},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08347779512405396}],"concepts":[{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.6675279140472412},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6110002994537354},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5648360848426819},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5134309530258179},{"id":"https://openalex.org/C50292564","wikidata":"https://www.wikidata.org/wiki/Q2462783","display_name":"Computational learning theory","level":3,"score":0.4968624413013458},{"id":"https://openalex.org/C53051483","wikidata":"https://www.wikidata.org/wiki/Q861555","display_name":"Cube (algebra)","level":2,"score":0.4827117621898651},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4693409204483032},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.46746090054512024},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.45523715019226074},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.44125375151634216},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.434699147939682},{"id":"https://openalex.org/C176248197","wikidata":"https://www.wikidata.org/wiki/Q458526","display_name":"Probably approximately correct learning","level":4,"score":0.431287556886673},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3601437211036682},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3118411600589752},{"id":"https://openalex.org/C77967617","wikidata":"https://www.wikidata.org/wiki/Q4677561","display_name":"Active learning (machine learning)","level":2,"score":0.13975957036018372},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.12437647581100464},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08347779512405396},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/060670705","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060670705","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:repository.cmu.edu:compsci-2171","is_oa":false,"landing_page_url":"http://repository.cmu.edu/compsci/1168","pdf_url":null,"source":{"id":"https://openalex.org/S4306400668","display_name":"Research Showcase @ Carnegie Mellon University (Carnegie Mellon University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I74973139","host_organization_name":"Carnegie Mellon University","host_organization_lineage":["https://openalex.org/I74973139"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Computer Science Department","raw_type":"text"},{"id":"pmh:doi:10.1184/r1/6606884","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"Journal contribution"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.433.2580","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.433.2580","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www1.cs.columbia.edu/~rocco/Public/FOS-discrete-distributions-journal-final.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4869637327","display_name":"ITR Medium Award:     Computational Complexity Theory 2003","funder_award_id":"0324906","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5412610454","display_name":"CAREER:  Efficient Learning Algorithms for Rich Function Classes","funder_award_id":"0347282","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6671297155","display_name":null,"funder_award_id":"CAREER","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","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":7,"referenced_works":["https://openalex.org/W1981367467","https://openalex.org/W1995897489","https://openalex.org/W2022135397","https://openalex.org/W2029058452","https://openalex.org/W2178116779","https://openalex.org/W4206351426","https://openalex.org/W4238472918"],"related_works":["https://openalex.org/W2060490057","https://openalex.org/W2324678319","https://openalex.org/W245150611","https://openalex.org/W207698748","https://openalex.org/W4382934725","https://openalex.org/W4280488330","https://openalex.org/W3005925191","https://openalex.org/W4221160330","https://openalex.org/W2216908642","https://openalex.org/W2027221236"],"abstract_inverted_index":{"We":[0,42,130],"consider":[1],"the":[2,14,25,57,119],"problem":[3,150],"of":[4,7,24,31,51,106,118,167],"learning":[5,16,48],"mixtures":[6],"product":[8,54,80,171],"distributions":[9,55,172],"over":[10,56,173],"discrete":[11],"domains":[12],"in":[13,90,151],"distribution":[15],"framework":[17],"introduced":[18],"by":[19,100,144],"Kearns":[20],"et":[21],"al.":[22],"[Proceedings":[23],"$26$th":[26],"Annual":[27,121],"Symposium":[28],"on":[29,123],"Theory":[30],"Computing":[32],"(STOC),":[33],"Montr\u00e9al,":[34],"QC,":[35],"1994,":[36],"ACM,":[37],"New":[38],"York,":[39],"pp.":[40,128],"273\u2013282].":[41],"give":[43,132],"a":[44,49,147],"$\\operatorname{poly}(n/\\epsilon)$-time":[45,161],"algorithm":[46,137,162],"for":[47,65,76,97,177],"mixture":[50,166],"k":[52,141],"arbitrary":[53],"n-dimensional":[58],"Boolean":[59],"cube":[60],"$\\{0,1\\}^n$":[61],"to":[62,163],"accuracy":[63],"$\\epsilon$,":[64],"any":[66,165,178],"constant":[67],"k.":[68],"Previous":[69],"polynomial-time":[70,136],"algorithms":[71],"could":[72],"achieve":[73],"this":[74],"only":[75],"$k":[77,168],"=":[78,169,180],"2$":[79],"distributions;":[81],"our":[82,160],"result":[83],"answers":[84],"an":[85],"open":[86,149],"question":[87],"stated":[88],"independently":[89],"[M.":[91],"Cryan,":[92],"Learning":[93,125],"and":[94,111,114],"Approximation":[95],"Algorithms":[96],"Problems":[98],"Motivated":[99],"Evolutionary":[101],"Trees,":[102],"Ph.D.":[103],"thesis,":[104],"University":[105],"Warwick,":[107,108],"UK,":[109],"1999]":[110],"[Y.":[112],"Freund":[113],"Y.":[115],"Mansour,":[116],"Proceedings":[117],"$12$th":[120],"Conference":[122],"Computational":[124],"Theory,":[126],"1999,":[127],"183\u2013192].":[129],"further":[131],"evidence":[133],"that":[134],"no":[135],"can":[138],"succeed":[139],"when":[140],"is":[142],"superconstant,":[143],"reduction":[145],"from":[146],"difficult":[148],"PAC":[152],"(probably":[153],"approximately":[154],"correct)":[155],"learning.":[156],"Finally,":[157],"we":[158],"generalize":[159],"learn":[164],"O(1)$":[170],"$\\{0,1,":[174],"\\dots,":[175],"b-1\\}^n$,":[176],"$b":[179],"O(1)$.":[181]},"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":5}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}