{"id":"https://openalex.org/W2023627355","doi":"https://doi.org/10.1145/1993636.1993741","title":"Learning submodular functions","display_name":"Learning submodular functions","publication_year":2011,"publication_date":"2011-06-06","ids":{"openalex":"https://openalex.org/W2023627355","doi":"https://doi.org/10.1145/1993636.1993741","mag":"2023627355"},"language":"en","primary_location":{"id":"doi:10.1145/1993636.1993741","is_oa":true,"landing_page_url":"https://doi.org/10.1145/1993636.1993741","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/1993636.1993741","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the forty-third annual ACM symposium on Theory of computing","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://dl.acm.org/doi/pdf/10.1145/1993636.1993741","any_repository_has_fulltext":null},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068544954","display_name":"Maria-Florina Balcan","orcid":"https://orcid.org/0000-0002-9525-0103"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Maria-Florina Balcan","raw_affiliation_strings":["Georgia Institute of Technology, Atlanta, GA, USA","Georgia Institute of Technology Atlanta, GA, USA"],"affiliations":[{"raw_affiliation_string":"Georgia Institute of Technology, Atlanta, GA, USA","institution_ids":["https://openalex.org/I130701444"]},{"raw_affiliation_string":"Georgia Institute of Technology Atlanta, GA, USA","institution_ids":["https://openalex.org/I130701444"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102957872","display_name":"Nicholas J. A. Harvey","orcid":"https://orcid.org/0000-0001-5593-9785"},"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":"Nicholas J.A. Harvey","raw_affiliation_strings":["University of Waterloo, Waterloo, ON, Canada"],"affiliations":[{"raw_affiliation_string":"University of Waterloo, Waterloo, ON, Canada","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5068544954"],"corresponding_institution_ids":["https://openalex.org/I130701444"],"apc_list":null,"apc_paid":null,"fwci":8.4016,"has_fulltext":true,"cited_by_count":99,"citation_normalized_percentile":{"value":0.98182151,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"793","last_page":"802"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9995999932289124,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9984999895095825,"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/T12288","display_name":"Optimization and Search Problems","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/submodular-set-function","display_name":"Submodular set function","score":0.9635544419288635},{"id":"https://openalex.org/keywords/matroid","display_name":"Matroid","score":0.7373648881912231},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.5970910787582397},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5932590365409851},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.5881614089012146},{"id":"https://openalex.org/keywords/learnability","display_name":"Learnability","score":0.5157306790351868},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4876926839351654},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4858340919017792},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.47760888934135437},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.4409189522266388},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4380591809749603},{"id":"https://openalex.org/keywords/sample","display_name":"Sample (material)","score":0.433973491191864},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4113510251045227},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.37203899025917053},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1977142095565796}],"concepts":[{"id":"https://openalex.org/C178621042","wikidata":"https://www.wikidata.org/wiki/Q7631710","display_name":"Submodular set function","level":2,"score":0.9635544419288635},{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.7373648881912231},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.5970910787582397},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5932590365409851},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.5881614089012146},{"id":"https://openalex.org/C2777723229","wikidata":"https://www.wikidata.org/wiki/Q4367921","display_name":"Learnability","level":2,"score":0.5157306790351868},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4876926839351654},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4858340919017792},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.47760888934135437},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.4409189522266388},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4380591809749603},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.433973491191864},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4113510251045227},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37203899025917053},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1977142095565796},{"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1993636.1993741","is_oa":true,"landing_page_url":"https://doi.org/10.1145/1993636.1993741","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/1993636.1993741","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the forty-third annual ACM symposium on Theory of computing","raw_type":"proceedings-article"}],"best_oa_location":{"id":"doi:10.1145/1993636.1993741","is_oa":true,"landing_page_url":"https://doi.org/10.1145/1993636.1993741","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/1993636.1993741","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the forty-third annual ACM symposium on Theory of computing","raw_type":"proceedings-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2023627355.pdf","grobid_xml":"https://content.openalex.org/works/W2023627355.grobid-xml"},"referenced_works_count":74,"referenced_works":["https://openalex.org/W109692742","https://openalex.org/W187211397","https://openalex.org/W389907844","https://openalex.org/W749981671","https://openalex.org/W1486950299","https://openalex.org/W1489827011","https://openalex.org/W1494667986","https://openalex.org/W1498671329","https://openalex.org/W1519789693","https://openalex.org/W1520252399","https://openalex.org/W1542886316","https://openalex.org/W1554944419","https://openalex.org/W1564947197","https://openalex.org/W1572332593","https://openalex.org/W1574370680","https://openalex.org/W1576820654","https://openalex.org/W1595409123","https://openalex.org/W1680189815","https://openalex.org/W1897230935","https://openalex.org/W1970538402","https://openalex.org/W1973286131","https://openalex.org/W1984697505","https://openalex.org/W1989453388","https://openalex.org/W1998016322","https://openalex.org/W2018047324","https://openalex.org/W2019363670","https://openalex.org/W2029828838","https://openalex.org/W2031502124","https://openalex.org/W2035575256","https://openalex.org/W2042194938","https://openalex.org/W2061109699","https://openalex.org/W2065980363","https://openalex.org/W2068871408","https://openalex.org/W2069971337","https://openalex.org/W2070208123","https://openalex.org/W2080957551","https://openalex.org/W2090418561","https://openalex.org/W2092654494","https://openalex.org/W2100440346","https://openalex.org/W2102545534","https://openalex.org/W2106458073","https://openalex.org/W2106481801","https://openalex.org/W2106752752","https://openalex.org/W2107547393","https://openalex.org/W2110503949","https://openalex.org/W2128059732","https://openalex.org/W2134944545","https://openalex.org/W2142399242","https://openalex.org/W2144579822","https://openalex.org/W2148603752","https://openalex.org/W2155771856","https://openalex.org/W2157316274","https://openalex.org/W2168115971","https://openalex.org/W2176189934","https://openalex.org/W2258857078","https://openalex.org/W2478722229","https://openalex.org/W2483532815","https://openalex.org/W2496163386","https://openalex.org/W2787894218","https://openalex.org/W2953058253","https://openalex.org/W2962711478","https://openalex.org/W2963977715","https://openalex.org/W2988480584","https://openalex.org/W3122946301","https://openalex.org/W3144881883","https://openalex.org/W4210634265","https://openalex.org/W4238893454","https://openalex.org/W4241226388","https://openalex.org/W6613484142","https://openalex.org/W6634563818","https://openalex.org/W6807688996","https://openalex.org/W6813918715","https://openalex.org/W6858665454","https://openalex.org/W7071374342"],"related_works":["https://openalex.org/W4302791369","https://openalex.org/W2951285859","https://openalex.org/W2766040214","https://openalex.org/W2058299944","https://openalex.org/W4385627918","https://openalex.org/W4252399622","https://openalex.org/W4320232260","https://openalex.org/W1499990180","https://openalex.org/W4241672388","https://openalex.org/W2923536170"],"abstract_inverted_index":{"There":[0],"has":[1],"been":[2],"much":[3],"interest":[4],"in":[5,39,49],"the":[6,84,87,98,101,114,123,142],"machine":[7],"learning":[8,45,153],"and":[9,16,62,72,135,182],"algorithmic":[10],"game":[11],"theory":[12],"communities":[13],"on":[14,60,66,175],"understanding":[15],"using":[17],"submodular":[18,47],"functions.":[19],"Despite":[20],"this":[21,41,80,128],"substantial":[22],"interest,":[23],"little":[24],"is":[25,69,95,145],"known":[26],"about":[27],"their":[28],"learnability":[29],"from":[30,79,113],"data.":[31],"Motivated":[32],"by":[33],"applications,":[34],"such":[35],"as":[36],"pricing":[37],"goods":[38],"economics,":[40],"paper":[42],"considers":[43],"PAC-style":[44],"of":[46,57,86,100,127,133,180],"functions":[48],"a":[50,58,63,105,131,146,152,157,169,176,186],"distributional":[51],"setting.":[52],"A":[53],"problem":[54],"instance":[55],"consists":[56],"distribution":[59,144,148],"{0,1}n":[61,67],"real-valued":[64],"function":[65,88,102],"that":[68,155],"non-negative,":[70],"monotone,":[71],"submodular.":[73],"We":[74,121],"are":[75],"given":[76],"poly(n)":[77],"samples":[78],"distribution,":[81,116],"along":[82],"with":[83,117],"values":[85],"at":[89,108],"those":[90],"sample":[91,110],"points.":[92],"The":[93],"task":[94],"to":[96,103],"approximate":[97],"value":[99],"within":[104],"multiplicative":[106],"factor":[107],"subsequent":[109],"points":[111],"drawn":[112],"same":[115],"sufficiently":[118],"high":[119],"probability.":[120],"develop":[122],"first":[124],"theoretical":[125],"analysis":[126],"problem,":[129],"proving":[130],"number":[132],"important":[134],"nearly":[136],"tight":[137],"results.":[138],"For":[139],"instance,":[140],"if":[141],"underlying":[143],"product":[147],"then":[149],"we":[150,167,183],"give":[151],"algorithm":[154],"achieves":[156],"constant-factor":[158],"approximation":[159],"(under":[160],"some":[161],"assumptions).":[162],"However,":[163],"for":[164],"general":[165],"distributions":[166],"provide":[168],"surprising":[170],"Omega(n1/3)":[171],"lower":[172],"bound":[173],"based":[174],"new":[177],"interesting":[178],"class":[179],"matroids":[181],"also":[184],"show":[185],"O(n1/2)":[187],"upper":[188],"bound.":[189]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":14},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":12},{"year":2012,"cited_by_count":8}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}