{"id":"https://openalex.org/W2790260190","doi":"https://doi.org/10.1007/s11222-018-9810-x","title":"Learning causal structure from mixed data with missing values using Gaussian copula models","display_name":"Learning causal structure from mixed data with missing values using Gaussian copula models","publication_year":2018,"publication_date":"2018-03-17","ids":{"openalex":"https://openalex.org/W2790260190","doi":"https://doi.org/10.1007/s11222-018-9810-x","mag":"2790260190"},"language":"en","primary_location":{"id":"doi:10.1007/s11222-018-9810-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11222-018-9810-x","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs11222-018-9810-x.pdf","source":{"id":"https://openalex.org/S5437875","display_name":"Statistics and Computing","issn_l":"0960-3174","issn":["0960-3174","1573-1375"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Statistics and Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007%2Fs11222-018-9810-x.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5061709285","display_name":"Ruifei Cui","orcid":"https://orcid.org/0000-0001-7294-2935"},"institutions":[{"id":"https://openalex.org/I145872427","display_name":"Radboud University Nijmegen","ror":"https://ror.org/016xsfp80","country_code":"NL","type":"education","lineage":["https://openalex.org/I145872427"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Ruifei Cui","raw_affiliation_strings":["Radboud University Nijmegen, Nijmegen, The Netherlands"],"raw_orcid":"https://orcid.org/0000-0001-7294-2935","affiliations":[{"raw_affiliation_string":"Radboud University Nijmegen, Nijmegen, The Netherlands","institution_ids":["https://openalex.org/I145872427"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Perry Groot","orcid":null},"institutions":[{"id":"https://openalex.org/I145872427","display_name":"Radboud University Nijmegen","ror":"https://ror.org/016xsfp80","country_code":"NL","type":"education","lineage":["https://openalex.org/I145872427"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Perry Groot","raw_affiliation_strings":["Radboud University Nijmegen, Nijmegen, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Radboud University Nijmegen, Nijmegen, The Netherlands","institution_ids":["https://openalex.org/I145872427"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015444349","display_name":"Tom Heskes","orcid":"https://orcid.org/0000-0002-3398-5235"},"institutions":[{"id":"https://openalex.org/I145872427","display_name":"Radboud University Nijmegen","ror":"https://ror.org/016xsfp80","country_code":"NL","type":"education","lineage":["https://openalex.org/I145872427"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Tom Heskes","raw_affiliation_strings":["Radboud University Nijmegen, Nijmegen, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Radboud University Nijmegen, Nijmegen, The Netherlands","institution_ids":["https://openalex.org/I145872427"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5061709285"],"corresponding_institution_ids":["https://openalex.org/I145872427"],"apc_list":{"value":2690,"currency":"USD","value_usd":2690},"apc_paid":{"value":2690,"currency":"USD","value_usd":2690},"fwci":1.3065,"has_fulltext":true,"cited_by_count":17,"citation_normalized_percentile":{"value":0.85074627,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"29","issue":"2","first_page":"311","last_page":"333"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.9995999932289124,"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/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.9995999932289124,"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/T10136","display_name":"Statistical Methods and Inference","score":0.9868000149726868,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10243","display_name":"Statistical Methods and Bayesian Inference","score":0.9772999882698059,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/missing-data","display_name":"Missing data","score":0.7220635414123535},{"id":"https://openalex.org/keywords/copula","display_name":"Copula (linguistics)","score":0.6153517365455627},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5663389563560486},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.5334166884422302},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5193425416946411},{"id":"https://openalex.org/keywords/conditional-independence","display_name":"Conditional independence","score":0.47716182470321655},{"id":"https://openalex.org/keywords/sample-size-determination","display_name":"Sample size determination","score":0.46314215660095215},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3342527747154236},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.2490600347518921}],"concepts":[{"id":"https://openalex.org/C9357733","wikidata":"https://www.wikidata.org/wiki/Q6878417","display_name":"Missing data","level":2,"score":0.7220635414123535},{"id":"https://openalex.org/C17618745","wikidata":"https://www.wikidata.org/wiki/Q207509","display_name":"Copula (linguistics)","level":2,"score":0.6153517365455627},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5663389563560486},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.5334166884422302},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5193425416946411},{"id":"https://openalex.org/C79772020","wikidata":"https://www.wikidata.org/wiki/Q5159264","display_name":"Conditional independence","level":2,"score":0.47716182470321655},{"id":"https://openalex.org/C129848803","wikidata":"https://www.wikidata.org/wiki/Q2564360","display_name":"Sample size determination","level":2,"score":0.46314215660095215},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3342527747154236},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.2490600347518921},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s11222-018-9810-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11222-018-9810-x","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs11222-018-9810-x.pdf","source":{"id":"https://openalex.org/S5437875","display_name":"Statistics and Computing","issn_l":"0960-3174","issn":["0960-3174","1573-1375"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Statistics and Computing","raw_type":"journal-article"},{"id":"pmh:ru:oai:repository.ubn.ru.nl:2066/201508","is_oa":true,"landing_page_url":"http://hdl.handle.net/2066/201508","pdf_url":"http://hdl.handle.net/2066/201508","source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Statistics and Computing, 29, 311 - 333","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s11222-018-9810-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11222-018-9810-x","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs11222-018-9810-x.pdf","source":{"id":"https://openalex.org/S5437875","display_name":"Statistics and Computing","issn_l":"0960-3174","issn":["0960-3174","1573-1375"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Statistics and Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321013","display_name":"Radboud Universiteit","ror":"https://ror.org/016xsfp80"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2790260190.pdf","grobid_xml":"https://content.openalex.org/works/W2790260190.grobid-xml"},"referenced_works_count":63,"referenced_works":["https://openalex.org/W344345127","https://openalex.org/W1495663238","https://openalex.org/W1505477995","https://openalex.org/W1524326598","https://openalex.org/W1593793857","https://openalex.org/W1741702827","https://openalex.org/W1820867195","https://openalex.org/W1974134238","https://openalex.org/W1986014448","https://openalex.org/W1988694953","https://openalex.org/W1992535794","https://openalex.org/W1998760465","https://openalex.org/W2015630661","https://openalex.org/W2015671107","https://openalex.org/W2019935777","https://openalex.org/W2038816913","https://openalex.org/W2041769197","https://openalex.org/W2044758663","https://openalex.org/W2063698478","https://openalex.org/W2068331431","https://openalex.org/W2077870633","https://openalex.org/W2100358124","https://openalex.org/W2103012681","https://openalex.org/W2107011900","https://openalex.org/W2108628735","https://openalex.org/W2110322980","https://openalex.org/W2118938385","https://openalex.org/W2119436275","https://openalex.org/W2123271629","https://openalex.org/W2124379907","https://openalex.org/W2132547334","https://openalex.org/W2142972916","https://openalex.org/W2143891888","https://openalex.org/W2150002853","https://openalex.org/W2155573334","https://openalex.org/W2156267802","https://openalex.org/W2160951788","https://openalex.org/W2163687466","https://openalex.org/W2165190832","https://openalex.org/W2168652321","https://openalex.org/W2207421686","https://openalex.org/W2313407065","https://openalex.org/W2325963232","https://openalex.org/W2515506137","https://openalex.org/W2584044794","https://openalex.org/W2601072069","https://openalex.org/W2617100036","https://openalex.org/W2772121406","https://openalex.org/W2949422027","https://openalex.org/W2963893933","https://openalex.org/W3098635105","https://openalex.org/W3100089080","https://openalex.org/W3100153776","https://openalex.org/W3100838142","https://openalex.org/W3103539622","https://openalex.org/W3121957185","https://openalex.org/W4233413206","https://openalex.org/W4250908292","https://openalex.org/W4285719527","https://openalex.org/W4298716064","https://openalex.org/W4302423442","https://openalex.org/W6600136193","https://openalex.org/W6600137863"],"related_works":["https://openalex.org/W4380150146","https://openalex.org/W3024870410","https://openalex.org/W2410652950","https://openalex.org/W4283773154","https://openalex.org/W4312863644","https://openalex.org/W3088052873","https://openalex.org/W4297796976","https://openalex.org/W4386772697","https://openalex.org/W4280619202","https://openalex.org/W2995439826"],"abstract_inverted_index":{"We":[0,204],"consider":[1],"the":[2,25,54,63,70,77,91,103,151,187,190,196],"problem":[3],"of":[4,93,189,198],"causal":[5,172],"structure":[6,173],"learning":[7],"from":[8,17,73,126],"data":[9,37,43,78,104,128,214],"with":[10,34,57],"missing":[11,74,80,106],"values,":[12],"assumed":[13],"to":[14,41,48,67,121],"be":[15],"drawn":[16],"a":[18,117,166],"Gaussian":[19,31],"copula":[20,32],"model.":[21],"First,":[22],"we":[23,85,115],"extend":[24],"\u2018Rank":[26,94,110,175,199],"PC\u2019":[27,95,111,153,164,176,200],"algorithm,":[28],"designed":[29],"for":[30,69,155],"models":[33],"purely":[35],"continuous":[36],"(so-called":[38],"nonparanormal":[39],"models),":[40],"incomplete":[42,156],"by":[44],"applying":[45],"rank":[46],"correlation":[47,123,142,169],"pairwise":[49],"complete":[50],"observations":[51],"and":[52,96,144,171,185,201,215],"replacing":[53],"sample":[55,60,147,192],"size":[56,61,193],"an":[58,87,140,145],"effective":[59,146,191],"in":[62,150],"conditional":[64],"independence":[65],"tests":[66],"account":[68],"information":[71],"loss":[72],"values.":[75],"When":[76],"are":[79,105,137],"completely":[81],"at":[82,107],"random":[83,108],"(MCAR),":[84],"provide":[86],"error":[88],"bound":[89],"on":[90,208],"accuracy":[92],"show":[97],"its":[98],"high-dimensional":[99],"consistency.":[100],"However,":[101],"when":[102],"(MAR),":[109],"fails":[112],"dramatically.":[113],"Therefore,":[114],"propose":[116],"Gibbs":[118],"sampling":[119],"procedure":[120],"draw":[122],"matrix":[124,143,170],"samples":[125,136],"mixed":[127],"that":[129],"still":[130],"works":[131],"correctly":[132],"under":[133,177,183],"MAR.":[134],"These":[135],"translated":[138],"into":[139],"average":[141],"size,":[148],"resulting":[149],"\u2018Copula":[152,163,202],"algorithm":[154],"data.":[157,219],"Simulation":[158],"study":[159],"shows":[160],"that:":[161],"(1)":[162],"estimates":[165],"more":[167,181],"accurate":[168],"than":[174],"MCAR":[178],"and,":[179],"even":[180],"so,":[182],"MAR":[184],"(2)":[186],"usage":[188],"significantly":[194],"improves":[195],"performance":[197],"PC.\u2019":[203],"illustrate":[205],"our":[206],"methods":[207],"two":[209],"real-world":[210],"datasets:":[211],"riboflavin":[212],"production":[213],"chronic":[216],"fatigue":[217],"syndrome":[218]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}