{"id":"https://openalex.org/W2738072124","doi":"https://doi.org/10.1109/tnnls.2017.2716539","title":"Causal Inference on Multidimensional Data Using Free Probability Theory","display_name":"Causal Inference on Multidimensional Data Using Free Probability Theory","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2738072124","doi":"https://doi.org/10.1109/tnnls.2017.2716539","mag":"2738072124","pmid":"https://pubmed.ncbi.nlm.nih.gov/28727564"},"language":"en","primary_location":{"id":"doi:10.1109/tnnls.2017.2716539","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2017.2716539","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Neural Networks and Learning Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5026553094","display_name":"Furui Liu","orcid":"https://orcid.org/0000-0003-3997-3822"},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"HK","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Furui Liu","raw_affiliation_strings":["Department of Computer Science and Engineering, The Chinese University of Hong Kong, Hong Kong, China"],"raw_orcid":"https://orcid.org/0000-0003-3997-3822","affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, The Chinese University of Hong Kong, Hong Kong, China","institution_ids":["https://openalex.org/I177725633"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111431165","display_name":"Laiwan Chan","orcid":null},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"HK","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Lai-Wan Chan","raw_affiliation_strings":["Department of Computer Science and Engineering, The Chinese University of Hong Kong, Hong Kong, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, The Chinese University of Hong Kong, Hong Kong, China","institution_ids":["https://openalex.org/I177725633"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0327,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.8312245,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"29","issue":"7","first_page":"1","last_page":"11"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.9973000288009644,"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":0.9973000288009644,"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":0.9957000017166138,"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":0.9955000281333923,"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/reproducing-kernel-hilbert-space","display_name":"Reproducing kernel Hilbert space","score":0.685609757900238},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6273389458656311},{"id":"https://openalex.org/keywords/causal-inference","display_name":"Causal inference","score":0.5753636360168457},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.5712591409683228},{"id":"https://openalex.org/keywords/covariance-matrix","display_name":"Covariance matrix","score":0.5141199231147766},{"id":"https://openalex.org/keywords/conditional-independence","display_name":"Conditional independence","score":0.4896240830421448},{"id":"https://openalex.org/keywords/conditional-probability-distribution","display_name":"Conditional probability distribution","score":0.483434796333313},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.4682166576385498},{"id":"https://openalex.org/keywords/free-probability","display_name":"Free probability","score":0.4560449421405792},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.4405207335948944},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.4348496198654175},{"id":"https://openalex.org/keywords/independence","display_name":"Independence (probability theory)","score":0.431957870721817},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3890400230884552},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.36815476417541504},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.3430953919887543},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3036451041698456},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.28655749559402466},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.23308661580085754},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.21880760788917542},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.20948675274848938}],"concepts":[{"id":"https://openalex.org/C80884492","wikidata":"https://www.wikidata.org/wiki/Q3345678","display_name":"Reproducing kernel Hilbert space","level":3,"score":0.685609757900238},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6273389458656311},{"id":"https://openalex.org/C158600405","wikidata":"https://www.wikidata.org/wiki/Q5054566","display_name":"Causal inference","level":2,"score":0.5753636360168457},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.5712591409683228},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.5141199231147766},{"id":"https://openalex.org/C79772020","wikidata":"https://www.wikidata.org/wiki/Q5159264","display_name":"Conditional independence","level":2,"score":0.4896240830421448},{"id":"https://openalex.org/C43555835","wikidata":"https://www.wikidata.org/wiki/Q2300258","display_name":"Conditional probability distribution","level":2,"score":0.483434796333313},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.4682166576385498},{"id":"https://openalex.org/C70120467","wikidata":"https://www.wikidata.org/wiki/Q515893","display_name":"Free probability","level":2,"score":0.4560449421405792},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.4405207335948944},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.4348496198654175},{"id":"https://openalex.org/C35651441","wikidata":"https://www.wikidata.org/wiki/Q625303","display_name":"Independence (probability theory)","level":2,"score":0.431957870721817},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3890400230884552},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36815476417541504},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.3430953919887543},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3036451041698456},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.28655749559402466},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.23308661580085754},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.21880760788917542},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.20948675274848938}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tnnls.2017.2716539","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2017.2716539","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Neural Networks and Learning Systems","raw_type":"journal-article"},{"id":"pmid:28727564","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/28727564","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on neural networks and learning systems","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":57,"referenced_works":["https://openalex.org/W76426102","https://openalex.org/W284239745","https://openalex.org/W754039215","https://openalex.org/W1582879937","https://openalex.org/W1603640438","https://openalex.org/W1628268552","https://openalex.org/W1638081485","https://openalex.org/W1850984366","https://openalex.org/W1869602175","https://openalex.org/W1900965308","https://openalex.org/W1946137962","https://openalex.org/W2051302879","https://openalex.org/W2064052856","https://openalex.org/W2077933344","https://openalex.org/W2083689856","https://openalex.org/W2105766378","https://openalex.org/W2132507555","https://openalex.org/W2132547334","https://openalex.org/W2146531590","https://openalex.org/W2146641075","https://openalex.org/W2147881172","https://openalex.org/W2151226328","https://openalex.org/W2160536246","https://openalex.org/W2165582599","https://openalex.org/W2212660284","https://openalex.org/W2242222096","https://openalex.org/W2271150192","https://openalex.org/W2284008599","https://openalex.org/W2347112004","https://openalex.org/W2418306335","https://openalex.org/W2463241543","https://openalex.org/W2887306455","https://openalex.org/W2949383815","https://openalex.org/W2952408234","https://openalex.org/W3021064838","https://openalex.org/W3119651796","https://openalex.org/W3124338716","https://openalex.org/W3133236490","https://openalex.org/W4302423442","https://openalex.org/W4394651393","https://openalex.org/W6603161191","https://openalex.org/W6622092433","https://openalex.org/W6634665167","https://openalex.org/W6635962543","https://openalex.org/W6636890744","https://openalex.org/W6638924413","https://openalex.org/W6639134244","https://openalex.org/W6639820547","https://openalex.org/W6679709731","https://openalex.org/W6679853467","https://openalex.org/W6681517296","https://openalex.org/W6682361391","https://openalex.org/W6684389209","https://openalex.org/W6688325169","https://openalex.org/W6690366730","https://openalex.org/W6718795669","https://openalex.org/W6754216367"],"related_works":["https://openalex.org/W4294753120","https://openalex.org/W3112629828","https://openalex.org/W4226305864","https://openalex.org/W3215282106","https://openalex.org/W29041363","https://openalex.org/W2183503534","https://openalex.org/W1999592931","https://openalex.org/W4225992581","https://openalex.org/W2592465853","https://openalex.org/W580973011"],"abstract_inverted_index":{"In":[0],"this":[1,109],"paper,":[2],"we":[3,37,113],"deal":[4],"with":[5,59],"the":[6,17,20,23,26,30,40,44,48,60,64,68,87,95,101,115],"problem":[7],"of":[8,22,29,43,47,63,67,108,124],"inferring":[9],"causal":[10,88,102],"relations":[11],"for":[12],"multidimensional":[13],"data.":[14],"Based":[15],"on":[16],"postulate":[18],"that":[19,39,80,112,136],"distribution":[21,28,126],"cause":[24,33,49],"and":[25,98,128,156],"conditional":[27,65],"effect":[31,69],"given":[32,70],"are":[34],"generated":[35],"independently,":[36],"show":[38,135],"covariance":[41,61,122],"matrix":[42,62],"mean":[45],"embedding":[46,66],"in":[50,86,94,143],"reproducing":[51],"kernel":[52],"Hilbert":[53],"space":[54],"(RKHS)":[55],"is":[56,84,111],"free":[57],"independent":[58],"cause.":[71],"This,":[72],"called":[73],"freeness":[74,119,138],"condition,":[75],"induces":[76],"a":[77,81,118,131],"cause-effect":[78],"asymmetry":[79],"designed":[82],"measurement":[83],"0":[85,93],"direction":[89],"but":[90],"smaller":[91],"than":[92],"anticausal":[96],"direction,":[97],"it":[99,129],"uncovers":[100],"direction.":[103],"One":[104],"important":[105],"novel":[106],"aspect":[107],"paper":[110],"interpret":[114],"independence":[116],"as":[117],"condition":[120],"between":[121],"matrices":[123],"RKHS":[125],"embeddings,":[127],"has":[130],"wide":[132],"applicability.":[133],"We":[134],"our":[137],"condition-based":[139],"inference":[140],"method":[141],"succeeds":[142],"scenarios":[144],"like":[145],"additive":[146],"noise":[147],"cases,":[148],"where":[149],"other":[150],"methods":[151],"fail,":[152],"by":[153],"theoretical":[154],"analysis":[155],"experimental":[157],"results.":[158]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":4}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}