{"id":"https://openalex.org/W4389144895","doi":"https://doi.org/10.3390/e25121597","title":"Kernel-Based Independence Tests for Causal Structure Learning on Functional Data","display_name":"Kernel-Based Independence Tests for Causal Structure Learning on Functional Data","publication_year":2023,"publication_date":"2023-11-28","ids":{"openalex":"https://openalex.org/W4389144895","doi":"https://doi.org/10.3390/e25121597","pmid":"https://pubmed.ncbi.nlm.nih.gov/38136477"},"language":"en","primary_location":{"id":"doi:10.3390/e25121597","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e25121597","pdf_url":"https://www.mdpi.com/1099-4300/25/12/1597/pdf?version=1701223480","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/25/12/1597/pdf?version=1701223480","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068717798","display_name":"Felix Laumann","orcid":"https://orcid.org/0000-0002-2822-6517"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Felix Laumann","raw_affiliation_strings":["Department of Mathematics, Imperial College London, London SW7 2BX, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Imperial College London, London SW7 2BX, UK","institution_ids":["https://openalex.org/I47508984"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086287200","display_name":"Julius von K\u00fcgelgen","orcid":"https://orcid.org/0000-0001-6469-4118"},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]},{"id":"https://openalex.org/I4210135521","display_name":"Max Planck Institute for Intelligent Systems","ror":"https://ror.org/04fq9j139","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210135521"]}],"countries":["DE","GB"],"is_corresponding":false,"raw_author_name":"Julius von K\u00fcgelgen","raw_affiliation_strings":["Department of Engineering, University of Cambridge, Cambridge CB2 0QQ, UK","Max Planck Institute for Intelligent Systems, 72076 T\u00fcbingen, Germany"],"raw_orcid":"https://orcid.org/0000-0001-6469-4118","affiliations":[{"raw_affiliation_string":"Department of Engineering, University of Cambridge, Cambridge CB2 0QQ, UK","institution_ids":["https://openalex.org/I241749"]},{"raw_affiliation_string":"Max Planck Institute for Intelligent Systems, 72076 T\u00fcbingen, Germany","institution_ids":["https://openalex.org/I4210135521"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101787663","display_name":"Jun-Hyung Park","orcid":"https://orcid.org/0000-0002-7900-3743"},"institutions":[{"id":"https://openalex.org/I4210135521","display_name":"Max Planck Institute for Intelligent Systems","ror":"https://ror.org/04fq9j139","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210135521"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Junhyung Park","raw_affiliation_strings":["Max Planck Institute for Intelligent Systems, 72076 T\u00fcbingen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Max Planck Institute for Intelligent Systems, 72076 T\u00fcbingen, Germany","institution_ids":["https://openalex.org/I4210135521"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044005697","display_name":"Bernhard Sch\u00f6lkopf","orcid":"https://orcid.org/0000-0002-8177-0925"},"institutions":[{"id":"https://openalex.org/I4210135521","display_name":"Max Planck Institute for Intelligent Systems","ror":"https://ror.org/04fq9j139","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210135521"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Bernhard Sch\u00f6lkopf","raw_affiliation_strings":["Max Planck Institute for Intelligent Systems, 72076 T\u00fcbingen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Max Planck Institute for Intelligent Systems, 72076 T\u00fcbingen, Germany","institution_ids":["https://openalex.org/I4210135521"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058010593","display_name":"Mauricio Barahona","orcid":"https://orcid.org/0000-0002-1089-5675"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Mauricio Barahona","raw_affiliation_strings":["Department of Mathematics, Imperial College London, London SW7 2BX, UK"],"raw_orcid":"https://orcid.org/0000-0002-1089-5675","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Imperial College London, London SW7 2BX, UK","institution_ids":["https://openalex.org/I47508984"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5058010593","https://openalex.org/A5068717798"],"corresponding_institution_ids":["https://openalex.org/I47508984"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.8284,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.79090135,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"25","issue":"12","first_page":"1597","last_page":"1597"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.9883000254631042,"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":0.9883000254631042,"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":0.984499990940094,"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/T11871","display_name":"Advanced Statistical Methods and Models","score":0.977400004863739,"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/conditional-independence","display_name":"Conditional independence","score":0.5774855613708496},{"id":"https://openalex.org/keywords/independence","display_name":"Independence (probability theory)","score":0.5214332938194275},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5124159455299377},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4199942946434021},{"id":"https://openalex.org/keywords/reproducing-kernel-hilbert-space","display_name":"Reproducing kernel Hilbert space","score":0.41603556275367737},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.40381112694740295},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.397713840007782},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.3585037291049957},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.32663148641586304},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2699838876724243}],"concepts":[{"id":"https://openalex.org/C79772020","wikidata":"https://www.wikidata.org/wiki/Q5159264","display_name":"Conditional independence","level":2,"score":0.5774855613708496},{"id":"https://openalex.org/C35651441","wikidata":"https://www.wikidata.org/wiki/Q625303","display_name":"Independence (probability theory)","level":2,"score":0.5214332938194275},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5124159455299377},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4199942946434021},{"id":"https://openalex.org/C80884492","wikidata":"https://www.wikidata.org/wiki/Q3345678","display_name":"Reproducing kernel Hilbert space","level":3,"score":0.41603556275367737},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.40381112694740295},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.397713840007782},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.3585037291049957},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.32663148641586304},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2699838876724243},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/e25121597","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e25121597","pdf_url":"https://www.mdpi.com/1099-4300/25/12/1597/pdf?version=1701223480","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmid:38136477","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/38136477","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":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:pubmedcentral.nih.gov:10742995","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/10742995","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC10742995/pdf/entropy-25-01597.pdf","source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"},{"id":"pmh:oai:doaj.org/article:499b1e38cf9447a7bbe32abf68f24547","is_oa":true,"landing_page_url":"https://doaj.org/article/499b1e38cf9447a7bbe32abf68f24547","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 25, Iss 12, p 1597 (2023)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/e25121597","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e25121597","pdf_url":"https://www.mdpi.com/1099-4300/25/12/1597/pdf?version=1701223480","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2453345397","display_name":null,"funder_award_id":"EP/N014529/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7417950124","display_name":"EPSRC Centre for Mathematics of Precision Healthcare","funder_award_id":"EP/N014529/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7907426250","display_name":null,"funder_award_id":"390727645","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G850745309","display_name":null,"funder_award_id":"EP/N014529/","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G8556661049","display_name":null,"funder_award_id":"390727645","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G8915364236","display_name":null,"funder_award_id":"2064/1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320319997","display_name":"Nuffield Foundation","ror":"https://ror.org/0281jqk77"},{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4389144895.pdf"},"referenced_works_count":57,"referenced_works":["https://openalex.org/W609741286","https://openalex.org/W1752598806","https://openalex.org/W1822973471","https://openalex.org/W1850984366","https://openalex.org/W1977446441","https://openalex.org/W2025371899","https://openalex.org/W2042809187","https://openalex.org/W2054402839","https://openalex.org/W2075027296","https://openalex.org/W2079656335","https://openalex.org/W2083278075","https://openalex.org/W2092426949","https://openalex.org/W2097556898","https://openalex.org/W2116993992","https://openalex.org/W2143891888","https://openalex.org/W2145979309","https://openalex.org/W2151226328","https://openalex.org/W2159408738","https://openalex.org/W2165582599","https://openalex.org/W2178225550","https://openalex.org/W2181523240","https://openalex.org/W2418306335","https://openalex.org/W2593118993","https://openalex.org/W2725028560","https://openalex.org/W2752146117","https://openalex.org/W2792581694","https://openalex.org/W2797510035","https://openalex.org/W2891002711","https://openalex.org/W2900354931","https://openalex.org/W2948579453","https://openalex.org/W2949383815","https://openalex.org/W2949505632","https://openalex.org/W2963026013","https://openalex.org/W2963535485","https://openalex.org/W2981798823","https://openalex.org/W3004574756","https://openalex.org/W3042860357","https://openalex.org/W3080666959","https://openalex.org/W3101150805","https://openalex.org/W3106063097","https://openalex.org/W3111141355","https://openalex.org/W3122373963","https://openalex.org/W3122756704","https://openalex.org/W3133932964","https://openalex.org/W4289261842","https://openalex.org/W4292156489","https://openalex.org/W4302423442","https://openalex.org/W6639134244","https://openalex.org/W6675134017","https://openalex.org/W6675356903","https://openalex.org/W6676726796","https://openalex.org/W6679709731","https://openalex.org/W6682361391","https://openalex.org/W6688325169","https://openalex.org/W6746467546","https://openalex.org/W6773055369","https://openalex.org/W6782199181"],"related_works":["https://openalex.org/W2018264451","https://openalex.org/W2591253179","https://openalex.org/W4212827636","https://openalex.org/W4287671600","https://openalex.org/W2141366819","https://openalex.org/W3004408979","https://openalex.org/W2042697870","https://openalex.org/W4234882900","https://openalex.org/W4387349426","https://openalex.org/W2184820914"],"abstract_inverted_index":{"Measurements":[0],"of":[1,36,102,156,161],"systems":[2],"taken":[3],"along":[4,70],"a":[5,119,126],"continuous":[6],"functional":[7,72,90,100,166],"dimension,":[8],"such":[9,59],"as":[10,34,61],"time":[11],"or":[12],"space,":[13],"are":[14,54],"ubiquitous":[15],"in":[16],"many":[17],"fields,":[18],"from":[19],"the":[20,43,68,71,97,103,130,137,157],"physical":[21],"and":[22,27,51,86,108,159,171,180,190],"biological":[23],"sciences":[24],"to":[25,58,99,117,177],"economics":[26],"engineering.":[28],"Such":[29],"measurements":[30],"can":[31],"be":[32],"viewed":[33],"realisations":[35],"an":[37,149],"underlying":[38],"smooth":[39],"process":[40],"sampled":[41],"over":[42],"continuum.":[44],"However,":[45],"traditional":[46],"methods":[47],"for":[48,83,89,121,129],"independence":[49,88,105,123,140],"testing":[50],"causal":[52,182],"learning":[53,184],"not":[55,64,94],"directly":[56],"applicable":[57],"data,":[60],"they":[62],"do":[63],"take":[65],"into":[66],"account":[67],"dependence":[69],"dimension.":[73],"By":[74],"using":[75],"specifically":[76],"designed":[77],"kernels,":[78],"we":[79,172],"introduce":[80,118],"statistical":[81],"tests":[82,163],"bivariate,":[84],"joint,":[85],"conditional":[87,122,131,139],"variables.":[91],"Our":[92,153],"method":[93],"only":[95],"extends":[96],"applicability":[98],"data":[101,167],"Hilbert\u2013Schmidt":[104,138],"criterion":[106,141],"(hsic)":[107],"its":[109],"d-variate":[110],"version":[111],"(d-hsic),":[112],"but":[113],"also":[114],"allows":[115],"us":[116],"test":[120,133],"by":[124],"defining":[125],"novel":[127],"statistic":[128],"permutation":[132],"(cpt)":[134],"based":[135],"on":[136,164],"(hscic),":[142],"with":[143],"optimised":[144],"regularisation":[145],"strength":[146],"estimated":[147],"through":[148],"evaluation":[150],"rejection":[151],"rate.":[152],"empirical":[154],"results":[155],"size":[158],"power":[160],"these":[162],"synthetic":[165,188],"show":[168],"good":[169],"performance,":[170],"then":[173],"exemplify":[174],"their":[175],"application":[176],"several":[178],"constraint-":[179],"regression-based":[181],"structure":[183],"problems,":[185],"including":[186],"both":[187],"examples":[189],"real":[191],"socioeconomic":[192],"data.":[193]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
