{"id":"https://openalex.org/W2966994809","doi":"https://doi.org/10.3390/e21080787","title":"Geometric Estimation of Multivariate Dependency","display_name":"Geometric Estimation of Multivariate Dependency","publication_year":2019,"publication_date":"2019-08-12","ids":{"openalex":"https://openalex.org/W2966994809","doi":"https://doi.org/10.3390/e21080787","mag":"2966994809","pmid":"https://pubmed.ncbi.nlm.nih.gov/33267500"},"language":"en","primary_location":{"id":"doi:10.3390/e21080787","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e21080787","pdf_url":"https://www.mdpi.com/1099-4300/21/8/787/pdf","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":["arxiv","crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/21/8/787/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Salimeh Yasaei Sekeh","orcid":"https://orcid.org/0000-0002-4630-5593"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan\u2013Ann Arbor","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Salimeh Yasaei Sekeh","raw_affiliation_strings":["Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI 48109, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI 48109, USA","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"last","author":{"id":null,"display_name":"Alfred O. Hero","orcid":null},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan\u2013Ann Arbor","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Alfred O. Hero","raw_affiliation_strings":["Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI 48109, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI 48109, USA","institution_ids":["https://openalex.org/I27837315"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I27837315"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.203,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.81426702,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"21","issue":"8","first_page":"787","last_page":"787"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.7269999980926514,"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"}},"topics":[{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.7269999980926514,"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/T12417","display_name":"Morphological variations and asymmetry","score":0.08560000360012054,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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":0.03460000082850456,"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/estimator","display_name":"Estimator","score":0.7591999769210815},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.5968999862670898},{"id":"https://openalex.org/keywords/spanning-tree","display_name":"Spanning tree","score":0.5360999703407288},{"id":"https://openalex.org/keywords/dependency","display_name":"Dependency (UML)","score":0.5164999961853027},{"id":"https://openalex.org/keywords/multivariate-kernel-density-estimation","display_name":"Multivariate kernel density estimation","score":0.39480000734329224},{"id":"https://openalex.org/keywords/minimum-spanning-tree","display_name":"Minimum spanning tree","score":0.38350000977516174},{"id":"https://openalex.org/keywords/density-estimation","display_name":"Density estimation","score":0.38029998540878296},{"id":"https://openalex.org/keywords/minimum-variance-unbiased-estimator","display_name":"Minimum-variance unbiased estimator","score":0.3783000111579895},{"id":"https://openalex.org/keywords/consistent-estimator","display_name":"Consistent estimator","score":0.37529999017715454}],"concepts":[{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.7591999769210815},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7533000111579895},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.5968999862670898},{"id":"https://openalex.org/C64331007","wikidata":"https://www.wikidata.org/wiki/Q831672","display_name":"Spanning tree","level":2,"score":0.5360999703407288},{"id":"https://openalex.org/C19768560","wikidata":"https://www.wikidata.org/wiki/Q320727","display_name":"Dependency (UML)","level":2,"score":0.5164999961853027},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.421099990606308},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.41679999232292175},{"id":"https://openalex.org/C84894716","wikidata":"https://www.wikidata.org/wiki/Q6935135","display_name":"Multivariate kernel density estimation","level":5,"score":0.39480000734329224},{"id":"https://openalex.org/C13743678","wikidata":"https://www.wikidata.org/wiki/Q240464","display_name":"Minimum spanning tree","level":2,"score":0.38350000977516174},{"id":"https://openalex.org/C189508267","wikidata":"https://www.wikidata.org/wiki/Q17088227","display_name":"Density estimation","level":3,"score":0.38029998540878296},{"id":"https://openalex.org/C165646398","wikidata":"https://www.wikidata.org/wiki/Q3755281","display_name":"Minimum-variance unbiased estimator","level":3,"score":0.3783000111579895},{"id":"https://openalex.org/C164172150","wikidata":"https://www.wikidata.org/wiki/Q1782585","display_name":"Consistent estimator","level":4,"score":0.37529999017715454},{"id":"https://openalex.org/C177384507","wikidata":"https://www.wikidata.org/wiki/Q1149000","display_name":"Multivariate normal distribution","level":3,"score":0.3644999861717224},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3278999924659729},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.3197000026702881},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.3183000087738037},{"id":"https://openalex.org/C71134354","wikidata":"https://www.wikidata.org/wiki/Q458825","display_name":"Kernel density estimation","level":3,"score":0.3061999976634979},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.30399999022483826},{"id":"https://openalex.org/C65778772","wikidata":"https://www.wikidata.org/wiki/Q12345341","display_name":"Asymptotic distribution","level":3,"score":0.30149999260902405},{"id":"https://openalex.org/C18653775","wikidata":"https://www.wikidata.org/wiki/Q1333358","display_name":"Joint probability distribution","level":2,"score":0.2935999929904938},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.28679999709129333},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.272599995136261},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.27059999108314514},{"id":"https://openalex.org/C191393472","wikidata":"https://www.wikidata.org/wiki/Q15222032","display_name":"Bias of an estimator","level":4,"score":0.2587999999523163},{"id":"https://openalex.org/C199163554","wikidata":"https://www.wikidata.org/wiki/Q1681619","display_name":"Univariate","level":3,"score":0.25369998812675476}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.3390/e21080787","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e21080787","pdf_url":"https://www.mdpi.com/1099-4300/21/8/787/pdf","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:33267500","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33267500","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:arXiv.org:1905.08594","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1905.08594","pdf_url":"https://arxiv.org/pdf/1905.08594","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"pmh:oai:doaj.org/article:52b26ab5920d400990c5203cef3a63c6","is_oa":true,"landing_page_url":"https://doaj.org/article/52b26ab5920d400990c5203cef3a63c6","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"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 21, Iss 8, p 787 (2019)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/21/8/787/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/e21080787","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"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","raw_type":"Text"},{"id":"pmh:oai:osti.gov:1614538","is_oa":true,"landing_page_url":"https://www.osti.gov/biblio/1614538","pdf_url":null,"source":{"id":"https://openalex.org/S4306402487","display_name":"OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I139351228","host_organization_name":"Office of Scientific and Technical Information","host_organization_lineage":["https://openalex.org/I139351228"],"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":null},{"id":"pmh:oai:pubmedcentral.nih.gov:7515316","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7515316","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","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":"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"}],"best_oa_location":{"id":"doi:10.3390/e21080787","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e21080787","pdf_url":"https://www.mdpi.com/1099-4300/21/8/787/pdf","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/G3897956840","display_name":null,"funder_award_id":"DE-NA0002534","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G5385673730","display_name":null,"funder_award_id":"W911NF-15-1-","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G7452299184","display_name":null,"funder_award_id":"W911NF","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G8346236733","display_name":null,"funder_award_id":"W911NF-15-1-0479","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G8998121839","display_name":null,"funder_award_id":"911NF","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"}],"funders":[{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2966994809.pdf","grobid_xml":"https://content.openalex.org/works/W2966994809.grobid-xml"},"referenced_works_count":42,"referenced_works":["https://openalex.org/W152055444","https://openalex.org/W1489238841","https://openalex.org/W1574463154","https://openalex.org/W1673728053","https://openalex.org/W1839657926","https://openalex.org/W1981050900","https://openalex.org/W1992068214","https://openalex.org/W2008901952","https://openalex.org/W2014809761","https://openalex.org/W2025890108","https://openalex.org/W2027390033","https://openalex.org/W2030203876","https://openalex.org/W2045650933","https://openalex.org/W2058930359","https://openalex.org/W2067298033","https://openalex.org/W2068276287","https://openalex.org/W2092939357","https://openalex.org/W2116402476","https://openalex.org/W2118561568","https://openalex.org/W2134465553","https://openalex.org/W2142357860","https://openalex.org/W2148633389","https://openalex.org/W2149197198","https://openalex.org/W2154053567","https://openalex.org/W2155742999","https://openalex.org/W2188155116","https://openalex.org/W2218423201","https://openalex.org/W2267671267","https://openalex.org/W2329026497","https://openalex.org/W2519513981","https://openalex.org/W2585429527","https://openalex.org/W2593829254","https://openalex.org/W2915025989","https://openalex.org/W2962779416","https://openalex.org/W2963855069","https://openalex.org/W2990196151","https://openalex.org/W4206419526","https://openalex.org/W4238668637","https://openalex.org/W4388311561","https://openalex.org/W6674555952","https://openalex.org/W6677267524","https://openalex.org/W6684316217"],"related_works":[],"abstract_inverted_index":{"This":[0,37],"paper":[1],"proposes":[2],"a":[3,9,23,41,125,154,168],"geometric":[4,26,47,164],"estimator":[5,17,38,102,138,166],"of":[6,11,18,62,69,76,103,112,129,136,142,161,170],"dependency":[7,19,165],"between":[8,58],"pair":[10],"multivariate":[12,35,64,149],"random":[13],"variables.":[14],"The":[15,72,99],"proposed":[16,100,163],"is":[20,52,105],"based":[21],"on":[22],"randomly":[24,126],"permuted":[25,127],"graph":[27],"(the":[28],"minimal":[29,114],"spanning":[30,115,118],"tree)":[31],"over":[32,119],"the":[33,46,55,59,63,67,70,77,110,121,137,143,159],"two":[34],"samples.":[36],"converges":[39],"to":[40,54,96,107,153],"quantity":[42],"that":[43],"we":[44],"call":[45],"mutual":[48],"information":[49],"(GMI),":[50],"which":[51],"equivalent":[53],"Henze-Penrose":[56],"divergence.":[57],"joint":[60],"distribution":[61],"samples":[65],"and":[66,124,139,145],"product":[68],"marginals.":[71],"GMI":[73,104],"has":[74],"many":[75],"same":[78],"properties":[79],"as":[80],"standard":[81],"MI":[82],"but":[83],"can":[84],"be":[85],"estimated":[86],"from":[87],"empirical":[88,101],"data":[89,123],"without":[90],"density":[91,150],"estimation;":[92],"making":[93],"it":[94],"scalable":[95],"large":[97],"datasets.":[98],"simple":[106],"implement,":[108],"involving":[109],"construction":[111],"an":[113],"tree":[116],"(MST)":[117],"both":[120],"original":[122],"version":[128],"this":[130],"data.":[131],"We":[132,157],"establish":[133],"asymptotic":[134],"convergence":[135,140],"rates":[141],"bias":[144],"variance":[146],"for":[147],"smooth":[148],"functions":[151],"belonging":[152],"H\u00f6lder":[155],"class.":[156],"demonstrate":[158],"advantages":[160],"our":[162],"in":[167],"series":[169],"experiments.":[171]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2019-08-22T00:00:00"}