{"id":"https://openalex.org/W3089530995","doi":"https://doi.org/10.1111/biom.13531","title":"Reducing subspace models for large\u2010scale covariance regression","display_name":"Reducing subspace models for large\u2010scale covariance regression","publication_year":2021,"publication_date":"2021-08-30","ids":{"openalex":"https://openalex.org/W3089530995","doi":"https://doi.org/10.1111/biom.13531","mag":"3089530995","pmid":"https://pubmed.ncbi.nlm.nih.gov/34458980"},"language":"en","primary_location":{"id":"doi:10.1111/biom.13531","doi":"https://doi.org/10.1111/biom.13531","is_oa":false,"landing_page_url":"https://doi.org/10.1111/biom.13531","pdf_url":null,"source":{"id":"https://openalex.org/S8265502","display_name":"Biometrics","issn_l":"0006-341X","issn":["0006-341X","1541-0420"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","doyens","jufo-2","ki-jl-2","medline","norway-2","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Biometrics","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["arxiv","crossref","datacite","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2010.00503","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011032570","display_name":"Alexander M. Franks","orcid":"https://orcid.org/0000-0002-9329-206X","observed_orcids":["https://orcid.org/0000-0002-9329-206X"]},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Alexander M. Franks","raw_affiliation_strings":["Department of Statistics and Applied Probability University of California Santa Barbara Santa Barbara California USA"],"raw_orcid":"https://orcid.org/0000-0002-9329-206X","affiliations":[{"raw_affiliation_string":"Department of Statistics and Applied Probability University of California Santa Barbara Santa Barbara California USA","institution_ids":["https://openalex.org/I154570441"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5011032570"],"corresponding_institution_ids":["https://openalex.org/I154570441"],"apc_list":{"value":3000,"currency":"USD","value_usd":3000},"apc_paid":null,"fwci":0.5544,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.64058069,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"78","issue":"4","first_page":"1604","last_page":"1613"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.8637999892234802,"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":0.8637999892234802,"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":0.051100000739097595,"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/T13141","display_name":"Statistical Methods and Applications","score":0.028699999675154686,"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/envelope-model","display_name":"envelope model","score":0.7250000238418579},{"id":"https://openalex.org/keywords/large-p-small-n","display_name":"large p small n","score":0.777999997138977},{"id":"https://openalex.org/keywords/low-dimensional-subspace","display_name":"low-dimensional subspace","score":0.7300000190734863},{"id":"https://openalex.org/keywords/monte-carlo-em-algorithm","display_name":"Monte Carlo EM algorithm","score":0.8769999742507935}],"concepts":[{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.7592777013778687},{"id":"https://openalex.org/C119043178","wikidata":"https://www.wikidata.org/wiki/Q320723","display_name":"Covariate","level":2,"score":0.6614461541175842},{"id":"https://openalex.org/C137250428","wikidata":"https://www.wikidata.org/wiki/Q5178897","display_name":"Covariance function","level":3,"score":0.5508931279182434},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.5459673404693604},{"id":"https://openalex.org/C2776502983","wikidata":"https://www.wikidata.org/wiki/Q690182","display_name":"Contrast (vision)","level":2,"score":0.524422287940979},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.5159388184547424},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.5023012161254883},{"id":"https://openalex.org/C111350023","wikidata":"https://www.wikidata.org/wiki/Q1191869","display_name":"Markov chain Monte Carlo","level":3,"score":0.48374295234680176},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48154550790786743},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.453762948513031},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.4523915648460388},{"id":"https://openalex.org/C119340705","wikidata":"https://www.wikidata.org/wiki/Q1628597","display_name":"Analysis of covariance","level":2,"score":0.43485337495803833},{"id":"https://openalex.org/C152877465","wikidata":"https://www.wikidata.org/wiki/Q208042","display_name":"Regression analysis","level":2,"score":0.42224496603012085},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.4209979772567749},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.4090711772441864},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4060893952846527},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2197074592113495},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.13361257314682007},{"id":"https://openalex.org/C58640448","wikidata":"https://www.wikidata.org/wiki/Q42515","display_name":"Cartography","level":1,"score":0.06736740469932556},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D009010","descriptor_name":"Monte Carlo Method","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false}],"locations_count":5,"locations":[{"id":"doi:10.1111/biom.13531","doi":"https://doi.org/10.1111/biom.13531","is_oa":false,"landing_page_url":"https://doi.org/10.1111/biom.13531","pdf_url":null,"source":{"id":"https://openalex.org/S8265502","display_name":"Biometrics","issn_l":"0006-341X","issn":["0006-341X","1541-0420"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","doyens","jufo-2","ki-jl-2","medline","norway-2","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Biometrics","raw_type":"journal-article"},{"id":"pmid:34458980","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/34458980","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,"listed_in":[],"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":"Biometrics","raw_type":"Journal Article"},{"id":"pmh:oai:arXiv.org:2010.00503","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2010.00503","pdf_url":"https://arxiv.org/pdf/2010.00503","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"mag:3089530995","doi":null,"is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/2010.00503","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2010.00503","doi":"https://doi.org/10.48550/arxiv.2010.00503","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2010.00503","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2010.00503","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2010.00503","pdf_url":"https://arxiv.org/pdf/2010.00503","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G2368497891","display_name":"Multi-group covariance estimation for metabolomic analysis with applications to neurodegenerative disease","funder_award_id":"1r03ca211160-01","funder_id":"https://openalex.org/F4320332161","funder_display_name":"National Institutes of Health"},{"id":"https://openalex.org/G8395683368","display_name":null,"funder_award_id":"R03 CA211160","funder_id":"https://openalex.org/F4320337351","funder_display_name":"National Cancer Institute"}],"funders":[{"id":"https://openalex.org/F4320332161","display_name":"National Institutes of Health","ror":"https://ror.org/01cwqze88"},{"id":"https://openalex.org/F4320337351","display_name":"National Cancer Institute","ror":"https://ror.org/040gcmg81"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3089530995.pdf","grobid_xml":"https://content.openalex.org/works/W3089530995.grobid-xml"},"referenced_works_count":69,"referenced_works":["https://openalex.org/W276882634","https://openalex.org/W1491459594","https://openalex.org/W1520752838","https://openalex.org/W1537539030","https://openalex.org/W1538574688","https://openalex.org/W1547176439","https://openalex.org/W1822348759","https://openalex.org/W1968463597","https://openalex.org/W1968813633","https://openalex.org/W1971400022","https://openalex.org/W1972337487","https://openalex.org/W1976327004","https://openalex.org/W1986143174","https://openalex.org/W1998278676","https://openalex.org/W2022806724","https://openalex.org/W2047834101","https://openalex.org/W2049633694","https://openalex.org/W2050523089","https://openalex.org/W2067314238","https://openalex.org/W2071346966","https://openalex.org/W2086953401","https://openalex.org/W2091634599","https://openalex.org/W2093404056","https://openalex.org/W2094397891","https://openalex.org/W2110144299","https://openalex.org/W2110510087","https://openalex.org/W2115161662","https://openalex.org/W2118588291","https://openalex.org/W2132555912","https://openalex.org/W2155684712","https://openalex.org/W2159000911","https://openalex.org/W2165009258","https://openalex.org/W2188880327","https://openalex.org/W2316745147","https://openalex.org/W2317167530","https://openalex.org/W2342807339","https://openalex.org/W2400314691","https://openalex.org/W2427719991","https://openalex.org/W2509064655","https://openalex.org/W2516128490","https://openalex.org/W2582903958","https://openalex.org/W2590362710","https://openalex.org/W2625298147","https://openalex.org/W2763292376","https://openalex.org/W2779789722","https://openalex.org/W2796559433","https://openalex.org/W2913666085","https://openalex.org/W2919057641","https://openalex.org/W2947451721","https://openalex.org/W2955756096","https://openalex.org/W2963780177","https://openalex.org/W2997355229","https://openalex.org/W3004363624","https://openalex.org/W3021249782","https://openalex.org/W3036228244","https://openalex.org/W3099006712","https://openalex.org/W3145586229","https://openalex.org/W4200283578","https://openalex.org/W4206653059","https://openalex.org/W4211085285","https://openalex.org/W4213068077","https://openalex.org/W4229766664","https://openalex.org/W4245274258","https://openalex.org/W4248415074","https://openalex.org/W4249856617","https://openalex.org/W4252992828","https://openalex.org/W4254259096","https://openalex.org/W4294326454","https://openalex.org/W6632226763"],"related_works":["https://openalex.org/W2516128490","https://openalex.org/W2155684712","https://openalex.org/W7099484950","https://openalex.org/W3036228244","https://openalex.org/W4400446852","https://openalex.org/W7154472189","https://openalex.org/W2316745147","https://openalex.org/W1977234859","https://openalex.org/W2947451721","https://openalex.org/W1998278676"],"abstract_inverted_index":{"We":[0,47,87,103],"develop":[1,113],"an":[2],"envelope":[3,22,121],"model":[4,93],"for":[5],"joint":[6],"mean":[7,26],"and":[8,65,72,114],"covariance":[9,33,39],"regression":[10],"in":[11,62],"the":[12,32,78,83,89,99,119],"large":[13],"p,":[14],"small":[15],"n":[16],"setting.":[17],"In":[18],"contrast":[19],"to":[20,54,76,112],"existing":[21],"methods,":[23],"which":[24],"improve":[25],"estimates":[27,30],"by":[28,41],"incorporating":[29,42],"of":[31,70,91,101,118],"structure,":[34],"we":[35],"focus":[36],"on":[37,82,94,98],"identifying":[38],"heterogeneity":[40],"information":[43],"about":[44],"mean-level":[45],"differences.":[46],"use":[48,74],"a":[49,56,68,95],"Monte":[50],"Carlo":[51],"EM":[52],"algorithm":[53],"identify":[55],"low-dimensional":[57,85],"subspace":[58],"that":[59,108],"explains":[60],"differences":[61],"both":[63],"means":[64],"covariances":[66],"as":[67],"function":[69],"covariates,":[71],"then":[73],"MCMC":[75],"estimate":[77],"posterior":[79],"uncertainty":[80],"conditional":[81],"inferred":[84],"subspace.":[86],"demonstrate":[88],"utility":[90],"our":[92],"motivating":[96],"application":[97],"metabolomics":[100],"aging.":[102],"also":[104],"provide":[105],"R":[106],"code":[107],"can":[109],"be":[110],"used":[111],"test":[115],"other":[116],"generalizations":[117],"response":[120],"model.":[122]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2}],"updated_date":"2026-11-03T10:50:19.383937","created_date":"2020-10-08T00:00:00"}
