{"id":"https://openalex.org/W2768146717","doi":"https://doi.org/10.23919/ecc.2018.8550107","title":"Sparse Inverse Covariance Estimation for Chordal Structures","display_name":"Sparse Inverse Covariance Estimation for Chordal Structures","publication_year":2018,"publication_date":"2018-06-01","ids":{"openalex":"https://openalex.org/W2768146717","doi":"https://doi.org/10.23919/ecc.2018.8550107","mag":"2768146717"},"language":"en","primary_location":{"id":"doi:10.23919/ecc.2018.8550107","is_oa":false,"landing_page_url":"https://doi.org/10.23919/ecc.2018.8550107","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2018 European Control Conference (ECC)","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1711.09131","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5061966752","display_name":"Salar Fattahi","orcid":"https://orcid.org/0000-0001-7986-3148"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Salar Fattahi","raw_affiliation_strings":["Department of Industrial Engineering and Operations Research, University of California, Berkeley","Department of Industrial Engineering and Operations Research University of California, Berkeley"],"affiliations":[{"raw_affiliation_string":"Department of Industrial Engineering and Operations Research, University of California, Berkeley","institution_ids":["https://openalex.org/I95457486"]},{"raw_affiliation_string":"Department of Industrial Engineering and Operations Research University of California, Berkeley","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079119611","display_name":"Richard Y. Zhang","orcid":"https://orcid.org/0000-0003-3980-2791"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Richard Y. Zhang","raw_affiliation_strings":["Department of Industrial Engineering and Operations Research, University of California, Berkeley","Department of Industrial Engineering and Operations Research University of California, Berkeley"],"affiliations":[{"raw_affiliation_string":"Department of Industrial Engineering and Operations Research, University of California, Berkeley","institution_ids":["https://openalex.org/I95457486"]},{"raw_affiliation_string":"Department of Industrial Engineering and Operations Research University of California, Berkeley","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072786751","display_name":"Somayeh Sojoudi","orcid":"https://orcid.org/0000-0001-7177-7712"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Somayeh Sojoudi","raw_affiliation_strings":["Somayeh Sojoudi is with the Departments of Electrical Engineering and Computer Sciences and Mechanical Engineering, University of California, Berkeley"],"affiliations":[{"raw_affiliation_string":"Somayeh Sojoudi is with the Departments of Electrical Engineering and Computer Sciences and Mechanical Engineering, University of California, Berkeley","institution_ids":["https://openalex.org/I95457486"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5061966752"],"corresponding_institution_ids":["https://openalex.org/I95457486"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0150519,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"837","last_page":"844"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.9991000294685364,"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":0.9991000294685364,"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/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.9965999722480774,"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/T11273","display_name":"Advanced Graph Neural Networks","score":0.9919000267982483,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6402357220649719},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.6067590117454529},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.6053669452667236},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.5722503662109375},{"id":"https://openalex.org/keywords/thresholding","display_name":"Thresholding","score":0.5693167448043823},{"id":"https://openalex.org/keywords/covariance-matrix","display_name":"Covariance matrix","score":0.5359348654747009},{"id":"https://openalex.org/keywords/estimation-of-covariance-matrices","display_name":"Estimation of covariance matrices","score":0.4952498972415924},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.4665643274784088},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4664447009563446},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.431260883808136},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.41451412439346313},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3893061876296997},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2799290418624878},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2625623941421509},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1566656231880188},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.14909011125564575},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1207338273525238},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.08478015661239624}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6402357220649719},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.6067590117454529},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.6053669452667236},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5722503662109375},{"id":"https://openalex.org/C191178318","wikidata":"https://www.wikidata.org/wiki/Q2256906","display_name":"Thresholding","level":3,"score":0.5693167448043823},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.5359348654747009},{"id":"https://openalex.org/C180877172","wikidata":"https://www.wikidata.org/wiki/Q5401390","display_name":"Estimation of covariance matrices","level":3,"score":0.4952498972415924},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.4665643274784088},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4664447009563446},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.431260883808136},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.41451412439346313},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3893061876296997},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2799290418624878},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2625623941421509},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1566656231880188},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.14909011125564575},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1207338273525238},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.08478015661239624},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.23919/ecc.2018.8550107","is_oa":false,"landing_page_url":"https://doi.org/10.23919/ecc.2018.8550107","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2018 European Control Conference (ECC)","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1711.09131","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1711.09131","pdf_url":"https://arxiv.org/pdf/1711.09131","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":"","raw_type":"text"},{"id":"mag:2768146717","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1711.09131.pdf","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1711.09131","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1711.09131","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1711.09131","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1711.09131","pdf_url":"https://arxiv.org/pdf/1711.09131","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":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1072749480","display_name":null,"funder_award_id":"FA9550-17","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G1523888516","display_name":null,"funder_award_id":"FA9550-","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G260750634","display_name":null,"funder_award_id":"FA9550-17-1","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G4504108201","display_name":null,"funder_award_id":"N00014-17-1","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G460220646","display_name":null,"funder_award_id":"D16AP00002","funder_id":"https://openalex.org/F4320332180","funder_display_name":"Defense Advanced Research Projects Agency"},{"id":"https://openalex.org/G4751570384","display_name":null,"funder_award_id":"4-17-1-","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G5046129341","display_name":null,"funder_award_id":"N00014-17-1-2933","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G5809100787","display_name":null,"funder_award_id":"FA9550","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G6098521345","display_name":null,"funder_award_id":"FA9550","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G7714977823","display_name":null,"funder_award_id":"FA9550-17-1-0163","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G8876996369","display_name":null,"funder_award_id":"N00014","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"}],"funders":[{"id":"https://openalex.org/F4320332180","display_name":"Defense Advanced Research Projects Agency","ror":"https://ror.org/02caytj08"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2768146717.pdf","grobid_xml":"https://content.openalex.org/works/W2768146717.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W1481640635","https://openalex.org/W1562509598","https://openalex.org/W1970786235","https://openalex.org/W2019377400","https://openalex.org/W2030828780","https://openalex.org/W2035080386","https://openalex.org/W2069959554","https://openalex.org/W2071143636","https://openalex.org/W2074360197","https://openalex.org/W2077309453","https://openalex.org/W2089465933","https://openalex.org/W2097581234","https://openalex.org/W2106424475","https://openalex.org/W2106802398","https://openalex.org/W2108294598","https://openalex.org/W2109357213","https://openalex.org/W2114682096","https://openalex.org/W2131242330","https://openalex.org/W2132555912","https://openalex.org/W2151128232","https://openalex.org/W2475483933","https://openalex.org/W2735788552","https://openalex.org/W4292070118","https://openalex.org/W6628737794","https://openalex.org/W6676051941","https://openalex.org/W6679560219","https://openalex.org/W6682227116","https://openalex.org/W6721381422"],"related_works":["https://openalex.org/W3193689872","https://openalex.org/W2258814563","https://openalex.org/W3134875073","https://openalex.org/W2631776726","https://openalex.org/W3119321585","https://openalex.org/W2591778798","https://openalex.org/W152374499","https://openalex.org/W3092119210","https://openalex.org/W2112428620","https://openalex.org/W3037011488","https://openalex.org/W3098494111","https://openalex.org/W3201566834","https://openalex.org/W2953064603","https://openalex.org/W2953389920","https://openalex.org/W2106904876","https://openalex.org/W2962741457","https://openalex.org/W3013109894","https://openalex.org/W2272355041","https://openalex.org/W37129894","https://openalex.org/W2950180286"],"abstract_inverted_index":{"In":[0],"this":[1,93],"paper,":[2],"we":[3,32,95],"consider":[4],"the":[5,15,36,40,48,54,75,89,101,111,130,143,152,168,171,189,194,203],"Graphical":[6],"Lasso":[7],"(GL),":[8],"a":[9,68,85,97,136,155,163,177],"popular":[10],"optimization":[11],"problem":[12,160,196],"for":[13,28,58,100,103,126,167],"learning":[14],"sparse":[16,59],"representations":[17],"of":[18,39,43,88],"high-dimensional":[19,127],"datasets,":[20],"which":[21],"is":[22,45,72,148],"well-known":[23],"to":[24,47,124,150,154,185],"be":[25,119],"computationally":[26],"expensive":[27],"large-scale":[29,181],"problems.":[30],"Recently,":[31],"have":[33,65],"shown":[34],"that":[35,71,110,142],"sparsity":[37],"pattern":[38],"optimal":[41,73],"solution":[42,70,99,166],"GL":[44,102,112,144,153,169,195],"equivalent":[46],"one":[49],"obtained":[50],"from":[51],"simply":[52],"thresholding":[53,114,146],"sample":[55,77,132,173],"covariance":[56,78,133,174],"matrix,":[57],"graphs":[60,104],"under":[61],"different":[62],"conditions.":[63],"We":[64,108,139],"also":[66],"derived":[67],"closed-form":[69,98,165],"when":[74,170],"thresholded":[76,131,172],"matrix":[79,134,158,175],"has":[80,135,176],"an":[81],"acyclic":[82],"structure.":[83,138,179],"As":[84],"major":[86],"generalization":[87],"previous":[90],"result,":[91],"in":[92,197,207],"paper":[94],"derive":[96],"with":[105,183],"chordal":[106,137,178],"structures.":[107],"show":[109,141],"and":[113,121,145,161],"equivalence":[115,147],"conditions":[116],"can":[117,192],"significantly":[118],"simplified":[120],"are":[122],"expected":[123],"hold":[125],"problems":[128,182],"if":[129],"then":[140],"enough":[149],"reduce":[151],"maximum":[156],"determinant":[157],"completion":[159],"drive":[162],"recursive":[164],"For":[180],"up":[184],"450":[186],"million":[187],"variables,":[188],"proposed":[190],"method":[191],"solve":[193],"less":[198],"than":[199,209],"2":[200,210],"minutes,":[201],"while":[202],"state-of-the-art":[204],"methods":[205],"converge":[206],"more":[208],"hours.":[211]},"counts_by_year":[],"updated_date":"2026-03-14T08:43:22.919905","created_date":"2025-10-10T00:00:00"}