{"id":"https://openalex.org/W2009686967","doi":"https://doi.org/10.1137/110861051","title":"Positive Definite Completion Problems for Bayesian Networks","display_name":"Positive Definite Completion Problems for Bayesian Networks","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2009686967","doi":"https://doi.org/10.1137/110861051","mag":"2009686967"},"language":"en","primary_location":{"id":"doi:10.1137/110861051","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110861051","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"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/A5076640906","display_name":"Emanuel Ben\u2010David","orcid":"https://orcid.org/0000-0002-4230-4497"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Emanuel Ben-David","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5091424272","display_name":"Bala Rajaratnam","orcid":"https://orcid.org/0000-0003-2570-8059"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bala Rajaratnam","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.70540391,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"33","issue":"2","first_page":"617","last_page":"638"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.9861999750137329,"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":0.9746000170707703,"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/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.837841272354126},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7684171199798584},{"id":"https://openalex.org/keywords/directed-acyclic-graph","display_name":"Directed acyclic graph","score":0.730357825756073},{"id":"https://openalex.org/keywords/directed-graph","display_name":"Directed graph","score":0.5796985626220703},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5437155961990356},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.500281810760498},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.499924898147583},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.48301446437835693},{"id":"https://openalex.org/keywords/matrix-completion","display_name":"Matrix completion","score":0.45206838846206665},{"id":"https://openalex.org/keywords/graphical-model","display_name":"Graphical model","score":0.4300026595592499},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.41200700402259827},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38976407051086426},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3340306282043457},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.21311062574386597},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.1853611171245575},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08233332633972168}],"concepts":[{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.837841272354126},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7684171199798584},{"id":"https://openalex.org/C74197172","wikidata":"https://www.wikidata.org/wiki/Q1195339","display_name":"Directed acyclic graph","level":2,"score":0.730357825756073},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.5796985626220703},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5437155961990356},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.500281810760498},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.499924898147583},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.48301446437835693},{"id":"https://openalex.org/C2778459887","wikidata":"https://www.wikidata.org/wiki/Q6787865","display_name":"Matrix completion","level":3,"score":0.45206838846206665},{"id":"https://openalex.org/C155846161","wikidata":"https://www.wikidata.org/wiki/Q1143367","display_name":"Graphical model","level":2,"score":0.4300026595592499},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.41200700402259827},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38976407051086426},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3340306282043457},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.21311062574386597},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.1853611171245575},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08233332633972168},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/110861051","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110861051","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1963510668","https://openalex.org/W2006704773","https://openalex.org/W2019963883","https://openalex.org/W2026097090","https://openalex.org/W2033120023","https://openalex.org/W2033310971","https://openalex.org/W2038711071","https://openalex.org/W2062124264","https://openalex.org/W2103972604","https://openalex.org/W2121454540","https://openalex.org/W2611328865","https://openalex.org/W3098045107","https://openalex.org/W3100744870","https://openalex.org/W4238253035"],"related_works":["https://openalex.org/W79495945","https://openalex.org/W1505105018","https://openalex.org/W2035724326","https://openalex.org/W2443765813","https://openalex.org/W4302568932","https://openalex.org/W2146569528","https://openalex.org/W17595654","https://openalex.org/W1998712144","https://openalex.org/W4287028074","https://openalex.org/W4287021714"],"abstract_inverted_index":{"A":[0],"positive":[1,26,40,102],"definite":[2,27,41,103],"completion":[3,42,104],"problem":[4],"pertains":[5],"to":[6,60,91,119,135],"determining":[7],"whether":[8,76],"the":[9,45,49,93,101,110,121,141,144,155,158],"unspecified":[10],"positions":[11],"of":[12,25,39,51,56,85,100,112,123,146,153,157],"a":[13,22,77,147,151],"partial":[14,78,160],"(or":[15],"incomplete)":[16],"matrix":[17,79,149],"can":[18,80,128],"be":[19,81,130],"completed":[20,82,94,148],"in":[21,83,109],"desired":[23,46],"subclass":[24],"matrices.":[28,95],"In":[29],"this":[30],"paper":[31],"we":[32],"study":[33],"an":[34,98],"important":[35],"and":[36,53,88,116,143],"new":[37],"class":[38,122],"problems":[43],"where":[44],"subclasses":[47],"are":[48],"spaces":[50,87],"covariance":[52],"inverse-covariance":[54],"matrices":[55],"probabilistic":[57],"models":[58],"corresponding":[59,159],"Bayesian":[61],"networks":[62],"(also":[63],"known":[64],"as":[65,150],"directed":[66,113,124],"acyclic":[67,114,125],"graph":[68],"models).":[69],"We":[70,96,132],"provide":[71],"fast":[72],"procedures":[73],"that":[74],"determine":[75],"either":[84],"these":[86],"thereafter":[89],"proceed":[90,118,134],"construct":[92],"prove":[97],"analogue":[99],"result":[105],"for":[106,140],"undirected":[107],"graphs":[108,126],"context":[111],"graphs,":[115],"thus":[117],"characterize":[120],"which":[127],"always":[129],"completed.":[131],"also":[133],"give":[136],"closed":[137],"form":[138],"expressions":[139],"inverse":[142],"determinant":[145],"function":[152],"only":[154],"elements":[156],"matrix.":[161]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}