{"id":"https://openalex.org/W4386075187","doi":"https://doi.org/10.1109/isit54713.2023.10206857","title":"The Exact Determinant of a Specific Class of Sparse Positive Definite Matrices","display_name":"The Exact Determinant of a Specific Class of Sparse Positive Definite Matrices","publication_year":2023,"publication_date":"2023-06-25","ids":{"openalex":"https://openalex.org/W4386075187","doi":"https://doi.org/10.1109/isit54713.2023.10206857"},"language":"en","primary_location":{"id":"doi:10.1109/isit54713.2023.10206857","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit54713.2023.10206857","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2023 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-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/A5074058937","display_name":"Mehdi Molkaraie","orcid":"https://orcid.org/0000-0001-9260-5071"},"institutions":[{"id":"https://openalex.org/I170486558","display_name":"Pompeu Fabra University","ror":"https://ror.org/04n0g0b29","country_code":"ES","type":"education","lineage":["https://openalex.org/I170486558"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Mehdi Molkaraie","raw_affiliation_strings":["Universitat Pompeu Fabra,Barcelona,Spain,08018"],"affiliations":[{"raw_affiliation_string":"Universitat Pompeu Fabra,Barcelona,Spain,08018","institution_ids":["https://openalex.org/I170486558"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5074058937"],"corresponding_institution_ids":["https://openalex.org/I170486558"],"apc_list":null,"apc_paid":null,"fwci":0.2009,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.49447111,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"1038","last_page":"1043"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11321","display_name":"Error Correcting Code Techniques","score":0.9944000244140625,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T11321","display_name":"Error Correcting Code Techniques","score":0.9944000244140625,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.9861000180244446,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9690999984741211,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/graphical-model","display_name":"Graphical model","score":0.7792282104492188},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.6659886837005615},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.5926060676574707},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5822467803955078},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.546777606010437},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5216379761695862},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4811362326145172},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.45368728041648865},{"id":"https://openalex.org/keywords/equivalence-class","display_name":"Equivalence class (music)","score":0.44681575894355774},{"id":"https://openalex.org/keywords/covariance-matrix","display_name":"Covariance matrix","score":0.4449368715286255},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.4427887201309204},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.43413257598876953},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.20805633068084717},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.0795908272266388}],"concepts":[{"id":"https://openalex.org/C155846161","wikidata":"https://www.wikidata.org/wiki/Q1143367","display_name":"Graphical model","level":2,"score":0.7792282104492188},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.6659886837005615},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.5926060676574707},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5822467803955078},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.546777606010437},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5216379761695862},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4811362326145172},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.45368728041648865},{"id":"https://openalex.org/C2777044963","wikidata":"https://www.wikidata.org/wiki/Q5384707","display_name":"Equivalence class (music)","level":2,"score":0.44681575894355774},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.4449368715286255},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.4427887201309204},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43413257598876953},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.20805633068084717},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0795908272266388},{"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/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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/isit54713.2023.10206857","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit54713.2023.10206857","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2023 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W113136616","https://openalex.org/W1503398984","https://openalex.org/W1506342804","https://openalex.org/W1839953896","https://openalex.org/W1969649155","https://openalex.org/W1998997296","https://openalex.org/W2000191307","https://openalex.org/W2071489416","https://openalex.org/W2095702447","https://openalex.org/W2099111195","https://openalex.org/W2102802796","https://openalex.org/W2106110343","https://openalex.org/W2130152237","https://openalex.org/W2132890668","https://openalex.org/W2137813581","https://openalex.org/W2138628599","https://openalex.org/W2139584447","https://openalex.org/W2154899352","https://openalex.org/W2324309783","https://openalex.org/W2736472142","https://openalex.org/W2913798276","https://openalex.org/W2963586518","https://openalex.org/W3216533581","https://openalex.org/W4231501374","https://openalex.org/W4238253035","https://openalex.org/W4388323202","https://openalex.org/W6638719645"],"related_works":["https://openalex.org/W3006682748","https://openalex.org/W1502458949","https://openalex.org/W1097487277","https://openalex.org/W2323830966","https://openalex.org/W188032563","https://openalex.org/W2949964783","https://openalex.org/W2768610039","https://openalex.org/W2362838148","https://openalex.org/W3121250382","https://openalex.org/W2054802669"],"abstract_inverted_index":{"For":[0],"a":[1,11,109],"specific":[2],"class":[3],"of":[4,17,38,62,66,76,111],"sparse":[5],"Gaussian":[6,115],"graphical":[7,25,100,116],"models,":[8],"we":[9,105],"provide":[10],"closed-form":[12,87],"solution":[13],"for":[14],"the":[15,18,24,29,47,59,63,67,77,93,98],"determinant":[16],"covariance":[19,30],"matrix.":[20],"In":[21,102],"our":[22],"framework,":[23],"interaction":[26],"model":[27],"(i.e.,":[28],"selection":[31],"model)":[32],"is":[33,46,55,89],"equal":[34],"to":[35],"replacement":[36],"product":[37],"${\\mathcal{K}_n}$":[39,45],"and":[40,83],"${\\mathcal{K}_{n":[41],"-":[42],"1}}$,":[43],"where":[44],"complete":[48],"graph":[49],"with":[50],"n":[51],"vertices.":[52],"Our":[53],"analysis":[54],"based":[56],"on":[57,97],"taking":[58],"Fourier":[60],"transform":[61],"local":[64],"factors":[65],"model,":[68],"which":[69],"can":[70],"be":[71],"viewed":[72],"as":[73],"an":[74],"application":[75],"Normal":[78],"Factor":[79],"Graph":[80],"Duality":[81],"Theorem":[82],"holographic":[84],"algorithms.":[85],"The":[86],"expression":[88],"obtained":[90],"by":[91],"applying":[92],"Matrix":[94],"Determinant":[95],"Lemma":[96],"transformed":[99],"model.":[101],"this":[103],"context,":[104],"will":[106],"also":[107],"define":[108],"notion":[110],"equivalence":[112],"between":[113],"two":[114],"models.":[117]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
