{"id":"https://openalex.org/W3176003262","doi":"https://doi.org/10.3390/e23070807","title":"Variational Message Passing and Local Constraint Manipulation in Factor Graphs","display_name":"Variational Message Passing and Local Constraint Manipulation in Factor Graphs","publication_year":2021,"publication_date":"2021-06-24","ids":{"openalex":"https://openalex.org/W3176003262","doi":"https://doi.org/10.3390/e23070807","mag":"3176003262","pmid":"https://pubmed.ncbi.nlm.nih.gov/34202913"},"language":"en","primary_location":{"id":"doi:10.3390/e23070807","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23070807","pdf_url":"https://www.mdpi.com/1099-4300/23/7/807/pdf?version=1624979470","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":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/23/7/807/pdf?version=1624979470","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5077888111","display_name":"\u0130smai\u0307l \u015een\u00f6z","orcid":"https://orcid.org/0000-0001-7355-2138"},"institutions":[{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"\u0130smail \u015een\u00f6z","raw_affiliation_strings":["Department of Electrical Engineering, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands"],"raw_orcid":"https://orcid.org/0000-0001-7355-2138","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands","institution_ids":["https://openalex.org/I83019370"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066120388","display_name":"Thijs van de Laar","orcid":"https://orcid.org/0000-0003-3936-5368"},"institutions":[{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Thijs van de Laar","raw_affiliation_strings":["Department of Electrical Engineering, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands","institution_ids":["https://openalex.org/I83019370"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080299484","display_name":"Dmitry Bagaev","orcid":"https://orcid.org/0000-0001-9655-7986"},"institutions":[{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Dmitry Bagaev","raw_affiliation_strings":["Department of Electrical Engineering, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands","institution_ids":["https://openalex.org/I83019370"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022330444","display_name":"Bert de Vries","orcid":"https://orcid.org/0000-0003-0839-174X"},"institutions":[{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Bert de de Vries","raw_affiliation_strings":["Department of Electrical Engineering, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands","GN Hearing, JF Kennedylaan 2, 5612 AB Eindhoven, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands","institution_ids":["https://openalex.org/I83019370"]},{"raw_affiliation_string":"GN Hearing, JF Kennedylaan 2, 5612 AB Eindhoven, The Netherlands","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5077888111"],"corresponding_institution_ids":["https://openalex.org/I83019370"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":3.2688,"has_fulltext":true,"cited_by_count":30,"citation_normalized_percentile":{"value":0.93128909,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":99},"biblio":{"volume":"23","issue":"7","first_page":"807","last_page":"807"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.9990000128746033,"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"}},"topics":[{"id":"https://openalex.org/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.9990000128746033,"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.9976999759674072,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9961000084877014,"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/factor-graph","display_name":"Factor graph","score":0.8155906200408936},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.6636303663253784},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.6274138689041138},{"id":"https://openalex.org/keywords/message-passing","display_name":"Message passing","score":0.5400872826576233},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5028747916221619},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.47738808393478394},{"id":"https://openalex.org/keywords/graphical-model","display_name":"Graphical model","score":0.4495684504508972},{"id":"https://openalex.org/keywords/bayesian-inference","display_name":"Bayesian inference","score":0.4485102593898773},{"id":"https://openalex.org/keywords/bayesian-network","display_name":"Bayesian network","score":0.4438934922218323},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.41737261414527893},{"id":"https://openalex.org/keywords/belief-propagation","display_name":"Belief propagation","score":0.4135759174823761},{"id":"https://openalex.org/keywords/free-energy-principle","display_name":"Free energy principle","score":0.4107322692871094},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.3798217475414276},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3702516555786133},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3512173891067505},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.33922111988067627},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.32370591163635254},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.22393742203712463},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.15891239047050476}],"concepts":[{"id":"https://openalex.org/C159246509","wikidata":"https://www.wikidata.org/wiki/Q5428725","display_name":"Factor graph","level":3,"score":0.8155906200408936},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.6636303663253784},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.6274138689041138},{"id":"https://openalex.org/C854659","wikidata":"https://www.wikidata.org/wiki/Q1859284","display_name":"Message passing","level":2,"score":0.5400872826576233},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5028747916221619},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.47738808393478394},{"id":"https://openalex.org/C155846161","wikidata":"https://www.wikidata.org/wiki/Q1143367","display_name":"Graphical model","level":2,"score":0.4495684504508972},{"id":"https://openalex.org/C160234255","wikidata":"https://www.wikidata.org/wiki/Q812535","display_name":"Bayesian inference","level":3,"score":0.4485102593898773},{"id":"https://openalex.org/C33724603","wikidata":"https://www.wikidata.org/wiki/Q812540","display_name":"Bayesian network","level":2,"score":0.4438934922218323},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.41737261414527893},{"id":"https://openalex.org/C152948882","wikidata":"https://www.wikidata.org/wiki/Q4060686","display_name":"Belief propagation","level":3,"score":0.4135759174823761},{"id":"https://openalex.org/C33553690","wikidata":"https://www.wikidata.org/wiki/Q17014702","display_name":"Free energy principle","level":2,"score":0.4107322692871094},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.3798217475414276},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3702516555786133},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3512173891067505},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.33922111988067627},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32370591163635254},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.22393742203712463},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.15891239047050476},{"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/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.3390/e23070807","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23070807","pdf_url":"https://www.mdpi.com/1099-4300/23/7/807/pdf?version=1624979470","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:34202913","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/34202913","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:pure.tue.nl:openaire/bb94be80-5a3d-46b4-8e71-338b567b9c2d","is_oa":true,"landing_page_url":"https://research.tue.nl/en/publications/bb94be80-5a3d-46b4-8e71-338b567b9c2d","pdf_url":null,"source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Senoz, I, van de Laar, T W, Bagaev, D & de Vries, A 2021, 'Variational Message Passing and Local Constraint Manipulation in Factor Graphs', Entropy, vol. 23, no. 7, 807. https://doi.org/10.3390/e23070807","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:doaj.org/article:1448b570b0064cc1aa63143cbe66b3e8","is_oa":false,"landing_page_url":"https://doaj.org/article/1448b570b0064cc1aa63143cbe66b3e8","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 23, Iss 7, p 807 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/23/7/807/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e23070807","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; Volume 23; Issue 7; Pages: 807","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:8303273","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/8303273","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"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"},{"id":"pmh:tue:oai:pure.tue.nl:publications/bb94be80-5a3d-46b4-8e71-338b567b9c2d","is_oa":true,"landing_page_url":"https://research.tue.nl/nl/publications/bb94be80-5a3d-46b4-8e71-338b567b9c2d","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, 23(7):807. Multidisciplinary Digital Publishing Institute (MDPI)","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.3390/e23070807","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23070807","pdf_url":"https://www.mdpi.com/1099-4300/23/7/807/pdf?version=1624979470","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":[{"score":0.699999988079071,"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W3176003262.pdf"},"referenced_works_count":73,"referenced_works":["https://openalex.org/W26187695","https://openalex.org/W53464817","https://openalex.org/W88520345","https://openalex.org/W1514444828","https://openalex.org/W1515707554","https://openalex.org/W1546392582","https://openalex.org/W1647070782","https://openalex.org/W1659783081","https://openalex.org/W1795258949","https://openalex.org/W1934021597","https://openalex.org/W1965555277","https://openalex.org/W1983001515","https://openalex.org/W1984037602","https://openalex.org/W1985839769","https://openalex.org/W2049633694","https://openalex.org/W2052958516","https://openalex.org/W2052963087","https://openalex.org/W2054091988","https://openalex.org/W2091990110","https://openalex.org/W2103878673","https://openalex.org/W2106131716","https://openalex.org/W2115166723","https://openalex.org/W2117663940","https://openalex.org/W2120340025","https://openalex.org/W2120575449","https://openalex.org/W2137813581","https://openalex.org/W2139584447","https://openalex.org/W2142176084","https://openalex.org/W2147008239","https://openalex.org/W2150859678","https://openalex.org/W2156094048","https://openalex.org/W2156358825","https://openalex.org/W2157376352","https://openalex.org/W2159080219","https://openalex.org/W2160679028","https://openalex.org/W2169415915","https://openalex.org/W2171056452","https://openalex.org/W2202981647","https://openalex.org/W2271522117","https://openalex.org/W2286197641","https://openalex.org/W2290583360","https://openalex.org/W2293292859","https://openalex.org/W2296319761","https://openalex.org/W2396077723","https://openalex.org/W2398757277","https://openalex.org/W2604395440","https://openalex.org/W2604706952","https://openalex.org/W2730151709","https://openalex.org/W2898878670","https://openalex.org/W2899947052","https://openalex.org/W2903198223","https://openalex.org/W2903598832","https://openalex.org/W2929539807","https://openalex.org/W2949670190","https://openalex.org/W2952905572","https://openalex.org/W2953199373","https://openalex.org/W3020913839","https://openalex.org/W3081029288","https://openalex.org/W3081305292","https://openalex.org/W3099172207","https://openalex.org/W3132290407","https://openalex.org/W4211049957","https://openalex.org/W4230618008","https://openalex.org/W4232464081","https://openalex.org/W4250589301","https://openalex.org/W4293052541","https://openalex.org/W6631886430","https://openalex.org/W6632080362","https://openalex.org/W6655557675","https://openalex.org/W6678397451","https://openalex.org/W6682671827","https://openalex.org/W6683539749","https://openalex.org/W6764090083"],"related_works":["https://openalex.org/W2122977448","https://openalex.org/W2124250880","https://openalex.org/W4301665663","https://openalex.org/W2963109230","https://openalex.org/W4388627352","https://openalex.org/W4368755698","https://openalex.org/W3180766726","https://openalex.org/W3177262287","https://openalex.org/W2757022491","https://openalex.org/W2978729728"],"abstract_inverted_index":{"Accurate":[0],"evaluation":[1,166],"of":[2,52,70,85,99,111,154,167,178],"Bayesian":[3],"model":[4,16,44,100,174],"evidence":[5,19,101,187],"for":[6,66,114,128,173],"a":[7,12,81,108,124],"given":[8],"data":[9],"set":[10],"is":[11,38,56],"fundamental":[13],"problem":[14],"in":[15,24,62,117,170],"development.":[17],"Since":[18],"evaluations":[20],"are":[21],"usually":[22],"intractable,":[23],"practice":[25],"variational":[26,115],"free":[27],"energy":[28],"(VFE)":[29],"minimization":[30],"provides":[31],"an":[32,39,92,137],"attractive":[33],"alternative,":[34],"as":[35,136,151],"the":[36,53,60,63,67,71,86,132,140,152,156,168],"VFE":[37],"upper":[40],"bound":[41],"on":[42],"negative":[43],"log-evidence":[45],"(NLE).":[46],"In":[47,103],"order":[48],"to":[49,58,80,139],"improve":[50,186],"tractability":[51,96],"VFE,":[54],"it":[55],"common":[57],"manipulate":[59],"constraints":[61],"search":[64],"space":[65],"posterior":[68],"distribution":[69],"latent":[72],"variables.":[73],"Unfortunately,":[74],"constraint":[75,89,112],"manipulation":[76,90,113],"may":[77],"also":[78],"lead":[79],"less":[82],"accurate":[83],"estimate":[84],"NLE.":[87],"Thus,":[88],"implies":[91],"engineering":[93],"trade-off":[94],"between":[95],"and":[97,176],"accuracy":[98],"estimation.":[102],"this":[104],"paper,":[105],"we":[106,130],"develop":[107],"unifying":[109],"account":[110],"inference":[116,182],"models":[118],"that":[119,184],"can":[120],"be":[121],"represented":[122],"by":[123],"(Forney-style)":[125],"factor":[126,171],"graph,":[127],"which":[129],"identify":[131],"Bethe":[133,158],"Free":[134,159],"Energy":[135,160],"approximation":[138],"VFE.":[141],"We":[142],"derive":[143],"well-known":[144],"message":[145,180],"passing":[146],"algorithms":[147,183],"from":[148],"first":[149],"principles,":[150],"result":[153],"minimizing":[155],"constrained":[157],"(BFE).":[161],"The":[162],"proposed":[163],"method":[164],"supports":[165],"BFE":[169],"graphs":[172],"scoring":[175],"development":[177],"new":[179],"passing-based":[181],"potentially":[185],"estimation":[188],"accuracy.":[189]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":2}],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2025-10-10T00:00:00"}
