{"id":"https://openalex.org/W1908709377","doi":"https://doi.org/10.48550/arxiv.1212.2512","title":"A Generalized Mean Field Algorithm for Variational Inference in Exponential Families","display_name":"A Generalized Mean Field Algorithm for Variational Inference in Exponential Families","publication_year":2012,"publication_date":"2012-10-19","ids":{"openalex":"https://openalex.org/W1908709377","doi":"https://doi.org/10.48550/arxiv.1212.2512","mag":"1908709377"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:1212.2512","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1212.2512","pdf_url":"https://arxiv.org/pdf/1212.2512","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"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1212.2512","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5009547049","display_name":"Eric P. Xing","orcid":"https://orcid.org/0009-0005-9158-4201","observed_orcids":["https://orcid.org/0009-0005-9158-4201","https://orcid.org/0000-0002-3683-4280"]},"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":"Xing, Eric P.","raw_affiliation_strings":["Computer Science Division University of California, Berkeley CA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science Division University of California, Berkeley CA","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049812527","display_name":"Michael I. Jordan","orcid":"https://orcid.org/0000-0001-8935-817X","observed_orcids":["https://orcid.org/0000-0001-8935-817X","https://orcid.org/0000-0002-2177-0405","https://orcid.org/0000-0002-5776-2626"]},"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":"Jordan, Michael I.","raw_affiliation_strings":["Computer Science and Statistics, University of California, Berkeley CA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science and Statistics, University of California, Berkeley CA#TAB#","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007305440","display_name":"Stuart Russell","orcid":"https://orcid.org/0000-0001-5252-4306","observed_orcids":["https://orcid.org/0000-0001-5252-4306"]},"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":"Russell, Stuart","raw_affiliation_strings":["Computer Science Division University of California, Berkeley CA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science Division University of California, Berkeley CA","institution_ids":["https://openalex.org/I95457486"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I95457486"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":163,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.9330999851226807,"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":0.9330999851226807,"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":0.041200000792741776,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.0038999998942017555,"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/mean-field-approximation","display_name":"mean-field approximation","score":0.8140000104904175},{"id":"https://openalex.org/keywords/variational-bayesian-inference","display_name":"variational inference","score":0.9900000095367432},{"id":"https://openalex.org/keywords/exponential-family","display_name":"exponential family","score":0.7369999885559082},{"id":"https://openalex.org/keywords/approximate-inference","display_name":"approximate inference","score":0.45500001311302185}],"concepts":[{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.6595548391342163},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6571674346923828},{"id":"https://openalex.org/C55974624","wikidata":"https://www.wikidata.org/wiki/Q1188504","display_name":"Exponential family","level":2,"score":0.5910539627075195},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4379056692123413},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4337950050830841},{"id":"https://openalex.org/C2777472644","wikidata":"https://www.wikidata.org/wiki/Q16968992","display_name":"Approximate inference","level":3,"score":0.4314131736755371},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3348931670188904},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2682647109031677},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1369183361530304}],"mesh":[],"locations_count":4,"locations":[{"id":"pmh:oai:arXiv.org:1212.2512","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1212.2512","pdf_url":"https://arxiv.org/pdf/1212.2512","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:1908709377","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1212.2512","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":"pmh:oai:CiteSeerX.psu:10.1.1.7.6058","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.7.6058","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.berkeley.edu/~jordan/papers/xing-uai03.ps.gz","raw_type":"text"},{"id":"doi:10.48550/arxiv.1212.2512","doi":"https://doi.org/10.48550/arxiv.1212.2512","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1212.2512","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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1212.2512","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1212.2512","pdf_url":"https://arxiv.org/pdf/1212.2512","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":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W1525921156","https://openalex.org/W1528056001","https://openalex.org/W1796935230","https://openalex.org/W1934021597","https://openalex.org/W2098084154","https://openalex.org/W2162995719","https://openalex.org/W2963814856"],"related_works":["https://openalex.org/W2286776387","https://openalex.org/W2791013227","https://openalex.org/W1678658122","https://openalex.org/W2949487824","https://openalex.org/W2951091626","https://openalex.org/W2530211015","https://openalex.org/W2923501483","https://openalex.org/W2802272870","https://openalex.org/W3201782785","https://openalex.org/W2767418616","https://openalex.org/W3116747493","https://openalex.org/W2889856677","https://openalex.org/W2187669537","https://openalex.org/W2770053753","https://openalex.org/W2089969354","https://openalex.org/W2952766117","https://openalex.org/W2624324495","https://openalex.org/W3157564439","https://openalex.org/W2754322148","https://openalex.org/W2188679690"],"abstract_inverted_index":{"The":[0],"mean":[1,66,98],"field":[2,67,99],"methods,":[3],"which":[4,110],"entail":[5],"approximating":[6],"intractable":[7,77],"probability":[8],"distributions":[9,12,78,85],"variationally":[10],"with":[11,198],"from":[13],"a":[14,54,64,73,80,94,123,132,136,144],"tractable":[15,84,186],"family,":[16],"enjoy":[17],"high":[18],"efficiency,":[19],"guaranteed":[20],"convergence,":[21],"and":[22,41,142,156,195],"provide":[23],"lower":[24],"bounds":[25],"on":[26,69,192,200],"the":[27,38,113,116,153,165,175,182],"true":[28],"likelihood.":[29],"But":[30],"due":[31],"to":[32,72,150,158,206],"requirement":[33],"for":[34,102],"model-specific":[35,128],"derivation":[36],"of":[37,76,83,96,118,138,146,184,189],"optimization":[39,88,114],"equations":[40,149],"unclear":[42],"inference":[43,57,104,177,193],"quality":[44],"in":[45,105],"various":[46],"models,":[47,109],"it":[48],"is":[49,122,210],"not":[50],"widely":[51],"used":[52],"as":[53],"generic":[55,124],"approximate":[56,103],"algorithm.":[58],"In":[59],"this":[60],"paper,":[61],"we":[62],"discuss":[63],"generalized":[65,97],"theory":[68],"variational":[70],"approximation":[71,209],"broad":[74],"class":[75,95,117],"using":[79],"rich":[81],"set":[82,137,145],"via":[86],"constrained":[87],"over":[89,115],"distribution":[90],"spaces.":[91],"We":[92,179],"present":[93],"(GMF)":[100],"algorithms":[101],"complex":[106,133],"exponential":[107],"family":[108,187],"entails":[111],"limiting":[112],"cluster-factorizable":[119],"distributions.":[120],"GMF":[121,197],"method":[125],"requiring":[126],"no":[127],"derivations.":[129],"It":[130],"factors":[131],"model":[134],"into":[135],"disjoint":[139],"variable":[140],"clusters,":[141],"uses":[143],"canonical":[147,202],"fix-point":[148],"iteratively":[151],"update":[152],"cluster":[154,161],"distributions,":[155],"converge":[157],"locally":[159],"optimal":[160],"marginals":[162],"that":[163],"preserve":[164],"original":[166],"dependency":[167],"structure":[168],"within":[169],"each":[170],"cluster,":[171],"hence,":[172],"fully":[173],"decomposed":[174],"overall":[176],"problem.":[178],"empirically":[180],"analyzed":[181],"effect":[183],"different":[185,190],"(clusters":[188],"granularity)":[191],"quality,":[194],"compared":[196],"BP":[199],"several":[201],"models.":[203],"Possible":[204],"extension":[205],"higher-order":[207],"MF":[208],"also":[211],"discussed.":[212]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":12},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":12},{"year":2013,"cited_by_count":9},{"year":2012,"cited_by_count":11}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2025-10-10T00:00:00"}