{"id":"https://openalex.org/W3015528301","doi":"https://doi.org/10.48550/arxiv.1208.6338","title":"A Widely Applicable Bayesian Information Criterion","display_name":"A Widely Applicable Bayesian Information Criterion","publication_year":2012,"publication_date":"2012-08-31","ids":{"openalex":"https://openalex.org/W3015528301","doi":"https://doi.org/10.48550/arxiv.1208.6338","mag":"3015528301"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:1208.6338","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1208.6338","pdf_url":"https://arxiv.org/pdf/1208.6338","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","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1208.6338","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086744222","display_name":"WatanabeSumio","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I114531698","display_name":"Tokyo Institute of Technology","ror":"https://ror.org/0112mx960","country_code":"JP","type":"education","lineage":["https://openalex.org/I114531698","https://openalex.org/I4400009020"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Watanabe, Sumio","raw_affiliation_strings":["Department of Computational Intelligence and Systems Science Tokyo Institute of Technology Mailbox G5-19 , 4259 Nagatsuta , Midori-ku Yokohama , Japan 226-8502"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computational Intelligence and Systems Science Tokyo Institute of Technology Mailbox G5-19 , 4259 Nagatsuta , Midori-ku Yokohama , Japan 226-8502","institution_ids":["https://openalex.org/I114531698"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5086744222"],"corresponding_institution_ids":["https://openalex.org/I114531698"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":748,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"1","first_page":"867","last_page":"897"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.5205000042915344,"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":0.5205000042915344,"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":0.06989999860525131,"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/T10243","display_name":"Statistical Methods and Bayesian Inference","score":0.06560000032186508,"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/marginal-likelihood","display_name":"marginal likelihood","score":0.7149999737739563},{"id":"https://openalex.org/keywords/birational-invariants","display_name":"birational invariants","score":0.7110000252723694},{"id":"https://openalex.org/keywords/inverse-temperature","display_name":"inverse temperature","score":0.6019999980926514},{"id":"https://openalex.org/keywords/asymptotic-expansion","display_name":"asymptotic expansion","score":0.7910000085830688},{"id":"https://openalex.org/keywords/posterior-distribution","display_name":"posterior distribution","score":0.42899999022483826},{"id":"https://openalex.org/keywords/model-selection","display_name":"model selection","score":0.6480000019073486}],"concepts":[{"id":"https://openalex.org/C29406490","wikidata":"https://www.wikidata.org/wiki/Q1420659","display_name":"Fisher information","level":2,"score":0.7942402362823486},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.594143807888031},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.5551316738128662},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.5036529898643494},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.48086100816726685},{"id":"https://openalex.org/C168136583","wikidata":"https://www.wikidata.org/wiki/Q1988242","display_name":"Bayesian information criterion","level":2,"score":0.4223543405532837},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3998059332370758},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3646266460418701},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.26088714599609375}],"mesh":[],"locations_count":5,"locations":[{"id":"pmh:oai:arXiv.org:1208.6338","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1208.6338","pdf_url":"https://arxiv.org/pdf/1208.6338","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":"pmh:oai:CiteSeerX.psu:10.1.1.755.766","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.755.766","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1208.6338.pdf","raw_type":"text"},{"id":"doi:10.48550/arxiv.1208.6338","doi":"https://doi.org/10.48550/arxiv.1208.6338","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1208.6338","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":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"mag:2117076645","doi":null,"is_oa":false,"landing_page_url":"https://www.jmlr.org/papers/volume14/watanabe13a/watanabe13a.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S118988714","display_name":"Journal of Machine Learning Research","issn_l":"1532-4435","issn":["1532-4435","1533-7928"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","ccf-a","cwts-core","dongbi-a","jufo-3","ki-jl-2","norway-2","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718","https://openalex.org/P4310316440"],"host_organization_lineage_names":["The MIT Press","Massachusetts Institute of Technology"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":"Journal of Machine Learning Research","raw_type":null},{"id":"mag:3015528301","doi":null,"is_oa":false,"landing_page_url":"https://dl.acm.org/doi/10.5555/2567709.2502609","pdf_url":null,"source":{"id":"https://openalex.org/S118988714","display_name":"Journal of Machine Learning Research","issn_l":"1532-4435","issn":["1532-4435","1533-7928"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","ccf-a","cwts-core","dongbi-a","jufo-3","ki-jl-2","norway-2","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718","https://openalex.org/P4310316440"],"host_organization_lineage_names":["The MIT Press","Massachusetts Institute of Technology"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":"Journal of Machine Learning Research","raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1208.6338","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1208.6338","pdf_url":"https://arxiv.org/pdf/1208.6338","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":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3015528301.pdf","grobid_xml":"https://content.openalex.org/works/W3015528301.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W1542359973","https://openalex.org/W1594725708","https://openalex.org/W1656717670","https://openalex.org/W1753618630","https://openalex.org/W1942683912","https://openalex.org/W1968936725","https://openalex.org/W1976611840","https://openalex.org/W1978102570","https://openalex.org/W2012644626","https://openalex.org/W2034133761","https://openalex.org/W2060383267","https://openalex.org/W2089684512","https://openalex.org/W2103606110","https://openalex.org/W2106568142","https://openalex.org/W2110009816","https://openalex.org/W2110230349","https://openalex.org/W2119801007","https://openalex.org/W2120217353","https://openalex.org/W2146855196","https://openalex.org/W2159626963","https://openalex.org/W2167721584","https://openalex.org/W2292751606","https://openalex.org/W2328022084","https://openalex.org/W2480605450","https://openalex.org/W2483609603","https://openalex.org/W2883466814","https://openalex.org/W3006027310"],"related_works":["https://openalex.org/W2085025588","https://openalex.org/W7095818207","https://openalex.org/W7208228172","https://openalex.org/W2549145499","https://openalex.org/W4401821140","https://openalex.org/W2483646144","https://openalex.org/W2970192821","https://openalex.org/W4390016993","https://openalex.org/W2949522784","https://openalex.org/W2054282473"],"abstract_inverted_index":{"A":[0],"statistical":[1,40,122,212,221,245],"model":[2,89,213],"or":[3],"a":[4,14,17,87,94,98,163,211,220,233,238],"learning":[5],"machine":[6],"is":[7,20,28,35,47,90,188,214,237],"called":[8,36],"regular":[9,39],"if":[10,23,210],"the":[11,42,50,62,82,101,110,140,158,171,177,181,189,200,205],"map":[12],"taking":[13],"parameter":[15],"to":[16,138],"probability":[18],"distribution":[19,179],"one-to-one":[21],"and":[22,217],"its":[24],"Fisher":[25],"information":[26,65,167,231],"matrix":[27],"always":[29],"positive":[30],"definite.":[31],"If":[32],"otherwise,":[33],"it":[34,78,134,236],"singular.":[37],"In":[38,157],"models,":[41],"Bayes":[43,54,64,83,141,206],"free":[44,84,142,207],"energy,":[45,208],"which":[46],"defined":[48],"by":[49,61,93,170,219],"minus":[51],"logarithm":[52],"of":[53,86,108,112,118,191,241],"marginal":[55],"likelihood,":[56],"can":[57,225],"be":[58,226],"asymptotically":[59,91],"approximated":[60],"Schwarz":[63],"criterion":[66,168],"(BIC),":[67],"whereas":[68],"in":[69,114,120],"singular":[70,88,215,244],"models":[71,123],"such":[72],"approximation":[73],"does":[74],"not":[75],"hold.":[76],"Recently,":[77],"was":[79],"proved":[80],"that":[81,197],"energy":[85,143],"given":[92],"generalized":[95,239],"formula":[96],"using":[97,144],"birational":[99],"invariant,":[100],"real":[102],"log":[103,173],"canonical":[104],"threshold":[105],"(RLCT),":[106],"instead":[107],"half":[109],"number":[111,190],"parameters":[113],"BIC.":[115],"Theoretical":[116],"values":[117],"RLCTs":[119],"several":[121],"are":[124],"now":[125],"being":[126],"discovered":[127],"based":[128],"on":[129,152],"algebraic":[130],"geometrical":[131],"methodology.":[132],"However,":[133],"has":[135,199],"been":[136],"difficult":[137],"estimate":[139],"only":[145],"training":[146,192],"samples,":[147],"because":[148],"an":[149,153],"RLCT":[150],"depends":[151],"unknown":[154],"true":[155,234],"distribution.":[156],"present":[159],"paper,":[160],"we":[161],"define":[162],"widely":[164],"applicable":[165],"Bayesian":[166],"(WBIC)":[169],"average":[172],"likelihood":[174],"function":[175],"over":[176],"posterior":[178],"with":[180],"inverse":[182],"temperature":[183],"$1/\\log":[184],"n$,":[185],"where":[186],"$n$":[187],"samples.":[193],"We":[194],"mathematically":[195],"prove":[196],"WBIC":[198,224],"same":[201],"asymptotic":[202],"expansion":[203],"as":[204],"even":[209],"for":[216],"unrealizable":[218],"model.":[222],"Since":[223],"numerically":[227],"calculated":[228],"without":[229],"any":[230],"about":[232],"distribution,":[235],"version":[240],"BIC":[242],"onto":[243],"models.":[246]},"counts_by_year":[{"year":2026,"cited_by_count":10},{"year":2025,"cited_by_count":65},{"year":2024,"cited_by_count":83},{"year":2023,"cited_by_count":75},{"year":2022,"cited_by_count":78},{"year":2021,"cited_by_count":117},{"year":2020,"cited_by_count":99},{"year":2019,"cited_by_count":87},{"year":2018,"cited_by_count":44},{"year":2017,"cited_by_count":41},{"year":2016,"cited_by_count":20},{"year":2015,"cited_by_count":15},{"year":2014,"cited_by_count":10},{"year":2013,"cited_by_count":2}],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2020-04-17T00:00:00"}