{"id":"https://openalex.org/W2013367791","doi":"https://doi.org/10.1109/isit.2012.6283654","title":"The Bethe approximation of the pattern maximum likelihood distribution","display_name":"The Bethe approximation of the pattern maximum likelihood distribution","publication_year":2012,"publication_date":"2012-07-01","ids":{"openalex":"https://openalex.org/W2013367791","doi":"https://doi.org/10.1109/isit.2012.6283654","mag":"2013367791"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2012.6283654","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2012.6283654","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 IEEE International Symposium on Information Theory Proceedings","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/A5028154201","display_name":"Pascal O. Vontobel","orcid":"https://orcid.org/0000-0002-6180-258X"},"institutions":[{"id":"https://openalex.org/I1324840837","display_name":"Hewlett-Packard (United States)","ror":"https://ror.org/059rn9488","country_code":"US","type":"company","lineage":["https://openalex.org/I1324840837"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Pascal O. Vontobel","raw_affiliation_strings":["Hewlett Packard Laboratories, Palo Alto, CA, USA","Hewlett Packard Laboratories, 1501 Page Mill Road, Palo Alto, CA 94304 USA"],"affiliations":[{"raw_affiliation_string":"Hewlett Packard Laboratories, Palo Alto, CA, USA","institution_ids":["https://openalex.org/I1324840837"]},{"raw_affiliation_string":"Hewlett Packard Laboratories, 1501 Page Mill Road, Palo Alto, CA 94304 USA","institution_ids":["https://openalex.org/I1324840837"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5028154201"],"corresponding_institution_ids":["https://openalex.org/I1324840837"],"apc_list":null,"apc_paid":null,"fwci":2.1407,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.88145065,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"1","issue":null,"first_page":"2012","last_page":"2016"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9993000030517578,"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/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9993000030517578,"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/T11269","display_name":"Algorithms and Data Compression","score":0.993399977684021,"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/T11447","display_name":"Blind Source Separation Techniques","score":0.9930999875068665,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/mathematics","display_name":"Mathematics","score":0.6128121018409729},{"id":"https://openalex.org/keywords/gibbs-sampling","display_name":"Gibbs sampling","score":0.5491726994514465},{"id":"https://openalex.org/keywords/maximization","display_name":"Maximization","score":0.5347009897232056},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5039612650871277},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.48515042662620544},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.4568132162094116},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.4518647789955139},{"id":"https://openalex.org/keywords/markov-chain-monte-carlo","display_name":"Markov chain Monte Carlo","score":0.4288245141506195},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.4245489835739136},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.4149458408355713},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.40627825260162354},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.3960834741592407},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3791098892688751},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3394755721092224},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18319058418273926},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.12718185782432556},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1243707537651062},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12340977787971497}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6128121018409729},{"id":"https://openalex.org/C158424031","wikidata":"https://www.wikidata.org/wiki/Q1191905","display_name":"Gibbs sampling","level":3,"score":0.5491726994514465},{"id":"https://openalex.org/C2776330181","wikidata":"https://www.wikidata.org/wiki/Q18358244","display_name":"Maximization","level":2,"score":0.5347009897232056},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5039612650871277},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48515042662620544},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.4568132162094116},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.4518647789955139},{"id":"https://openalex.org/C111350023","wikidata":"https://www.wikidata.org/wiki/Q1191869","display_name":"Markov chain Monte Carlo","level":3,"score":0.4288245141506195},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.4245489835739136},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.4149458408355713},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.40627825260162354},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.3960834741592407},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3791098892688751},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3394755721092224},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18319058418273926},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.12718185782432556},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1243707537651062},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12340977787971497},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/isit.2012.6283654","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2012.6283654","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 IEEE International Symposium on Information Theory Proceedings","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","score":0.8999999761581421,"display_name":"Affordable and clean energy"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W1512303236","https://openalex.org/W1520400698","https://openalex.org/W1553031635","https://openalex.org/W1594620223","https://openalex.org/W1628027163","https://openalex.org/W1654945559","https://openalex.org/W1801773550","https://openalex.org/W1873671735","https://openalex.org/W2081455211","https://openalex.org/W2096798913","https://openalex.org/W2105570447","https://openalex.org/W2114495039","https://openalex.org/W2120340025","https://openalex.org/W2149338213","https://openalex.org/W2163450622","https://openalex.org/W2169415915","https://openalex.org/W2169991579","https://openalex.org/W2964191357","https://openalex.org/W3105113057","https://openalex.org/W3106495992","https://openalex.org/W3125447679","https://openalex.org/W4254313632","https://openalex.org/W4293052541","https://openalex.org/W4300694379","https://openalex.org/W6630598384","https://openalex.org/W6631302289","https://openalex.org/W6633066995","https://openalex.org/W6635664649","https://openalex.org/W6636654744","https://openalex.org/W6639370665","https://openalex.org/W6683632250","https://openalex.org/W6785854280"],"related_works":["https://openalex.org/W3125971950","https://openalex.org/W1580681286","https://openalex.org/W2116700007","https://openalex.org/W2175355783","https://openalex.org/W2953308468","https://openalex.org/W1579866848","https://openalex.org/W3139342328","https://openalex.org/W2622204791","https://openalex.org/W2066716418","https://openalex.org/W2905524938"],"abstract_inverted_index":{"Among":[0],"all":[1],"memoryless":[2,20],"source":[3,21],"distributions,":[4],"the":[5,12,16,30,34,60,93,105,144,154,182,195,209,218,233,243],"pattern":[6],"maximum":[7],"likelihood":[8],"(PML)":[9],"distribution":[10,13,32,184,235],"is":[11,80,126,141,200],"which":[14],"maximizes":[15,33],"probability":[17],"that":[18,111,123,131],"a":[19,23,26,37,47,52,84,89,150,188],"produces":[22],"string":[24],"with":[25,247],"given":[27],"pattern.":[28],"Equivalently,":[29],"PML":[31,183,191,234,244],"permanent":[35],"of":[36,51,62,92,198,205,230,232,242],"certain":[38],"non-negative":[39],"matrix.":[40],"We":[41],"reformulate":[42],"this":[43,63,124,167,174],"maximization":[44],"problem":[45,50,70,215],"as":[46],"double":[48],"minimization":[49,102,164],"suitable":[53],"Gibbs":[54,94,145],"free":[55,95,146,156,220],"energy":[56,96,147,157,221],"function.":[57,168],"Because":[58],"finding":[59],"minimum":[61,85],"function":[64,97,148,158],"appears":[65],"intractable":[66],"for":[67,75,194,212,251],"practically":[68,213],"relevant":[69,214],"sizes,":[71],"one":[72],"must":[73],"look":[74],"tractable":[76,151],"approximations.":[77],"One":[78,120],"approach":[79,125,140,176,211],"to":[81,128,142,160,166,181,202,225,237],"approximately":[82],"find":[83],"(or":[86,185],"at":[87,186],"least":[88,187],"local":[90],"minimum)":[91],"by":[98,114,134,149],"applying":[99],"an":[100,129,162],"alternating":[101,163],"algorithm":[103,130,165],"where":[104],"steps":[106],"are":[107,112],"based":[108],"on":[109],"quantities":[110],"obtained":[113],"Markov":[115],"chain":[116],"Monte":[117],"Carlo":[118],"sampling.":[119],"can":[121],"show":[122],"equivalent":[127],"was":[132],"proposed":[133],"Orlitsky":[135],"et":[136],"al.":[137],"An":[138],"alternative":[139],"replace":[143],"approximation":[152],"like":[153],"Bethe":[155,253],"and":[159,236],"apply":[161],"As":[169],"it":[170],"turns":[171],"out,":[172],"empirically,":[173],"latter":[175],"gives":[177],"very":[178],"good":[179],"approximations":[180],"locally":[189],"optimal":[190],"distribution),":[192],"and,":[193],"same":[196],"level":[197],"accuracy,":[199],"two":[201],"three":[203],"orders":[204],"magnitude":[206],"faster":[207],"than":[208],"former":[210],"sizes.":[216],"Moreover,":[217],"above":[219],"framework":[222],"allows":[223],"us":[224],"simplify":[226],"some":[227,239],"earlier":[228],"proofs":[229],"properties":[231,241],"derive":[238],"new":[240],"distribution,":[245],"along":[246],"obtaining":[248],"similar":[249],"results":[250],"its":[252],"approximation.":[254]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}