{"id":"https://openalex.org/W2100464897","doi":"https://doi.org/10.1109/tit.2010.2040897","title":"A Constructive Proof of the Existence of Viterbi Processes","display_name":"A Constructive Proof of the Existence of Viterbi Processes","publication_year":2010,"publication_date":"2010-03-24","ids":{"openalex":"https://openalex.org/W2100464897","doi":"https://doi.org/10.1109/tit.2010.2040897","mag":"2100464897"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2010.2040897","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2010.2040897","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/0804.2138","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"J\u00fcri Lember","orcid":null},"institutions":[{"id":"https://openalex.org/I56085075","display_name":"University of Tartu","ror":"https://ror.org/03z77qz90","country_code":"EE","type":"education","lineage":["https://openalex.org/I56085075"]}],"countries":["EE"],"is_corresponding":false,"raw_author_name":"J\u00fcri Lember","raw_affiliation_strings":["Institute of Mathematical Statistics, Tartu University, Tartu, Estonia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematical Statistics, Tartu University, Tartu, Estonia","institution_ids":["https://openalex.org/I56085075"]}]},{"author_position":"last","author":{"id":null,"display_name":"Alexey Alexandrovich Koloydenko","orcid":null},"institutions":[{"id":"https://openalex.org/I184558857","display_name":"Royal Holloway University of London","ror":"https://ror.org/04g2vpn86","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I184558857"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Alexey Alexandrovich Koloydenko","raw_affiliation_strings":["Mathematics Department of Royal Holloway, University of London, Egham, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Department of Royal Holloway, University of London, Egham, UK","institution_ids":["https://openalex.org/I184558857"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.8646,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.87967712,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"56","issue":"4","first_page":"2017","last_page":"2033"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.302700012922287,"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":0.302700012922287,"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":0.20569999516010284,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.03440000116825104,"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/viterbi-algorithm","display_name":"Viterbi algorithm","score":0.892300009727478},{"id":"https://openalex.org/keywords/iterative-viterbi-decoding","display_name":"Iterative Viterbi decoding","score":0.6798999905586243},{"id":"https://openalex.org/keywords/hidden-markov-model","display_name":"Hidden Markov model","score":0.6467000246047974},{"id":"https://openalex.org/keywords/soft-output-viterbi-algorithm","display_name":"Soft output Viterbi algorithm","score":0.5928999781608582},{"id":"https://openalex.org/keywords/forward-algorithm","display_name":"Forward algorithm","score":0.5303999781608582},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.5008999705314636},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.49309998750686646},{"id":"https://openalex.org/keywords/limiting","display_name":"Limiting","score":0.4553999900817871},{"id":"https://openalex.org/keywords/markov-model","display_name":"Markov model","score":0.4316999912261963}],"concepts":[{"id":"https://openalex.org/C60582962","wikidata":"https://www.wikidata.org/wiki/Q83886","display_name":"Viterbi algorithm","level":3,"score":0.892300009727478},{"id":"https://openalex.org/C113638808","wikidata":"https://www.wikidata.org/wiki/Q6094410","display_name":"Iterative Viterbi decoding","level":5,"score":0.6798999905586243},{"id":"https://openalex.org/C23224414","wikidata":"https://www.wikidata.org/wiki/Q176769","display_name":"Hidden Markov model","level":2,"score":0.6467000246047974},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6431999802589417},{"id":"https://openalex.org/C130319729","wikidata":"https://www.wikidata.org/wiki/Q83886","display_name":"Soft output Viterbi algorithm","level":5,"score":0.5928999781608582},{"id":"https://openalex.org/C196455857","wikidata":"https://www.wikidata.org/wiki/Q5473264","display_name":"Forward algorithm","level":5,"score":0.5303999781608582},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.5008999705314636},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4952999949455261},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.49309998750686646},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.4553999900817871},{"id":"https://openalex.org/C163836022","wikidata":"https://www.wikidata.org/wiki/Q6771326","display_name":"Markov model","level":3,"score":0.4316999912261963},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.42239999771118164},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.40529999136924744},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3741999864578247},{"id":"https://openalex.org/C2908861384","wikidata":"https://www.wikidata.org/wiki/Q203337","display_name":"Pulmonologists","level":2,"score":0.3569999933242798},{"id":"https://openalex.org/C196956702","wikidata":"https://www.wikidata.org/wiki/Q6795829","display_name":"Maximum-entropy Markov model","level":5,"score":0.3434000015258789},{"id":"https://openalex.org/C54907487","wikidata":"https://www.wikidata.org/wiki/Q7915688","display_name":"Variable-order Markov model","level":4,"score":0.3260999917984009},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3142000138759613},{"id":"https://openalex.org/C64939953","wikidata":"https://www.wikidata.org/wiki/Q3859882","display_name":"Hidden semi-Markov model","level":5,"score":0.3142000138759613},{"id":"https://openalex.org/C117379686","wikidata":"https://www.wikidata.org/wiki/Q6996459","display_name":"Viterbi decoder","level":3,"score":0.3068000078201294},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.30559998750686646},{"id":"https://openalex.org/C189973286","wikidata":"https://www.wikidata.org/wiki/Q176695","display_name":"Markov property","level":4,"score":0.3018999993801117},{"id":"https://openalex.org/C28490314","wikidata":"https://www.wikidata.org/wiki/Q189436","display_name":"Speech recognition","level":1,"score":0.2962999939918518},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.29170000553131104},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.27090001106262207},{"id":"https://openalex.org/C106666656","wikidata":"https://www.wikidata.org/wiki/Q6771323","display_name":"Markov kernel","level":5,"score":0.27079999446868896},{"id":"https://openalex.org/C163540672","wikidata":"https://www.wikidata.org/wiki/Q1115431","display_name":"Markov renewal process","level":5,"score":0.26930001378059387},{"id":"https://openalex.org/C202854965","wikidata":"https://www.wikidata.org/wiki/Q3044470","display_name":"Constructive proof","level":2,"score":0.26820001006126404},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.2680000066757202},{"id":"https://openalex.org/C79772020","wikidata":"https://www.wikidata.org/wiki/Q5159264","display_name":"Conditional independence","level":2,"score":0.26759999990463257},{"id":"https://openalex.org/C49781872","wikidata":"https://www.wikidata.org/wiki/Q1045555","display_name":"Maximum likelihood","level":2,"score":0.26589998602867126},{"id":"https://openalex.org/C98735484","wikidata":"https://www.wikidata.org/wiki/Q186971","display_name":"Time reversibility","level":5,"score":0.2567000091075897}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tit.2010.2040897","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2010.2040897","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:0804.2138","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0804.2138","pdf_url":"https://arxiv.org/pdf/0804.2138","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:0804.2138","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0804.2138","pdf_url":"https://arxiv.org/pdf/0804.2138","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1480376833","https://openalex.org/W1968668741","https://openalex.org/W1972679863","https://openalex.org/W1990005915","https://openalex.org/W1991133427","https://openalex.org/W2016813284","https://openalex.org/W2060193840","https://openalex.org/W2087284982","https://openalex.org/W2098390086","https://openalex.org/W2098958777","https://openalex.org/W2125838338","https://openalex.org/W2131119226","https://openalex.org/W2137055005","https://openalex.org/W2145834489","https://openalex.org/W2151443911","https://openalex.org/W4245668478","https://openalex.org/W4250389103","https://openalex.org/W6632107086"],"related_works":[],"abstract_inverted_index":{"Since":[0],"the":[1,96,118,125,204,218,261],"early":[2],"days":[3],"of":[4,21,99,122,171,217,263,278],"digital":[5],"communication,":[6],"hidden":[7],"Markov":[8,74],"models":[9],"(HMMs)":[10],"have":[11,211,246],"now":[12],"been":[13,212,230],"also":[14,201],"routinely":[15],"used":[16],"in":[17,26,233,267],"speech":[18],"recognition,":[19],"processing":[20],"natural":[22],"languages,":[23],"images,":[24],"and":[25,120,252,272],"bioinformatics.":[27],"In":[28],"an":[29],"HMM":[30,123],"<i":[31,38,52,59,76,83,100,109,132,139,143,149,153,160,167,172,178,184,190,195,222],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[32,35,39,42,46,53,56,60,63,77,80,84,87,101,104,110,113,133,140,144,147,150,154,157,161,164,168,173,176,179,185,188,191,196,223],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">(X</i>":[33],"<sub":[34,41,45,55,62,79,86,103,112,146,156,163,175,187],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">t</sub>":[36,43,105,114],",":[37,50,58,82,159],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">Y</i>":[40,78,85,111,174],")":[44,170],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">t":[47],"\u00bf":[48,225],"1</sub>":[49],"observations":[51],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">X</i>":[54,61,102],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">1</sub>":[57,81,158],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sub>":[64,88,165],",...":[65],"are":[66,200,256],"assumed":[67],"to":[68,117,128,214],"be":[69],"conditionally":[70],"independent":[71],"given":[72,181],"a":[73,130,236,268,274],"process":[75],",...,":[89,166],"which":[90,255],"itself":[91],"is":[92,124],"not":[93],"observed;":[94],"moreover,":[95],"conditional":[97],"distribution":[98],"depends":[106],"solely":[107],"on":[108,248],".":[115,193],"Central":[116],"theory":[119],"applications":[121],"Viterbi":[126,205,219,239,265],"algorithm":[127],"find":[129],"maximum":[131],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">a":[134,197],"posteriori</i>":[135,198],"probability":[136],"(MAP)":[137],"estimate":[138],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">v</i>":[141,155,162],"(":[142],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">x</i>":[145,186],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">1:</sub>":[148,177,189],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">T</i>":[151,180,192,224],")=(":[152],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">vT</i>":[169],"observed":[182],"data":[183],"Maximum":[194],"paths":[199],"known":[202],"as":[203],"paths,":[206],"or":[207],"alignments.":[208],"Recently,":[209],"attempts":[210,245],"made":[213],"study":[215],"behavior":[216],"alignments":[220,266],"when":[221],"\u00bf.":[226],"Thus,":[227],"it":[228],"has":[229],"shown":[231],"that":[232],"some":[234],"cases":[235],"well-defined":[237],"limiting":[238],"alignment":[240],"exists.":[241],"While":[242],"innovative,":[243],"these":[244],"relied":[247],"rather":[249],"strong":[250],"assumptions":[251],"involved":[253],"proofs":[254],"existential.":[257],"This":[258],"work":[259],"proves":[260],"existence":[262],"infinite":[264],"more":[269],"constructive":[270],"manner":[271],"for":[273],"very":[275],"general":[276],"class":[277],"HMMs.":[279]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2016-06-24T00:00:00"}