{"id":"https://openalex.org/W4395069926","doi":"https://doi.org/10.1109/tit.2024.3392983","title":"Kullback-Leibler Divergence and Akaike Information Criterion in General Hidden Markov Models","display_name":"Kullback-Leibler Divergence and Akaike Information Criterion in General Hidden Markov Models","publication_year":2024,"publication_date":"2024-04-24","ids":{"openalex":"https://openalex.org/W4395069926","doi":"https://doi.org/10.1109/tit.2024.3392983"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2024.3392983","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2024.3392983","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":["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/A5032872987","display_name":"Cheng\u2013Der Fuh","orcid":"https://orcid.org/0000-0003-4174-528X"},"institutions":[{"id":"https://openalex.org/I22265921","display_name":"National Central University","ror":"https://ror.org/00944ve71","country_code":"TW","type":"education","lineage":["https://openalex.org/I22265921"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Cheng-Der Fuh","raw_affiliation_strings":["Graduate Institute of Statistics, National Central University, Taoyuan City, Taiwan"],"raw_orcid":"https://orcid.org/0000-0003-4174-528X","affiliations":[{"raw_affiliation_string":"Graduate Institute of Statistics, National Central University, Taoyuan City, Taiwan","institution_ids":["https://openalex.org/I22265921"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049103599","display_name":"Chu-Lan Michael Kao","orcid":"https://orcid.org/0000-0001-8091-9946"},"institutions":[{"id":"https://openalex.org/I148366613","display_name":"National Yang Ming Chiao Tung University","ror":"https://ror.org/00se2k293","country_code":"TW","type":"education","lineage":["https://openalex.org/I148366613"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Chu-Lan Michael Kao","raw_affiliation_strings":["Institute of Statistics, National Yang Ming Chiao Tung University, Hsinchu, Taiwan"],"raw_orcid":"https://orcid.org/0000-0001-8091-9946","affiliations":[{"raw_affiliation_string":"Institute of Statistics, National Yang Ming Chiao Tung University, Hsinchu, Taiwan","institution_ids":["https://openalex.org/I148366613"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020164576","display_name":"Tianxiao Pang","orcid":null},"institutions":[{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tianxiao Pang","raw_affiliation_strings":["School of Mathematical Sciences, Zhejiang University, Hangzhou, China"],"raw_orcid":"https://orcid.org/0000-0002-0271-8070","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Zhejiang University, Hangzhou, China","institution_ids":["https://openalex.org/I76130692"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.5471,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.92996586,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"70","issue":"8","first_page":"5888","last_page":"5909"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10282","display_name":"Financial Risk and Volatility Modeling","score":0.9879999756813049,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10282","display_name":"Financial Risk and Volatility Modeling","score":0.9879999756813049,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9858999848365784,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9663000106811523,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/akaike-information-criterion","display_name":"Akaike information criterion","score":0.9528887271881104},{"id":"https://openalex.org/keywords/kullback\u2013leibler-divergence","display_name":"Kullback\u2013Leibler divergence","score":0.6735612154006958},{"id":"https://openalex.org/keywords/bayesian-information-criterion","display_name":"Bayesian information criterion","score":0.637170135974884},{"id":"https://openalex.org/keywords/hidden-markov-model","display_name":"Hidden Markov model","score":0.5925415754318237},{"id":"https://openalex.org/keywords/divergence","display_name":"Divergence (linguistics)","score":0.566108226776123},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5376677513122559},{"id":"https://openalex.org/keywords/maximum-entropy-markov-model","display_name":"Maximum-entropy Markov model","score":0.5032336115837097},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.48861104249954224},{"id":"https://openalex.org/keywords/information-theory","display_name":"Information theory","score":0.4359922707080841},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.4305015504360199},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.4252348244190216},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.37452080845832825},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.35732001066207886},{"id":"https://openalex.org/keywords/variable-order-markov-model","display_name":"Variable-order Markov model","score":0.3517765402793884},{"id":"https://openalex.org/keywords/markov-model","display_name":"Markov model","score":0.3219696581363678}],"concepts":[{"id":"https://openalex.org/C126674687","wikidata":"https://www.wikidata.org/wiki/Q1662573","display_name":"Akaike information criterion","level":2,"score":0.9528887271881104},{"id":"https://openalex.org/C171752962","wikidata":"https://www.wikidata.org/wiki/Q255166","display_name":"Kullback\u2013Leibler divergence","level":2,"score":0.6735612154006958},{"id":"https://openalex.org/C168136583","wikidata":"https://www.wikidata.org/wiki/Q1988242","display_name":"Bayesian information criterion","level":2,"score":0.637170135974884},{"id":"https://openalex.org/C23224414","wikidata":"https://www.wikidata.org/wiki/Q176769","display_name":"Hidden Markov model","level":2,"score":0.5925415754318237},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.566108226776123},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5376677513122559},{"id":"https://openalex.org/C196956702","wikidata":"https://www.wikidata.org/wiki/Q6795829","display_name":"Maximum-entropy Markov model","level":5,"score":0.5032336115837097},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.48861104249954224},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.4359922707080841},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.4305015504360199},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.4252348244190216},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37452080845832825},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.35732001066207886},{"id":"https://openalex.org/C54907487","wikidata":"https://www.wikidata.org/wiki/Q7915688","display_name":"Variable-order Markov model","level":4,"score":0.3517765402793884},{"id":"https://openalex.org/C163836022","wikidata":"https://www.wikidata.org/wiki/Q6771326","display_name":"Markov model","level":3,"score":0.3219696581363678},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2024.3392983","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2024.3392983","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"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.44999998807907104,"display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G5967223684","display_name":null,"funder_award_id":"21BTJ067","funder_id":"https://openalex.org/F4320309617","funder_display_name":"National Foundation for Science and Technology Development"}],"funders":[{"id":"https://openalex.org/F4320309617","display_name":"National Foundation for Science and Technology Development","ror":"https://ror.org/04rw64z44"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":81,"referenced_works":["https://openalex.org/W191281745","https://openalex.org/W1460189015","https://openalex.org/W1494941221","https://openalex.org/W1498046895","https://openalex.org/W1511694993","https://openalex.org/W1549809545","https://openalex.org/W1582706191","https://openalex.org/W1814500939","https://openalex.org/W1877414726","https://openalex.org/W1952343817","https://openalex.org/W1963566461","https://openalex.org/W1964143678","https://openalex.org/W1968668741","https://openalex.org/W1969223366","https://openalex.org/W1969570435","https://openalex.org/W1979575715","https://openalex.org/W1983722334","https://openalex.org/W1989113356","https://openalex.org/W1989549063","https://openalex.org/W1999538266","https://openalex.org/W1999996900","https://openalex.org/W2002644365","https://openalex.org/W2003333103","https://openalex.org/W2003867767","https://openalex.org/W2014378975","https://openalex.org/W2016529189","https://openalex.org/W2018672889","https://openalex.org/W2036525176","https://openalex.org/W2040478633","https://openalex.org/W2040526455","https://openalex.org/W2050352677","https://openalex.org/W2051235503","https://openalex.org/W2058815839","https://openalex.org/W2067145764","https://openalex.org/W2070047061","https://openalex.org/W2074812030","https://openalex.org/W2100495367","https://openalex.org/W2100877547","https://openalex.org/W2102716594","https://openalex.org/W2106038542","https://openalex.org/W2107935927","https://openalex.org/W2108470768","https://openalex.org/W2113651262","https://openalex.org/W2135582882","https://openalex.org/W2142635246","https://openalex.org/W2154421872","https://openalex.org/W2157403008","https://openalex.org/W2157895285","https://openalex.org/W2167055467","https://openalex.org/W2167191107","https://openalex.org/W2168730720","https://openalex.org/W2343136344","https://openalex.org/W2740178324","https://openalex.org/W2922422128","https://openalex.org/W2963786555","https://openalex.org/W3080277066","https://openalex.org/W3092633408","https://openalex.org/W3096602043","https://openalex.org/W3101593467","https://openalex.org/W3102220006","https://openalex.org/W3104447373","https://openalex.org/W3126140609","https://openalex.org/W3158131114","https://openalex.org/W3211649212","https://openalex.org/W4229628595","https://openalex.org/W4237712828","https://openalex.org/W4238519965","https://openalex.org/W4240987968","https://openalex.org/W4245655784","https://openalex.org/W4246784033","https://openalex.org/W4250206648","https://openalex.org/W4253944844","https://openalex.org/W4299325215","https://openalex.org/W4302617909","https://openalex.org/W4306738487","https://openalex.org/W6607775107","https://openalex.org/W6617744952","https://openalex.org/W6630191598","https://openalex.org/W6639497327","https://openalex.org/W6679825673","https://openalex.org/W6704161820"],"related_works":["https://openalex.org/W1566728629","https://openalex.org/W2617987378","https://openalex.org/W2509820422","https://openalex.org/W1502087262","https://openalex.org/W3187368641","https://openalex.org/W2626271282","https://openalex.org/W3122388856","https://openalex.org/W1946191587","https://openalex.org/W2088726129","https://openalex.org/W1998988312"],"abstract_inverted_index":{"To":[0],"characterize":[1],"the":[2,21,68,74,79],"Kullback-Leibler":[3,56],"divergence":[4,57],"and":[5,24,40,78,136],"Fisher":[6,69],"information":[7,103],"in":[8,14,108],"general":[9,109],"parametrized":[10],"hidden":[11,110],"Markov":[12,111],"models,":[13],"this":[15,50],"paper,":[16],"we":[17,53,95,114],"first":[18],"show":[19,54],"that":[20,55],"log":[22],"likelihood":[23],"its":[25],"derivatives":[26],"can":[27,58],"be":[28,59],"represented":[29],"as":[30],"an":[31,90],"additive":[32],"functional":[33],"of":[34,45,92,100,125],"a":[35,63,97,119],"Markovian":[36],"iterated":[37],"function":[38,65],"system,":[39],"then":[41],"provide":[42,96],"explicit":[43],"characterizations":[44],"these":[46],"two":[47],"quantities":[48],"through":[49],"representation.":[51],"Moreover,":[52],"locally":[60],"approximated":[61],"by":[62,67],"quadratic":[64],"determined":[66],"information.":[70],"Results":[71],"relating":[72],"to":[73,141],"Cram\u00e9r-Rao":[75],"lower":[76],"bound":[77],"H\u00e1jek-Le":[80],"Cam":[81],"local":[82],"asymptotic":[83],"minimax":[84],"theorem":[85],"are":[86],"also":[87],"given.":[88],"As":[89],"application":[91],"our":[93,143],"results,":[94],"theoretical":[98],"justification":[99],"using":[101],"Akaike":[102],"criterion":[104],"(AIC)":[105],"model":[106,124],"selection":[107],"models.":[112],"Last,":[113],"study":[115],"three":[116],"concrete":[117],"models:":[118],"Gaussian":[120],"vector":[121],"autoregressive-moving":[122],"average":[123],"order":[126],"<inline-formula":[127],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[128],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[129],"<tex-math":[130],"notation=\"LaTeX\">$(p,q)$":[131],"</tex-math></inline-formula>,":[132],"recurrent":[133],"neural":[134],"networks,":[135],"temporal":[137],"restricted":[138],"Boltzmann":[139],"machine,":[140],"illustrate":[142],"theory.":[144]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
