{"id":"https://openalex.org/W2181874702","doi":null,"title":"Bounds on Convergence of Entropy Rate Approximations in Hidden Markov Processes","display_name":"Bounds on Convergence of Entropy Rate Approximations in Hidden Markov Processes","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2181874702","mag":"2181874702"},"language":"en","primary_location":{"id":"mag:2181874702","doi":null,"is_oa":false,"landing_page_url":"http://csc.ucdavis.edu/~cmg/papers/Travers.UCDPhDDissertation2013.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null},"volume":null,"type":"article","is_traditional":true,"indexed_in":[],"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/A5072571608","display_name":"Nicholas F. Travers","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Nicholas F. Travers","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5072571608"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3488,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.48502674,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.7890999913215637,"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"}},"topics":[{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.7890999913215637,"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"}},{"id":"https://openalex.org/T13500","display_name":"Probability and Statistical Research","score":0.11630000174045563,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.01209999993443489,"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/entropy-rate","display_name":"entropy rate","score":0.7749999761581421},{"id":"https://openalex.org/keywords/hidden-markov-processes","display_name":"hidden Markov processes","score":0.9419999718666077},{"id":"https://openalex.org/keywords/convergence-rate","display_name":"convergence rate","score":0.8700000047683716},{"id":"https://openalex.org/keywords/exponential-bounds","display_name":"exponential bounds","score":0.9610000252723694},{"id":"https://openalex.org/keywords/state-uncertainty","display_name":"state uncertainty","score":0.7179999947547913}],"concepts":[{"id":"https://openalex.org/C196956702","wikidata":"https://www.wikidata.org/wiki/Q6795829","display_name":"Maximum-entropy Markov model","level":5,"score":0.7341238260269165},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7247956991195679},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.6303814053535461},{"id":"https://openalex.org/C64939953","wikidata":"https://www.wikidata.org/wiki/Q3859882","display_name":"Hidden semi-Markov model","level":5,"score":0.5617703795433044},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5581933856010437},{"id":"https://openalex.org/C125252325","wikidata":"https://www.wikidata.org/wiki/Q1345213","display_name":"Entropy rate","level":4,"score":0.5560956597328186},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.550254762172699},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5495898723602295},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5473402738571167},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5098335146903992},{"id":"https://openalex.org/C2983497884","wikidata":"https://www.wikidata.org/wiki/Q176452","display_name":"Finite state","level":3,"score":0.5023422241210938},{"id":"https://openalex.org/C23224414","wikidata":"https://www.wikidata.org/wiki/Q176769","display_name":"Hidden Markov model","level":2,"score":0.49677878618240356},{"id":"https://openalex.org/C163836022","wikidata":"https://www.wikidata.org/wiki/Q6771326","display_name":"Markov model","level":3,"score":0.495065838098526},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.46667349338531494},{"id":"https://openalex.org/C54907487","wikidata":"https://www.wikidata.org/wiki/Q7915688","display_name":"Variable-order Markov model","level":4,"score":0.43656036257743835},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.30317747592926025},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.17519009113311768},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17335990071296692},{"id":"https://openalex.org/C42047476","wikidata":"https://www.wikidata.org/wiki/Q6269544","display_name":"Joint quantum entropy","level":3,"score":0.15018102526664734},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10283428430557251},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09582185745239258},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:2181874702","doi":null,"is_oa":false,"landing_page_url":"http://csc.ucdavis.edu/~cmg/papers/Travers.UCDPhDDissertation2013.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W343139067","https://openalex.org/W580721429","https://openalex.org/W1484162783","https://openalex.org/W1532729789","https://openalex.org/W1551871633","https://openalex.org/W1600293573","https://openalex.org/W1919897963","https://openalex.org/W1966812932","https://openalex.org/W1970934692","https://openalex.org/W1986806140","https://openalex.org/W1990005915","https://openalex.org/W1990693325","https://openalex.org/W1995875735","https://openalex.org/W1997136004","https://openalex.org/W2002089154","https://openalex.org/W2003333103","https://openalex.org/W2007171567","https://openalex.org/W2013570924","https://openalex.org/W2013713816","https://openalex.org/W2043017246","https://openalex.org/W2048102092","https://openalex.org/W2048917793","https://openalex.org/W2057967605","https://openalex.org/W2059120410","https://openalex.org/W2075694080","https://openalex.org/W2082040833","https://openalex.org/W2084699771","https://openalex.org/W2099111195","https://openalex.org/W2115561524","https://openalex.org/W2124330979","https://openalex.org/W2125838338","https://openalex.org/W2126785155","https://openalex.org/W2128372030","https://openalex.org/W2140244239","https://openalex.org/W2151831732","https://openalex.org/W2157721994","https://openalex.org/W2166444569","https://openalex.org/W3105388688","https://openalex.org/W3105400922"],"related_works":["https://openalex.org/W2399691027","https://openalex.org/W2003278395","https://openalex.org/W2233956239","https://openalex.org/W7070745405","https://openalex.org/W2171143576","https://openalex.org/W2558641687","https://openalex.org/W1648275766","https://openalex.org/W7100168388","https://openalex.org/W2127434124","https://openalex.org/W2390431850"],"abstract_inverted_index":{"There":[0],"is":[1],"no":[2],"general":[3],"closed":[4],"form":[5],"expression":[6],"for":[7,46],"the":[8,17,26,38,43,63,76,82],"entropy":[9,28],"rate":[10,29,39],"of":[11,40,42,65,81],"a":[12,59],"hidden":[13,48,67],"Markov":[14,49,68],"process.":[15],"However,":[16],"finite":[18,47],"length":[19],"block":[20,44],"estimates":[21,45],"h(t)":[22],"often":[23],"converge":[24],"to":[25],"true":[27],"h":[30],"quite":[31],"rapidly.":[32],"We":[33],"establish":[34],"exponential":[35,73],"bounds":[36,74],"on":[37,75],"convergence":[41],"models":[50],"under":[51],"several":[52],"different":[53],"conditions,":[54],"including":[55],"exactness,":[56],"unifilarity,":[57],"and":[58,78],"flag-state":[60],"condition.":[61],"In":[62],"case":[64],"unifilar":[66],"models,":[69],"we":[70],"also":[71],"give":[72],"L1":[77],"a.s.":[79],"decay":[80],"state":[83],"uncertainty":[84],"Ut.":[85]},"counts_by_year":[{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}