{"id":"https://openalex.org/W7128630271","doi":"https://doi.org/10.1109/tit.2026.3663652","title":"The AEP for Hidden Markov Tree Models","display_name":"The AEP for Hidden Markov Tree Models","publication_year":2026,"publication_date":"2026-02-11","ids":{"openalex":"https://openalex.org/W7128630271","doi":"https://doi.org/10.1109/tit.2026.3663652"},"language":null,"primary_location":{"id":"doi:10.1109/tit.2026.3663652","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2026.3663652","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/A5075097635","display_name":"Zhiyan Shi","orcid":"https://orcid.org/0000-0002-3190-8121"},"institutions":[{"id":"https://openalex.org/I115592961","display_name":"Jiangsu University","ror":"https://ror.org/03jc41j30","country_code":"CN","type":"education","lineage":["https://openalex.org/I115592961"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhiyan Shi","raw_affiliation_strings":["School of Mathematical Sciences, Jiangsu University, Zhenjiang, China"],"raw_orcid":"https://orcid.org/0000-0002-3190-8121","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Jiangsu University, Zhenjiang, China","institution_ids":["https://openalex.org/I115592961"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5125661232","display_name":"Fan Xie","orcid":null},"institutions":[{"id":"https://openalex.org/I115592961","display_name":"Jiangsu University","ror":"https://ror.org/03jc41j30","country_code":"CN","type":"education","lineage":["https://openalex.org/I115592961"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Fan Xie","raw_affiliation_strings":["School of Mathematical Sciences, Jiangsu University, Zhenjiang, China"],"raw_orcid":"https://orcid.org/0009-0009-2629-8400","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Jiangsu University, Zhenjiang, China","institution_ids":["https://openalex.org/I115592961"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5125678433","display_name":"Bao Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I124841900","display_name":"Xuzhou University of Technology","ror":"https://ror.org/02315by94","country_code":"CN","type":"education","lineage":["https://openalex.org/I124841900"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bao Wang","raw_affiliation_strings":["School of Mathematics and Statistics, Xuzhou University of Technology, Xuzhou, China"],"raw_orcid":"https://orcid.org/0000-0001-7610-2001","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Xuzhou University of Technology, Xuzhou, China","institution_ids":["https://openalex.org/I124841900"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110165908","display_name":"Weiguo Yang","orcid":null},"institutions":[{"id":"https://openalex.org/I115592961","display_name":"Jiangsu University","ror":"https://ror.org/03jc41j30","country_code":"CN","type":"education","lineage":["https://openalex.org/I115592961"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Weiguo Yang","raw_affiliation_strings":["School of Mathematical Sciences, Jiangsu University, Zhenjiang, China"],"raw_orcid":"https://orcid.org/0000-0002-5312-0749","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Jiangsu University, Zhenjiang, China","institution_ids":["https://openalex.org/I115592961"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.18774091,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"72","issue":"4","first_page":"2029","last_page":"2042"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.2727000117301941,"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/T11269","display_name":"Algorithms and Data Compression","score":0.2727000117301941,"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/T11720","display_name":"Probability and Risk Models","score":0.08380000293254852,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.06939999759197235,"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/markov-chain","display_name":"Markov chain","score":0.7046999931335449},{"id":"https://openalex.org/keywords/variable-order-markov-model","display_name":"Variable-order Markov model","score":0.694100022315979},{"id":"https://openalex.org/keywords/hidden-semi-markov-model","display_name":"Hidden semi-Markov model","score":0.6898000240325928},{"id":"https://openalex.org/keywords/hidden-markov-model","display_name":"Hidden Markov model","score":0.6453999876976013},{"id":"https://openalex.org/keywords/markov-property","display_name":"Markov property","score":0.5934000015258789},{"id":"https://openalex.org/keywords/markov-model","display_name":"Markov model","score":0.5569000244140625},{"id":"https://openalex.org/keywords/maximum-entropy-markov-model","display_name":"Maximum-entropy Markov model","score":0.5346999764442444},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.5338000059127808}],"concepts":[{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.7046999931335449},{"id":"https://openalex.org/C54907487","wikidata":"https://www.wikidata.org/wiki/Q7915688","display_name":"Variable-order Markov model","level":4,"score":0.694100022315979},{"id":"https://openalex.org/C64939953","wikidata":"https://www.wikidata.org/wiki/Q3859882","display_name":"Hidden semi-Markov model","level":5,"score":0.6898000240325928},{"id":"https://openalex.org/C23224414","wikidata":"https://www.wikidata.org/wiki/Q176769","display_name":"Hidden Markov model","level":2,"score":0.6453999876976013},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6158000230789185},{"id":"https://openalex.org/C189973286","wikidata":"https://www.wikidata.org/wiki/Q176695","display_name":"Markov property","level":4,"score":0.5934000015258789},{"id":"https://openalex.org/C163836022","wikidata":"https://www.wikidata.org/wiki/Q6771326","display_name":"Markov model","level":3,"score":0.5569000244140625},{"id":"https://openalex.org/C196956702","wikidata":"https://www.wikidata.org/wiki/Q6795829","display_name":"Maximum-entropy Markov model","level":5,"score":0.5346999764442444},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.5338000059127808},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.5235000252723694},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4083999991416931},{"id":"https://openalex.org/C106666656","wikidata":"https://www.wikidata.org/wiki/Q6771323","display_name":"Markov kernel","level":5,"score":0.3637999892234802},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.35440000891685486},{"id":"https://openalex.org/C81081738","wikidata":"https://www.wikidata.org/wiki/Q55542","display_name":"Lossless compression","level":3,"score":0.35089999437332153},{"id":"https://openalex.org/C196455857","wikidata":"https://www.wikidata.org/wiki/Q5473264","display_name":"Forward algorithm","level":5,"score":0.3402999937534332},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3206000030040741},{"id":"https://openalex.org/C185767445","wikidata":"https://www.wikidata.org/wiki/Q207952","display_name":"Law of large numbers","level":3,"score":0.3125},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.30489999055862427},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.2808000147342682},{"id":"https://openalex.org/C163797641","wikidata":"https://www.wikidata.org/wiki/Q2067937","display_name":"Tree structure","level":3,"score":0.2718999981880188},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.2639999985694885},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.25679999589920044}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2026.3663652","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2026.3663652","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":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.8227832913398743}],"awards":[{"id":"https://openalex.org/G2186764255","display_name":"\u534a\u9a6c\u5c14\u53ef\u592b\u5207\u6362\u7cfb\u7edf\u7684\u7a33\u5b9a\u6027\u5206\u6790\u53ca\u5176\u9547\u5b9a\u63a7\u5236\u5668\u8bbe\u8ba1\u95ee\u9898\u7684\u7814\u7a76","funder_award_id":"12071408","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3100071003","display_name":"\u5173\u4e8e\u6811\u6307\u6807\u968f\u673a\u8fc7\u7a0b\u6781\u9650\u7406\u8bba\u7684\u8fdb\u4e00\u6b65\u7814\u7a76","funder_award_id":"11571142","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3388539572","display_name":null,"funder_award_id":"12071408,11601191,11571142","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5961068545","display_name":null,"funder_award_id":"11601191","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0],"asymptotic":[1,16],"equipartition":[2],"property":[3],"(AEP)":[4],"plays":[5],"an":[6],"important":[7],"role":[8],"in":[9,28],"establishing":[10],"lossless":[11],"source":[12],"coding":[13,17],"theorems":[14,18],"and":[15,25,43,62,67,94,130],"through":[19],"the":[20,37,44,80,88,128,131],"concepts":[21],"of":[22,40,57,90,104,124],"typical":[23,26],"sets":[24],"sequences":[27],"information":[29],"theory.":[30],"In":[31,70],"this":[32],"paper,":[33],"we":[34,52,85,119],"shall":[35],"study":[36,63],"strong":[38,102,122],"law":[39,103],"large":[41,105,125],"numbers":[42,106,126],"AEP":[45,132],"for":[46,107,127,133],"hidden":[47,58,72,108],"Markov":[48,59,73,82,92,109],"tree":[49,60,74,110],"models.":[50,135],"First,":[51],"give":[53],"a":[54,101,114],"strict":[55],"definition":[56,89],"models,":[61],"their":[64,95],"key":[65],"properties":[66],"equivalent":[68,96],"characterizations.":[69],"fact,":[71],"models":[75,111],"are":[76],"closely":[77],"related":[78],"to":[79],"tree-indexed":[81,91],"chains,":[83],"therefore,":[84],"also":[86,99],"introduce":[87],"chains":[93],"properties.":[97],"We":[98],"establish":[100],"indexed":[112],"by":[113],"Cayley":[115],"tree.":[116],"As":[117],"corollaries,":[118],"obtain":[120],"some":[121],"laws":[123],"parameters":[129],"these":[134]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-02-12T00:00:00"}
