{"id":"https://openalex.org/W2159403046","doi":"https://doi.org/10.1109/tit.2014.2334594","title":"Stationary and Transition Probabilities in Slow Mixing, Long Memory Markov Processes","display_name":"Stationary and Transition Probabilities in Slow Mixing, Long Memory Markov Processes","publication_year":2014,"publication_date":"2014-07-30","ids":{"openalex":"https://openalex.org/W2159403046","doi":"https://doi.org/10.1109/tit.2014.2334594","mag":"2159403046"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2014.2334594","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2014.2334594","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1301.6798","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5061425259","display_name":"Meysam Asadi","orcid":"https://orcid.org/0000-0003-1885-2802"},"institutions":[{"id":"https://openalex.org/I117965899","display_name":"University of Hawai\u02bbi at M\u0101noa","ror":"https://ror.org/01wspgy28","country_code":"US","type":"education","lineage":["https://openalex.org/I117965899"]},{"id":"https://openalex.org/I1331384533","display_name":"University of Hawaii System","ror":"https://ror.org/03tzaeb71","country_code":"US","type":"education","lineage":["https://openalex.org/I1331384533"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Meysam Asadi","raw_affiliation_strings":["Department of Electrical Engineering, University of Hawaii at M\u0101noa, Honolulu, HI, USA","Department of Electrical Engineering, University of Hawaii at M\u00bfnoa, Honolulu, HI, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Hawaii at M\u0101noa, Honolulu, HI, USA","institution_ids":["https://openalex.org/I117965899"]},{"raw_affiliation_string":"Department of Electrical Engineering, University of Hawaii at M\u00bfnoa, Honolulu, HI, USA","institution_ids":["https://openalex.org/I1331384533"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040578754","display_name":"Ramezan Paravi Torghabeh","orcid":null},"institutions":[{"id":"https://openalex.org/I117965899","display_name":"University of Hawai\u02bbi at M\u0101noa","ror":"https://ror.org/01wspgy28","country_code":"US","type":"education","lineage":["https://openalex.org/I117965899"]},{"id":"https://openalex.org/I1331384533","display_name":"University of Hawaii System","ror":"https://ror.org/03tzaeb71","country_code":"US","type":"education","lineage":["https://openalex.org/I1331384533"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ramezan Paravi Torghabeh","raw_affiliation_strings":["Department of Electrical Engineering, University of Hawaii at M\u0101noa, Honolulu, HI, USA","Department of Electrical Engineering, University of Hawaii at M\u00bfnoa, Honolulu, HI, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Hawaii at M\u0101noa, Honolulu, HI, USA","institution_ids":["https://openalex.org/I117965899"]},{"raw_affiliation_string":"Department of Electrical Engineering, University of Hawaii at M\u00bfnoa, Honolulu, HI, USA","institution_ids":["https://openalex.org/I1331384533"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030506196","display_name":"Narayana Santhanam","orcid":"https://orcid.org/0000-0001-6515-6311"},"institutions":[{"id":"https://openalex.org/I117965899","display_name":"University of Hawai\u02bbi at M\u0101noa","ror":"https://ror.org/01wspgy28","country_code":"US","type":"education","lineage":["https://openalex.org/I117965899"]},{"id":"https://openalex.org/I1331384533","display_name":"University of Hawaii System","ror":"https://ror.org/03tzaeb71","country_code":"US","type":"education","lineage":["https://openalex.org/I1331384533"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Narayana P. Santhanam","raw_affiliation_strings":["Department of Electrical Engineering, University of Hawaii at M\u0101noa, Honolulu, HI, USA","Department of Electrical Engineering, University of Hawaii at M\u00bfnoa, Honolulu, HI, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Hawaii at M\u0101noa, Honolulu, HI, USA","institution_ids":["https://openalex.org/I117965899"]},{"raw_affiliation_string":"Department of Electrical Engineering, University of Hawaii at M\u00bfnoa, Honolulu, HI, USA","institution_ids":["https://openalex.org/I1331384533"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4229,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.76390942,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"60","issue":"9","first_page":"5682","last_page":"5701"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9998999834060669,"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":0.9998999834060669,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9980999827384949,"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/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9954000115394592,"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/pointwise","display_name":"Pointwise","score":0.7387378811836243},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7278910279273987},{"id":"https://openalex.org/keywords/ergodic-theory","display_name":"Ergodic theory","score":0.6804690361022949},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5871182680130005},{"id":"https://openalex.org/keywords/mixing","display_name":"Mixing (physics)","score":0.5496564507484436},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.5493627190589905},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.5164783000946045},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3815554976463318},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.3007570207118988},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13913652300834656},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11224979162216187}],"concepts":[{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.7387378811836243},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7278910279273987},{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.6804690361022949},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5871182680130005},{"id":"https://openalex.org/C138777275","wikidata":"https://www.wikidata.org/wiki/Q6884054","display_name":"Mixing (physics)","level":2,"score":0.5496564507484436},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.5493627190589905},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.5164783000946045},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3815554976463318},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3007570207118988},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13913652300834656},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11224979162216187},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tit.2014.2334594","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2014.2334594","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:1301.6798","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1301.6798","pdf_url":"https://arxiv.org/pdf/1301.6798","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"},{"id":"mag:2159403046","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1301.6798v17","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1301.6798","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1301.6798","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1301.6798","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1301.6798","pdf_url":"https://arxiv.org/pdf/1301.6798","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":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2159403046.pdf","grobid_xml":"https://content.openalex.org/works/W2159403046.grobid-xml"},"referenced_works_count":52,"referenced_works":["https://openalex.org/W620844811","https://openalex.org/W1520752616","https://openalex.org/W1600293573","https://openalex.org/W1664909932","https://openalex.org/W1666830255","https://openalex.org/W1928112489","https://openalex.org/W1976625337","https://openalex.org/W1987149108","https://openalex.org/W1995713768","https://openalex.org/W1999120268","https://openalex.org/W2002411654","https://openalex.org/W2011485152","https://openalex.org/W2019848345","https://openalex.org/W2053807426","https://openalex.org/W2064975723","https://openalex.org/W2075672181","https://openalex.org/W2081839404","https://openalex.org/W2082092506","https://openalex.org/W2082967074","https://openalex.org/W2095963120","https://openalex.org/W2099111195","https://openalex.org/W2103396489","https://openalex.org/W2105342805","https://openalex.org/W2117090766","https://openalex.org/W2120379926","https://openalex.org/W2122133429","https://openalex.org/W2122962290","https://openalex.org/W2127323309","https://openalex.org/W2128741289","https://openalex.org/W2129902114","https://openalex.org/W2132119275","https://openalex.org/W2139789442","https://openalex.org/W2145380376","https://openalex.org/W2151835418","https://openalex.org/W2153942802","https://openalex.org/W2156427364","https://openalex.org/W2162863295","https://openalex.org/W2163294786","https://openalex.org/W2164783098","https://openalex.org/W2165808853","https://openalex.org/W2168256531","https://openalex.org/W2170352625","https://openalex.org/W2295428206","https://openalex.org/W2751862591","https://openalex.org/W2767593714","https://openalex.org/W3099153942","https://openalex.org/W4231916799","https://openalex.org/W4238893454","https://openalex.org/W4302617909","https://openalex.org/W4388297583","https://openalex.org/W4389015749","https://openalex.org/W6631192789"],"related_works":["https://openalex.org/W2949671275","https://openalex.org/W1488373927","https://openalex.org/W2890375136","https://openalex.org/W3101351113","https://openalex.org/W3136232832","https://openalex.org/W2059370436","https://openalex.org/W2127090196","https://openalex.org/W2417853429","https://openalex.org/W2141753389","https://openalex.org/W2136693436","https://openalex.org/W3125257211","https://openalex.org/W1993028513","https://openalex.org/W3123384377","https://openalex.org/W2489225089","https://openalex.org/W2302408044","https://openalex.org/W2891986369","https://openalex.org/W2769916088","https://openalex.org/W2101985079","https://openalex.org/W2018157723","https://openalex.org/W3119282993"],"abstract_inverted_index":{"We":[0],"observe":[1],"a":[2,15,113,126,145,151,206],"length-n":[3,127,207],"sample":[4,98,114,128,225],"generated":[5],"by":[6],"an":[7,132],"unknown,":[8],"stationary":[9,43,247],"ergodic":[10,89],"Markov":[11,90],"process":[12],"(model)":[13],"over":[14,84],"finite":[16],"alphabet":[17],"A.":[18],"Given":[19],"any":[20,94,97],"string":[21],"w":[22],"of":[23,30,35,45,72,87,115,183,237,256],"symbols":[24,36],"from":[25,260],"A":[26],"we":[27,123,199,218],"want":[28,200],"estimates":[29,169,236,243,259],"the":[31,42,85,101,108,140,181,201,223,238,246,254,257],"conditional":[32,239],"probability":[33,44],"distribution":[34],"following":[37],"w,":[38],"as":[39,41,180],"well":[40],"w.":[46],"Two":[47],"distinct":[48],"problems":[49],"that":[50,107,170],"complicate":[51],"estimation":[52],"in":[53,77,191,211],"this":[54,78],"setting":[55,79],"are:":[56],"1)":[57,235],"long":[58,179],"memory":[59,141,156],"and":[60,96,129,241,251],"2)":[61,242],"slow":[62,228],"mixing,":[63],"which":[64],"could":[65,104],"happen":[66],"even":[67],"with":[68,118,155,205,214],"only":[69,81],"one":[70],"bit":[71],"memory.":[73],"Any":[74],"consistent":[75,168],"estimator":[76,95,109],"can":[80,122],"converge":[82],"pointwise":[83,167],"class":[86],"all":[88],"models.":[91],"Namely,":[92],"given":[93],"size":[99,116],"n,":[100],"underlying":[102],"model":[103,154],"be":[105,137],"such":[106],"performs":[110],"poorly":[111],"on":[112,222],"n":[117,165],"high":[119],"probability.":[120],"But":[121],"look":[124],"at":[125],"identify":[130,232],"if":[131],"estimate":[133,150],"is":[134,142,148,188],"likely":[135],"to":[136,149,231,245],"accurate?":[138],"Since":[139],"unknown":[143],"a-priori,":[144],"natural":[146],"approach":[147],"potentially":[152],"coarser":[153],"k":[157,184],"<sub":[158,185],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[159,186],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n</sub>":[160,187],"=":[161],"O(log":[162],"n).":[163],"As":[164],"grows,":[166],"hold":[171],"eventually":[172],"almost":[173],"surely":[174],"(e.a.s.)":[175],"are":[176,249],"known":[177],"so":[178],"scaling":[182],"not":[189],"superlogarithmic":[190],"n.":[192],"Here,":[193],"rather":[194],"than":[195],"e.a.s.":[196],"convergence":[197],"results,":[198],"best":[202],"answers":[203],"possible":[204],"sample.":[208],"Combining":[209],"results":[210],"universal":[212],"compression":[213],"Aldous'":[215],"coupling":[216],"arguments,":[217],"obtain":[219],"sufficient":[220],"conditions":[221],"lengthn":[224],"(even":[226],"for":[227],"mixing":[229],"models)":[230],"when":[233],"naive:":[234],"probabilities":[240,248],"related":[244],"accurate,":[250],"also":[252],"bound":[253],"deviations":[255],"naive":[258],"true":[261],"values.":[262]},"counts_by_year":[{"year":2014,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2022-10-01T00:00:00"}