{"id":"https://openalex.org/W2887054207","doi":"https://doi.org/10.1515/cmam-2018-0027","title":"Tensor Train Spectral Method for Learning of Hidden Markov Models (HMM)","display_name":"Tensor Train Spectral Method for Learning of Hidden Markov Models (HMM)","publication_year":2018,"publication_date":"2018-08-11","ids":{"openalex":"https://openalex.org/W2887054207","doi":"https://doi.org/10.1515/cmam-2018-0027","mag":"2887054207"},"language":"en","primary_location":{"id":"doi:10.1515/cmam-2018-0027","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2018-0027","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","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/A5108013033","display_name":"Maxim Kuznetsov","orcid":"https://orcid.org/0000-0003-0311-4372"},"institutions":[{"id":"https://openalex.org/I125989756","display_name":"Skolkovo Institute of Science and Technology","ror":"https://ror.org/03f9nc143","country_code":"RU","type":"education","lineage":["https://openalex.org/I125989756"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"Maxim A. Kuznetsov","raw_affiliation_strings":["Skolkovo Institute of Science and Technology , Skolkovo Innovation Center Moscow, 143025 , Moscow , Russia"],"affiliations":[{"raw_affiliation_string":"Skolkovo Institute of Science and Technology , Skolkovo Innovation Center Moscow, 143025 , Moscow , Russia","institution_ids":["https://openalex.org/I125989756"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004111307","display_name":"Ivan Oseledets","orcid":"https://orcid.org/0000-0003-2071-2163"},"institutions":[{"id":"https://openalex.org/I125989756","display_name":"Skolkovo Institute of Science and Technology","ror":"https://ror.org/03f9nc143","country_code":"RU","type":"education","lineage":["https://openalex.org/I125989756"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Ivan V. Oseledets","raw_affiliation_strings":["Skolkovo Institute of Science and Technology , Skolkovo Innovation Center Moscow, 143025 , Moscow , Russia"],"affiliations":[{"raw_affiliation_string":"Skolkovo Institute of Science and Technology , Skolkovo Innovation Center Moscow, 143025 , Moscow , Russia","institution_ids":["https://openalex.org/I125989756"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5108013033"],"corresponding_institution_ids":["https://openalex.org/I125989756"],"apc_list":null,"apc_paid":null,"fwci":0.3681,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.49090909,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"19","issue":"1","first_page":"93","last_page":"99"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"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/T12303","display_name":"Tensor decomposition and applications","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"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/hidden-markov-model","display_name":"Hidden Markov model","score":0.8120858669281006},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.6695960760116577},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5180166363716125},{"id":"https://openalex.org/keywords/joint-probability-distribution","display_name":"Joint probability distribution","score":0.4913159906864166},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4873393476009369},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.471306174993515},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42728424072265625},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.4260948896408081},{"id":"https://openalex.org/keywords/sparse-approximation","display_name":"Sparse approximation","score":0.4128301739692688},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4020174741744995},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.35668426752090454},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.11332646012306213},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.07839491963386536}],"concepts":[{"id":"https://openalex.org/C23224414","wikidata":"https://www.wikidata.org/wiki/Q176769","display_name":"Hidden Markov model","level":2,"score":0.8120858669281006},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.6695960760116577},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5180166363716125},{"id":"https://openalex.org/C18653775","wikidata":"https://www.wikidata.org/wiki/Q1333358","display_name":"Joint probability distribution","level":2,"score":0.4913159906864166},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4873393476009369},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.471306174993515},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42728424072265625},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.4260948896408081},{"id":"https://openalex.org/C124066611","wikidata":"https://www.wikidata.org/wiki/Q28684319","display_name":"Sparse approximation","level":2,"score":0.4128301739692688},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4020174741744995},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35668426752090454},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.11332646012306213},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.07839491963386536}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1515/cmam-2018-0027","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2018-0027","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1825640910","https://openalex.org/W1993482030","https://openalex.org/W1995406764","https://openalex.org/W2000215628","https://openalex.org/W2024165284","https://openalex.org/W2038198231","https://openalex.org/W2086699924","https://openalex.org/W2088025933","https://openalex.org/W2088522763","https://openalex.org/W2097150846","https://openalex.org/W2103581346","https://openalex.org/W2105724942","https://openalex.org/W2108138101","https://openalex.org/W2125124498","https://openalex.org/W2125838338","https://openalex.org/W2132267493","https://openalex.org/W2149960632","https://openalex.org/W2152770371","https://openalex.org/W2463261572","https://openalex.org/W2759124989","https://openalex.org/W3148186152"],"related_works":["https://openalex.org/W2951801950","https://openalex.org/W1987264987","https://openalex.org/W4297670780","https://openalex.org/W1482189126","https://openalex.org/W2122857041","https://openalex.org/W162901985","https://openalex.org/W1539131693","https://openalex.org/W3102821031","https://openalex.org/W2361764490","https://openalex.org/W2155079033"],"abstract_inverted_index":{"Abstract":[0],"We":[1,92,133],"propose":[2,93],"a":[3,47,128],"new":[4],"algorithm":[5,95,140,144],"for":[6,34,96,118],"spectral":[7],"learning":[8],"of":[9,26,46,99,123,130,138,164],"Hidden":[10],"Markov":[11],"Models":[12],"(HMM).":[13],"In":[14],"contrast":[15],"to":[16],"the":[17,24,27,35,44,60,73,77,97,100,107,124,136,142,162],"standard":[18],"approach,":[19],"we":[20,67],"do":[21],"not":[22],"estimate":[23,33],"parameters":[25],"HMM":[28],"directly,":[29],"but":[30],"construct":[31],"an":[32,52,69,94],"joint":[36,48,79],"probability":[37,49,80],"distribution.":[38],"The":[39,121],"idea":[40],"is":[41,104,127,157,167],"based":[42,105],"on":[43,106],"representation":[45],"distribution":[50,81],"as":[51],"N-th-order":[53],"tensor":[54,61,125],"with":[55,84,87,141],"low":[56,85],"ranks":[57],"represented":[58],"in":[59,151],"train":[62],"(TT)":[63],"format.":[64],"Using":[65],"TT-format,":[66],"get":[68],"approximation":[70],"by":[71,145],"minimizing":[72],"Frobenius":[74],"distance":[75],"between":[76],"empirical":[78],"and":[82,113,148,153],"tensors":[83,89],"TT-ranks":[86],"core":[88],"normalization":[90],"constraints.":[91],"solution":[98],"optimization":[101],"problem":[102],"that":[103,155],"alternating":[108],"least":[109],"squares":[110],"(ALS)":[111],"approach":[112],"develop":[114],"its":[115],"fast":[116],"version":[117],"sparse":[119],"tensors.":[120],"order":[122],"d":[126],"parameter":[129],"our":[131,139],"algorithm.":[132],"have":[134],"compared":[135],"performance":[137],"existing":[143],"Hsu,":[146],"Kakade":[147],"Zhang":[149],"proposed":[150],"2009":[152],"found":[154],"it":[156],"much":[158],"more":[159],"robust":[160],"if":[161],"number":[163],"hidden":[165],"states":[166],"overestimated.":[168]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
