{"id":"https://openalex.org/W4410379403","doi":"https://doi.org/10.3389/fams.2025.1593680","title":"Expectation-maximization alternating least squares for tensor network logistic regression","display_name":"Expectation-maximization alternating least squares for tensor network logistic regression","publication_year":2025,"publication_date":"2025-05-14","ids":{"openalex":"https://openalex.org/W4410379403","doi":"https://doi.org/10.3389/fams.2025.1593680"},"language":"en","primary_location":{"id":"doi:10.3389/fams.2025.1593680","is_oa":true,"landing_page_url":"https://doi.org/10.3389/fams.2025.1593680","pdf_url":"https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2025.1593680/pdf","source":{"id":"https://openalex.org/S2597085352","display_name":"Frontiers in Applied Mathematics and Statistics","issn_l":"2297-4687","issn":["2297-4687"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320527","host_organization_name":"Frontiers Media","host_organization_lineage":["https://openalex.org/P4310320527"],"host_organization_lineage_names":["Frontiers Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Applied Mathematics and Statistics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2025.1593680/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016913204","display_name":"N Yamauchi","orcid":null},"institutions":[{"id":"https://openalex.org/I197274945","display_name":"Nagoya Institute of Technology","ror":"https://ror.org/055yf1005","country_code":"JP","type":"education","lineage":["https://openalex.org/I197274945"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Naoya Yamauchi","raw_affiliation_strings":["Department of Computer Science, Nagoya Institute of Technology, Aichi, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Nagoya Institute of Technology, Aichi, Japan","institution_ids":["https://openalex.org/I197274945"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031879419","display_name":"Hidekata Hontani","orcid":"https://orcid.org/0000-0001-9081-7740"},"institutions":[{"id":"https://openalex.org/I197274945","display_name":"Nagoya Institute of Technology","ror":"https://ror.org/055yf1005","country_code":"JP","type":"education","lineage":["https://openalex.org/I197274945"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Hidekata Hontani","raw_affiliation_strings":["Department of Computer Science, Nagoya Institute of Technology, Aichi, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Nagoya Institute of Technology, Aichi, Japan","institution_ids":["https://openalex.org/I197274945"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086158953","display_name":"Tatsuya Yokota","orcid":null},"institutions":[{"id":"https://openalex.org/I197274945","display_name":"Nagoya Institute of Technology","ror":"https://ror.org/055yf1005","country_code":"JP","type":"education","lineage":["https://openalex.org/I197274945"]},{"id":"https://openalex.org/I4210126580","display_name":"RIKEN Center for Advanced Intelligence Project","ror":"https://ror.org/03ckxwf91","country_code":"JP","type":"facility","lineage":["https://openalex.org/I4210110652","https://openalex.org/I4210126580"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Tatsuya Yokota","raw_affiliation_strings":["Department of Computer Science, Nagoya Institute of Technology, Aichi, Japan","RIKEN Center for Advanced Intelligence Project, Tokyo, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Nagoya Institute of Technology, Aichi, Japan","institution_ids":["https://openalex.org/I197274945"]},{"raw_affiliation_string":"RIKEN Center for Advanced Intelligence Project, Tokyo, Japan","institution_ids":["https://openalex.org/I4210126580"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5086158953"],"corresponding_institution_ids":["https://openalex.org/I197274945","https://openalex.org/I4210126580"],"apc_list":{"value":1285,"currency":"USD","value_usd":1285},"apc_paid":{"value":1285,"currency":"USD","value_usd":1285},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.09954751,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"11","issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":1.0,"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":1.0,"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"}},{"id":"https://openalex.org/T11304","display_name":"Advanced Neuroimaging Techniques and Applications","score":0.9955999851226807,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9757000207901001,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/logistic-regression","display_name":"Logistic regression","score":0.765217125415802},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5706425905227661},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.5516371726989746},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.49366649985313416},{"id":"https://openalex.org/keywords/total-least-squares","display_name":"Total least squares","score":0.4672030806541443},{"id":"https://openalex.org/keywords/regression","display_name":"Regression","score":0.4666208028793335},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.4548223614692688},{"id":"https://openalex.org/keywords/generalized-least-squares","display_name":"Generalized least squares","score":0.43981972336769104},{"id":"https://openalex.org/keywords/maximization","display_name":"Maximization","score":0.42139673233032227},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.3774319887161255},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.32683122158050537},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.32141736149787903},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.29244470596313477},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.23246663808822632},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.09059473872184753},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.06988388299942017}],"concepts":[{"id":"https://openalex.org/C151956035","wikidata":"https://www.wikidata.org/wiki/Q1132755","display_name":"Logistic regression","level":2,"score":0.765217125415802},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5706425905227661},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.5516371726989746},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.49366649985313416},{"id":"https://openalex.org/C169241690","wikidata":"https://www.wikidata.org/wiki/Q7828122","display_name":"Total least squares","level":3,"score":0.4672030806541443},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.4666208028793335},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.4548223614692688},{"id":"https://openalex.org/C188649462","wikidata":"https://www.wikidata.org/wiki/Q2246261","display_name":"Generalized least squares","level":3,"score":0.43981972336769104},{"id":"https://openalex.org/C2776330181","wikidata":"https://www.wikidata.org/wiki/Q18358244","display_name":"Maximization","level":2,"score":0.42139673233032227},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.3774319887161255},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.32683122158050537},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.32141736149787903},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29244470596313477},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.23246663808822632},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.09059473872184753},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.06988388299942017}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3389/fams.2025.1593680","is_oa":true,"landing_page_url":"https://doi.org/10.3389/fams.2025.1593680","pdf_url":"https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2025.1593680/pdf","source":{"id":"https://openalex.org/S2597085352","display_name":"Frontiers in Applied Mathematics and Statistics","issn_l":"2297-4687","issn":["2297-4687"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320527","host_organization_name":"Frontiers Media","host_organization_lineage":["https://openalex.org/P4310320527"],"host_organization_lineage_names":["Frontiers Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Applied Mathematics and Statistics","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:f143fa857a1e451cb8060a4f86bed9ff","is_oa":true,"landing_page_url":"https://doaj.org/article/f143fa857a1e451cb8060a4f86bed9ff","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Frontiers in Applied Mathematics and Statistics, Vol 11 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3389/fams.2025.1593680","is_oa":true,"landing_page_url":"https://doi.org/10.3389/fams.2025.1593680","pdf_url":"https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2025.1593680/pdf","source":{"id":"https://openalex.org/S2597085352","display_name":"Frontiers in Applied Mathematics and Statistics","issn_l":"2297-4687","issn":["2297-4687"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320527","host_organization_name":"Frontiers Media","host_organization_lineage":["https://openalex.org/P4310320527"],"host_organization_lineage_names":["Frontiers Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Applied Mathematics and Statistics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1079151630","display_name":"Optimization Theories, Algorithms, and Interfeces for General Tensor Decompositions","funder_award_id":"23K28109","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4410379403.pdf","grobid_xml":"https://content.openalex.org/works/W4410379403.grobid-xml"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W1798945469","https://openalex.org/W1991042426","https://openalex.org/W1993482030","https://openalex.org/W1995855984","https://openalex.org/W2000215628","https://openalex.org/W2024165284","https://openalex.org/W2031216664","https://openalex.org/W2049633694","https://openalex.org/W2097366995","https://openalex.org/W2099878672","https://openalex.org/W2119412403","https://openalex.org/W2141280932","https://openalex.org/W2152521833","https://openalex.org/W2154624311","https://openalex.org/W2431890537","https://openalex.org/W2508393166","https://openalex.org/W2516041031","https://openalex.org/W2559655401","https://openalex.org/W2963048316","https://openalex.org/W3101570982","https://openalex.org/W3166700906","https://openalex.org/W3168867926","https://openalex.org/W3177463154","https://openalex.org/W4212863985","https://openalex.org/W4284967345","https://openalex.org/W4367663118","https://openalex.org/W4400374436","https://openalex.org/W4404987128","https://openalex.org/W4408649329","https://openalex.org/W6638060716","https://openalex.org/W6674755931","https://openalex.org/W6679667936","https://openalex.org/W6682483229","https://openalex.org/W6717575008","https://openalex.org/W6729942461","https://openalex.org/W6796581206","https://openalex.org/W6874805848"],"related_works":["https://openalex.org/W2030255580","https://openalex.org/W2034819163","https://openalex.org/W4380487384","https://openalex.org/W2123913166","https://openalex.org/W3150673294","https://openalex.org/W2374560502","https://openalex.org/W2352570898","https://openalex.org/W2368940260","https://openalex.org/W2368345218","https://openalex.org/W1965270833"],"abstract_inverted_index":{"In":[0,81],"recent":[1],"years,":[2],"a":[3,17,24,28,62,86,147],"learning":[4,72,91],"method":[5,76,155],"for":[6,20,90],"classifiers":[7,93],"using":[8,23,57,73,95],"tensor":[9],"networks":[10],"(TNs)":[11],"has":[12],"attracted":[13],"attention.":[14],"When":[15],"constructing":[16],"classification":[18,159],"function":[19,26,135],"high-dimensional":[21],"data":[22],"basis":[25,32],"model,":[27],"huge":[29,55],"number":[30],"of":[31,50,165],"functions":[33],"and":[34,71,110,121,161],"coefficients":[35,56],"are":[36],"generally":[37],"required,":[38],"but":[39],"the":[40,48,54,68,74,153,157,163,166],"TN":[41,65,92],"model":[42],"makes":[43],"it":[44],"possible":[45],"to":[46,128,143,156],"avoid":[47],"curse":[49],"dimensionality":[51],"by":[52,94],"representing":[53],"TNs.":[58],"However,":[59],"there":[60],"is":[61],"problem":[63],"with":[64],"learning,":[66],"namely":[67],"gradient":[69,75],"vanishing,":[70],"cannot":[77],"be":[78,144],"performed":[79],"efficiently.":[80],"this":[82],"study,":[83],"we":[84,131],"propose":[85],"novel":[87],"optimization":[88],"algorithm":[89],"alternating":[96],"least":[97],"square":[98],"(ALS)":[99],"algorithm.":[100],"Unlike":[101],"conventional":[102],"gradient-based":[103],"methods,":[104],"which":[105],"suffer":[106],"from":[107,137],"vanishing":[108],"gradients":[109],"inefficient":[111],"training,":[112],"our":[113],"proposed":[114,154,167],"approach":[115],"can":[116],"effectively":[117],"minimize":[118],"squared":[119,149],"loss":[120,142],"logistic":[122,129,141],"loss.":[123,150],"To":[124],"make":[125],"ALS":[126],"applicable":[127],"regression,":[130],"introduce":[132],"an":[133],"auxiliary":[134],"derived":[136],"P\u00f3lya-Gamma":[138],"augmentation,":[139],"allowing":[140],"minimized":[145],"as":[146],"weighted":[148],"We":[151],"apply":[152],"MNIST":[158],"task":[160],"discuss":[162],"effectiveness":[164],"method.":[168]},"counts_by_year":[],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
