{"id":"https://openalex.org/W3157892620","doi":"https://doi.org/10.1137/21m1415911","title":"Active Learning of Tree Tensor Networks using Optimal Least Squares","display_name":"Active Learning of Tree Tensor Networks using Optimal Least Squares","publication_year":2023,"publication_date":"2023-07-17","ids":{"openalex":"https://openalex.org/W3157892620","doi":"https://doi.org/10.1137/21m1415911","mag":"3157892620"},"language":"en","primary_location":{"id":"doi:10.1137/21m1415911","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1137/21m1415911","pdf_url":null,"source":{"id":"https://openalex.org/S2911293512","display_name":"SIAM/ASA Journal on Uncertainty Quantification","issn_l":"2166-2525","issn":["2166-2525"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM/ASA Journal on Uncertainty Quantification","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2104.13436","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017081785","display_name":"C\u00e9cile Haberstich","orcid":null},"institutions":[{"id":"https://openalex.org/I2738703131","display_name":"Commissariat \u00e0 l'\u00c9nergie Atomique et aux \u00c9nergies Alternatives","ror":"https://ror.org/00jjx8s55","country_code":"FR","type":"government","lineage":["https://openalex.org/I2738703131"]},{"id":"https://openalex.org/I4210101455","display_name":"CEA DAM \u00cele-de-France","ror":"https://ror.org/00kn4eb29","country_code":"FR","type":"government","lineage":["https://openalex.org/I4210101455"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"C\u00e9cile Haberstich","raw_affiliation_strings":["CEA, DAM, DIF, F-91297, Arpajon, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CEA, DAM, DIF, F-91297, Arpajon, France","institution_ids":["https://openalex.org/I4210101455","https://openalex.org/I2738703131"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031143836","display_name":"Anthony Nouy","orcid":"https://orcid.org/0000-0002-2149-2986"},"institutions":[{"id":"https://openalex.org/I100445878","display_name":"\u00c9cole Centrale de Nantes","ror":"https://ror.org/03nh7d505","country_code":"FR","type":"education","lineage":["https://openalex.org/I100445878","https://openalex.org/I97188460"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210153365","display_name":"Laboratoire de Math\u00e9matiques Jean Leray","ror":"https://ror.org/04g1hjn96","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210141950","https://openalex.org/I4210153365","https://openalex.org/I97188460"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"A. Nouy","raw_affiliation_strings":["Centrale Nantes, LMJL UMR CNRS 6629, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centrale Nantes, LMJL UMR CNRS 6629, France","institution_ids":["https://openalex.org/I100445878","https://openalex.org/I4210153365","https://openalex.org/I1294671590"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032363972","display_name":"Guillaume Perrin","orcid":"https://orcid.org/0000-0002-0592-6094"},"institutions":[{"id":"https://openalex.org/I4210154111","display_name":"Universit\u00e9 Gustave Eiffel","ror":"https://ror.org/03x42jk29","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210154111"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"G. Perrin","raw_affiliation_strings":["COSYS, Universit\u00e9 Gustave Eiffel, 77420 Champs-sur-Marne, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"COSYS, Universit\u00e9 Gustave Eiffel, 77420 Champs-sur-Marne, France","institution_ids":["https://openalex.org/I4210154111"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.1931,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.31840194,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"11","issue":"3","first_page":"848","last_page":"876"},"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"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.992900013923645,"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"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9661999940872192,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/linear-subspace","display_name":"Linear subspace","score":0.7116913795471191},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.7023333311080933},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6127471923828125},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5789622664451599},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.4868108928203583},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.451664000749588},{"id":"https://openalex.org/keywords/principal-component-analysis","display_name":"Principal component analysis","score":0.4473497271537781},{"id":"https://openalex.org/keywords/dimensionality-reduction","display_name":"Dimensionality reduction","score":0.43843507766723633},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.43044590950012207},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4258502721786499},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.4189269542694092},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3596608340740204},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3420245051383972},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.27962273359298706},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1906859278678894},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09553715586662292},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.09085065126419067},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07199004292488098}],"concepts":[{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.7116913795471191},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.7023333311080933},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6127471923828125},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5789622664451599},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.4868108928203583},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.451664000749588},{"id":"https://openalex.org/C27438332","wikidata":"https://www.wikidata.org/wiki/Q2873","display_name":"Principal component analysis","level":2,"score":0.4473497271537781},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.43843507766723633},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.43044590950012207},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4258502721786499},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.4189269542694092},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3596608340740204},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3420245051383972},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.27962273359298706},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1906859278678894},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09553715586662292},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.09085065126419067},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07199004292488098},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/21m1415911","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1137/21m1415911","pdf_url":null,"source":{"id":"https://openalex.org/S2911293512","display_name":"SIAM/ASA Journal on Uncertainty Quantification","issn_l":"2166-2525","issn":["2166-2525"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM/ASA Journal on Uncertainty Quantification","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2104.13436","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2104.13436","pdf_url":"https://arxiv.org/pdf/2104.13436","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":"","raw_type":"text"},{"id":"pmh:oai:HAL:hal-03919916v1","is_oa":false,"landing_page_url":"https://hal.science/hal-03919916","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM/ASA Journal on Uncertainty Quantification, 2023, 11 (3), pp.848-876. &#x27E8;10.1137/21M1415911&#x27E9;","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2104.13436","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2104.13436","pdf_url":"https://arxiv.org/pdf/2104.13436","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":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W3157892620.pdf"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W1858056047","https://openalex.org/W1967538125","https://openalex.org/W1968376936","https://openalex.org/W1979098872","https://openalex.org/W2001518794","https://openalex.org/W2004587738","https://openalex.org/W2008657736","https://openalex.org/W2013912476","https://openalex.org/W2038198231","https://openalex.org/W2152828142","https://openalex.org/W2160251536","https://openalex.org/W2343408237","https://openalex.org/W2396770278","https://openalex.org/W2516041031","https://openalex.org/W2559655401","https://openalex.org/W2597164298","https://openalex.org/W2604272474","https://openalex.org/W2610645496","https://openalex.org/W2895724779","https://openalex.org/W2900176663","https://openalex.org/W2962845550","https://openalex.org/W2962947392","https://openalex.org/W2975849065","https://openalex.org/W2995427464","https://openalex.org/W3039249709","https://openalex.org/W3048815349","https://openalex.org/W3100193990","https://openalex.org/W3103888010","https://openalex.org/W3121797243","https://openalex.org/W3168339036","https://openalex.org/W3206326173","https://openalex.org/W4288938614","https://openalex.org/W4297907618","https://openalex.org/W4323539300"],"related_works":["https://openalex.org/W2579148721","https://openalex.org/W4387893611","https://openalex.org/W2347335694","https://openalex.org/W1964760042","https://openalex.org/W2091056927","https://openalex.org/W2067407580","https://openalex.org/W4317486777","https://openalex.org/W4389669152","https://openalex.org/W2038514069","https://openalex.org/W1967233468"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"propose":[4,98],"new":[5],"learning":[6],"algorithms":[7,131],"for":[8,46,54,78],"approximating\\nhigh-dimensional":[9],"functions":[10],"using":[11,61],"tree":[12,21,106],"tensor":[13,26,37,59,152],"networks":[14],"in":[15],"a":[16,19,33,40,65,94,139],"least-squares\\nsetting.":[17],"Given":[18],"dimension":[20,105],"or":[22],"architecture":[23],"of":[24,35,42,109,128,141,147,150],"the":[25,68,79,87,104,116,129,145],"network,":[27],"we\\nprovide":[28],"an":[29,74,99],"algorithm":[30,100],"that":[31,101,111,122,134],"generates":[32],"sequence":[34],"nested":[36],"subspaces":[38],"based\\non":[39],"generalization":[41],"principal":[43],"component":[44],"analysis":[45],"multivariate":[47],"functions.\\nAn":[48],"optimal":[49],"least-squares":[50],"method":[51],"is":[52],"used":[53],"computing":[55],"projections":[56],"onto":[57],"the\\ngenerated":[58],"subspaces,":[60],"samples":[62,142],"generated":[63,70],"from":[64],"distribution\\ndepending":[66],"on":[67],"previously":[69],"subspaces.":[71],"We":[72],"provide":[73],"error":[75],"bound":[76],"in\\nexpectation":[77],"obtained":[80],"approximation.":[81],"Practical":[82],"strategies":[83],"are":[84],"proposed\\nfor":[85],"adapting":[86],"feature":[88],"spaces":[89],"and":[90,132],"ranks":[91],"to":[92,113,120,144],"achieve":[93],"prescribed":[95],"error.":[96,123],"Also,\\nwe":[97],"progressively":[102],"constructs":[103],"by\\nsuitable":[107],"pairings":[108],"variables,":[110],"allows":[112],"further":[114],"reduce":[115],"number":[117,140,146],"of\\nsamples":[118],"necessary":[119],"reach":[121],"Numerical":[124],"examples":[125],"illustrate":[126],"the\\nperformance":[127],"proposed":[130],"show":[133],"stable":[135],"approximations":[136],"are\\nobtained":[137],"with":[138],"close":[143],"free":[148],"parameters":[149],"the\\nestimated":[151],"networks.\\n":[153]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2025-10-10T00:00:00"}
