{"id":"https://openalex.org/W2757782085","doi":"https://doi.org/10.1109/allerton.2017.8262854","title":"The layered structure of tensor estimation and its mutual information","display_name":"The layered structure of tensor estimation and its mutual information","publication_year":2017,"publication_date":"2017-10-01","ids":{"openalex":"https://openalex.org/W2757782085","doi":"https://doi.org/10.1109/allerton.2017.8262854","mag":"2757782085"},"language":"en","primary_location":{"id":"doi:10.1109/allerton.2017.8262854","is_oa":false,"landing_page_url":"https://doi.org/10.1109/allerton.2017.8262854","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2017 55th Annual Allerton Conference on Communication, Control, and Computing (Allerton)","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1709.10368","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057057294","display_name":"Jean Barbier","orcid":"https://orcid.org/0000-0002-2652-6727"},"institutions":[{"id":"https://openalex.org/I166337079","display_name":"Queen Mary University of London","ror":"https://ror.org/026zzn846","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I166337079"]},{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH","GB"],"is_corresponding":true,"raw_author_name":"Jean Barbier","raw_affiliation_strings":["Facult\u00e9 Informatique et Communications, Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne, Suisse","Probability and Applications Group, Queen Mary University of London, United-Kingdom","Laboratoire de Th\u00e9orie des Communications, Facult\u00e9 Informatique et Communications, Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne, 1015, Suisse"],"affiliations":[{"raw_affiliation_string":"Facult\u00e9 Informatique et Communications, Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne, Suisse","institution_ids":["https://openalex.org/I5124864"]},{"raw_affiliation_string":"Probability and Applications Group, Queen Mary University of London, United-Kingdom","institution_ids":["https://openalex.org/I166337079"]},{"raw_affiliation_string":"Laboratoire de Th\u00e9orie des Communications, Facult\u00e9 Informatique et Communications, Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne, 1015, Suisse","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038854134","display_name":"Nicolas Macris","orcid":"https://orcid.org/0000-0003-2189-7411"},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Nicolas Macris","raw_affiliation_strings":["Facult\u00e9 Informatique et Communications, Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne, Suisse","Laboratoire de Th\u00e9orie des Communications, Facult\u00e9 Informatique et Communications, Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne, 1015, Suisse"],"affiliations":[{"raw_affiliation_string":"Facult\u00e9 Informatique et Communications, Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne, Suisse","institution_ids":["https://openalex.org/I5124864"]},{"raw_affiliation_string":"Laboratoire de Th\u00e9orie des Communications, Facult\u00e9 Informatique et Communications, Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne, 1015, Suisse","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103183654","display_name":"L\u00e9o Miolane","orcid":"https://orcid.org/0000-0002-6416-4026"},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en informatique et en automatique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1326498283"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Leo Miolane","raw_affiliation_strings":["INRIA & Ecole Normale Sup\u00e9rieure, Paris, France","INRIA & Ecole Normale Sup\u00e9rieure, 75005, Paris, France"],"affiliations":[{"raw_affiliation_string":"INRIA & Ecole Normale Sup\u00e9rieure, Paris, France","institution_ids":["https://openalex.org/I1326498283"]},{"raw_affiliation_string":"INRIA & Ecole Normale Sup\u00e9rieure, 75005, Paris, France","institution_ids":["https://openalex.org/I1326498283"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5057057294"],"corresponding_institution_ids":["https://openalex.org/I166337079","https://openalex.org/I5124864"],"apc_list":null,"apc_paid":null,"fwci":0.8285,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.69692308,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"1056","last_page":"1063"},"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9943000078201294,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11447","display_name":"Blind Source Separation Techniques","score":0.9900000095367432,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/mathematical-proof","display_name":"Mathematical proof","score":0.6569669246673584},{"id":"https://openalex.org/keywords/mutual-information","display_name":"Mutual information","score":0.6374203562736511},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.6240442991256714},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6202627420425415},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.6064065098762512},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5652933716773987},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5317978262901306},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.4928891658782959},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4868389964103699},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.44854962825775146},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4046204686164856},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.35257700085639954},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34360024333000183},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.34189122915267944},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.33139437437057495},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.26242130994796753},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.16731908917427063},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.16007563471794128},{"id":"https://openalex.org/keywords/motion","display_name":"Motion (physics)","score":0.08675429224967957},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07591104507446289}],"concepts":[{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.6569669246673584},{"id":"https://openalex.org/C152139883","wikidata":"https://www.wikidata.org/wiki/Q252973","display_name":"Mutual information","level":2,"score":0.6374203562736511},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.6240442991256714},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6202627420425415},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.6064065098762512},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5652933716773987},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5317978262901306},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.4928891658782959},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4868389964103699},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.44854962825775146},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4046204686164856},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35257700085639954},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34360024333000183},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.34189122915267944},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.33139437437057495},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.26242130994796753},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.16731908917427063},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.16007563471794128},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.08675429224967957},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07591104507446289},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1109/allerton.2017.8262854","is_oa":false,"landing_page_url":"https://doi.org/10.1109/allerton.2017.8262854","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2017 55th Annual Allerton Conference on Communication, Control, and Computing (Allerton)","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1709.10368","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1709.10368","pdf_url":"https://arxiv.org/pdf/1709.10368","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:qmro.qmul.ac.uk:123456789/31347","is_oa":false,"landing_page_url":"http://qmro.qmul.ac.uk/xmlui/handle/123456789/31347","pdf_url":null,"source":{"id":"https://openalex.org/S4306400530","display_name":"Queen Mary Research Online (Queen Mary University of London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I166337079","host_organization_name":"Queen Mary University of London","host_organization_lineage":["https://openalex.org/I166337079"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Conference Proceeding"},{"id":"doi:10.48550/arxiv.1709.10368","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1709.10368","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"},{"id":"mag:2757782085","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1709.10368","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1709.10368","pdf_url":"https://arxiv.org/pdf/1709.10368","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":[{"id":"https://openalex.org/G4836148144","display_name":null,"funder_award_id":"20002","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G5256785375","display_name":null,"funder_award_id":"200021-","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G5941751334","display_name":"Spatial Coupling of Graphical Models in Communications, Signal Processing, Computer Science and Statistical Physics","funder_award_id":"156672","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G7160048158","display_name":null,"funder_award_id":"200021-156672","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G993971353","display_name":null,"funder_award_id":"200021","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"}],"funders":[{"id":"https://openalex.org/F4320320915","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052"},{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2757782085.pdf","grobid_xml":"https://content.openalex.org/works/W2757782085.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W132471885","https://openalex.org/W1572652170","https://openalex.org/W1659832490","https://openalex.org/W1922029667","https://openalex.org/W1971565000","https://openalex.org/W2001759212","https://openalex.org/W2024165284","https://openalex.org/W2082029531","https://openalex.org/W2086177078","https://openalex.org/W2101936356","https://openalex.org/W2116061856","https://openalex.org/W2116466689","https://openalex.org/W2119412403","https://openalex.org/W2129462326","https://openalex.org/W2160844215","https://openalex.org/W2161410247","https://openalex.org/W2167783913","https://openalex.org/W2332339252","https://openalex.org/W2332917886","https://openalex.org/W2469230926","https://openalex.org/W2483978192","https://openalex.org/W2566505556","https://openalex.org/W2610971674","https://openalex.org/W2746470301","https://openalex.org/W2963072996","https://openalex.org/W2964213728","https://openalex.org/W3098848552","https://openalex.org/W3103345129","https://openalex.org/W4210422269","https://openalex.org/W4240189201","https://openalex.org/W6718058154"],"related_works":["https://openalex.org/W2963215260","https://openalex.org/W2964213728","https://openalex.org/W2963765569","https://openalex.org/W2086177078","https://openalex.org/W2588219153","https://openalex.org/W568673721","https://openalex.org/W2157638198","https://openalex.org/W2111616148","https://openalex.org/W2082029531","https://openalex.org/W2120320178","https://openalex.org/W2502578691","https://openalex.org/W1980317018","https://openalex.org/W3196863862","https://openalex.org/W2099853640","https://openalex.org/W2950168472","https://openalex.org/W2401335853","https://openalex.org/W2996740905","https://openalex.org/W2528401498","https://openalex.org/W3127182566","https://openalex.org/W2092332806"],"abstract_inverted_index":{"We":[0,14,24,45],"consider":[1],"rank-one":[2],"non-symmetric":[3],"tensor":[4,56],"estimation":[5,57],"and":[6,96],"derive":[7],"simple":[8],"formulas":[9],"for":[10,64,68,79],"the":[11,17,51,65,69,74,77,80,86,101],"mutual":[12,66,102],"information.":[13],"start":[15],"by":[16],"order":[18,59,70,81,106],"2":[19,82],"problem,":[20,83],"namely":[21],"matrix":[22],"factorization.":[23],"treat":[25],"it":[26],"completely":[27],"in":[28,43,53,58,107],"a":[29,36,62,108],"simpler":[30],"fashion":[31],"than":[32],"previous":[33],"proofs":[34],"using":[35,85],"new":[37],"type":[38],"of":[39,55,76,89],"interpolation":[40],"method":[41],"developed":[42],"[1].":[44],"then":[46],"show":[47],"how":[48],"to":[49,60,98],"harness":[50],"structure":[52],"\u201clayers\u201d":[54],"obtain":[61,100],"formula":[63,78],"information":[67,103],"3":[71],"problem":[72],"from":[73],"knowledge":[75],"still":[84],"same":[87],"kind":[88],"interpolation.":[90],"Our":[91],"proof":[92],"technique":[93],"straightforwardly":[94],"generalizes":[95],"allows":[97],"rigorously":[99],"at":[104],"any":[105],"recursive":[109],"way.":[110]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
