{"id":"https://openalex.org/W2903326332","doi":"https://doi.org/10.23919/eusipco.2018.8553034","title":"Classification Asymptotics in the Random Matrix Regime","display_name":"Classification Asymptotics in the Random Matrix Regime","publication_year":2018,"publication_date":"2018-09-01","ids":{"openalex":"https://openalex.org/W2903326332","doi":"https://doi.org/10.23919/eusipco.2018.8553034","mag":"2903326332"},"language":"en","primary_location":{"id":"doi:10.23919/eusipco.2018.8553034","is_oa":false,"landing_page_url":"https://doi.org/10.23919/eusipco.2018.8553034","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2018 26th European Signal Processing Conference (EUSIPCO)","raw_type":"proceedings-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/A5021257434","display_name":"Romain Couillet","orcid":"https://orcid.org/0000-0001-5755-2090"},"institutions":[{"id":"https://openalex.org/I4210097418","display_name":"Laboratoire des signaux et syst\u00e8mes","ror":"https://ror.org/00skw9v43","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I277688954","https://openalex.org/I4210097418","https://openalex.org/I4210107720"]},{"id":"https://openalex.org/I4210107720","display_name":"CentraleSup\u00e9lec","ror":"https://ror.org/019tcpt25","country_code":"FR","type":"facility","lineage":["https://openalex.org/I277688954","https://openalex.org/I4210107720"]},{"id":"https://openalex.org/I2800493309","display_name":"Grain Inspection, Packers and Stockyards Administration","ror":"https://ror.org/056mcm922","country_code":"US","type":"government","lineage":["https://openalex.org/I1336096307","https://openalex.org/I2800493309"]},{"id":"https://openalex.org/I4210124956","display_name":"Grenoble Images Parole Signal Automatique","ror":"https://ror.org/02wrme198","country_code":"FR","type":"facility","lineage":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I4210124956","https://openalex.org/I899635006","https://openalex.org/I899635006"]}],"countries":["FR","US"],"is_corresponding":true,"raw_author_name":"Romain Couillet","raw_affiliation_strings":["CentraleSup\u00e9lec, University Grenobles-Alpes, France","GIPSA - Communication Information and Complex Systems","Laboratoire des signaux et syst\u00e8mes"],"affiliations":[{"raw_affiliation_string":"CentraleSup\u00e9lec, University Grenobles-Alpes, France","institution_ids":["https://openalex.org/I4210107720"]},{"raw_affiliation_string":"GIPSA - Communication Information and Complex Systems","institution_ids":["https://openalex.org/I4210124956","https://openalex.org/I2800493309"]},{"raw_affiliation_string":"Laboratoire des signaux et syst\u00e8mes","institution_ids":["https://openalex.org/I4210097418"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041005595","display_name":"Zhenyu Liao","orcid":"https://orcid.org/0000-0002-1915-8559"},"institutions":[{"id":"https://openalex.org/I4210097418","display_name":"Laboratoire des signaux et syst\u00e8mes","ror":"https://ror.org/00skw9v43","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I277688954","https://openalex.org/I4210097418","https://openalex.org/I4210107720"]},{"id":"https://openalex.org/I4210107720","display_name":"CentraleSup\u00e9lec","ror":"https://ror.org/019tcpt25","country_code":"FR","type":"facility","lineage":["https://openalex.org/I277688954","https://openalex.org/I4210107720"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Zhenyu Liao","raw_affiliation_strings":["CentraleSup\u00e9lec, University Grenobles-Alpes, France","Laboratoire des signaux et syst\u00e8mes"],"affiliations":[{"raw_affiliation_string":"CentraleSup\u00e9lec, University Grenobles-Alpes, France","institution_ids":["https://openalex.org/I4210107720"]},{"raw_affiliation_string":"Laboratoire des signaux et syst\u00e8mes","institution_ids":["https://openalex.org/I4210097418"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031616115","display_name":"Xiaoyi Mai","orcid":null},"institutions":[{"id":"https://openalex.org/I4210097418","display_name":"Laboratoire des signaux et syst\u00e8mes","ror":"https://ror.org/00skw9v43","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I277688954","https://openalex.org/I4210097418","https://openalex.org/I4210107720"]},{"id":"https://openalex.org/I4210107720","display_name":"CentraleSup\u00e9lec","ror":"https://ror.org/019tcpt25","country_code":"FR","type":"facility","lineage":["https://openalex.org/I277688954","https://openalex.org/I4210107720"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Xiaoyi Mai","raw_affiliation_strings":["CentraleSup\u00e9lec, University Grenobles-Alpes, France","Laboratoire des signaux et syst\u00e8mes"],"affiliations":[{"raw_affiliation_string":"CentraleSup\u00e9lec, University Grenobles-Alpes, France","institution_ids":["https://openalex.org/I4210107720"]},{"raw_affiliation_string":"Laboratoire des signaux et syst\u00e8mes","institution_ids":["https://openalex.org/I4210097418"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5021257434"],"corresponding_institution_ids":["https://openalex.org/I2800493309","https://openalex.org/I4210097418","https://openalex.org/I4210107720","https://openalex.org/I4210124956"],"apc_list":null,"apc_paid":null,"fwci":1.1402,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.8422456,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"1875","last_page":"1879"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9993000030517578,"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/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9993000030517578,"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/T10136","display_name":"Statistical Methods and Inference","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9972000122070312,"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/hyperparameter","display_name":"Hyperparameter","score":0.8920375108718872},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6220255494117737},{"id":"https://openalex.org/keywords/oracle","display_name":"Oracle","score":0.5933849215507507},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.5765717625617981},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.5740177035331726},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5722512602806091},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5479188561439514},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5362021327018738},{"id":"https://openalex.org/keywords/random-matrix","display_name":"Random matrix","score":0.5311951041221619},{"id":"https://openalex.org/keywords/discriminant","display_name":"Discriminant","score":0.4784676730632782},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.45057186484336853},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4461742043495178},{"id":"https://openalex.org/keywords/gaussian-process","display_name":"Gaussian process","score":0.43596649169921875},{"id":"https://openalex.org/keywords/linear-discriminant-analysis","display_name":"Linear discriminant analysis","score":0.4222024083137512},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.28056174516677856},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.09836792945861816},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09607282280921936}],"concepts":[{"id":"https://openalex.org/C8642999","wikidata":"https://www.wikidata.org/wiki/Q4171168","display_name":"Hyperparameter","level":2,"score":0.8920375108718872},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6220255494117737},{"id":"https://openalex.org/C55166926","wikidata":"https://www.wikidata.org/wiki/Q2892946","display_name":"Oracle","level":2,"score":0.5933849215507507},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.5765717625617981},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5740177035331726},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5722512602806091},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5479188561439514},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5362021327018738},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.5311951041221619},{"id":"https://openalex.org/C78397625","wikidata":"https://www.wikidata.org/wiki/Q192487","display_name":"Discriminant","level":2,"score":0.4784676730632782},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.45057186484336853},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4461742043495178},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.43596649169921875},{"id":"https://openalex.org/C69738355","wikidata":"https://www.wikidata.org/wiki/Q1228929","display_name":"Linear discriminant analysis","level":2,"score":0.4222024083137512},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.28056174516677856},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.09836792945861816},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09607282280921936},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C115903868","wikidata":"https://www.wikidata.org/wiki/Q80993","display_name":"Software engineering","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.23919/eusipco.2018.8553034","is_oa":false,"landing_page_url":"https://doi.org/10.23919/eusipco.2018.8553034","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2018 26th European Signal Processing Conference (EUSIPCO)","raw_type":"proceedings-article"},{"id":"pmh:oai:HAL:hal-01957686v1","is_oa":false,"landing_page_url":"https://hal.science/hal-01957686","pdf_url":null,"source":{"id":"https://openalex.org/S4406922461","display_name":"SPIRE - Sciences Po Institutional REpository","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"EUSIPCO 2018 - 26th European Signal Processing Conference, Sep 2018, Rome, Italy. &#x27E8;10.23919/eusipco.2018.8553034&#x27E9;","raw_type":"Conference papers"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.75}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W615589970","https://openalex.org/W1529202008","https://openalex.org/W1596717185","https://openalex.org/W1601795611","https://openalex.org/W1656240941","https://openalex.org/W1663973292","https://openalex.org/W1970790521","https://openalex.org/W2002276939","https://openalex.org/W2014747354","https://openalex.org/W2024514015","https://openalex.org/W2026131661","https://openalex.org/W2039953809","https://openalex.org/W2053744708","https://openalex.org/W2056099894","https://openalex.org/W2060581589","https://openalex.org/W2072184935","https://openalex.org/W2097714737","https://openalex.org/W2098971218","https://openalex.org/W2105502962","https://openalex.org/W2111072639","https://openalex.org/W2139823104","https://openalex.org/W2577176882","https://openalex.org/W2593320540","https://openalex.org/W2594163177","https://openalex.org/W2614751510","https://openalex.org/W2765732224","https://openalex.org/W2767026743","https://openalex.org/W2888778690","https://openalex.org/W2963144092","https://openalex.org/W2963650649","https://openalex.org/W2963720057","https://openalex.org/W3102351945","https://openalex.org/W4295535149","https://openalex.org/W6680434193"],"related_works":["https://openalex.org/W4390421286","https://openalex.org/W4280563792","https://openalex.org/W2141609920","https://openalex.org/W2912851808","https://openalex.org/W4294619368","https://openalex.org/W4380558509","https://openalex.org/W4286748465","https://openalex.org/W3118984993","https://openalex.org/W2144336328","https://openalex.org/W3196933554"],"abstract_inverted_index":{"This":[0],"article":[1],"discusses":[2],"the":[3,33,53,68],"asymptotic":[4],"performance":[5,54,70],"of":[6,55],"classical":[7],"machine":[8,56],"learning":[9],"classification":[10],"methods":[11],"(from":[12],"discriminant":[13],"analysis":[14],"to":[15,48],"neural":[16],"networks)":[17],"for":[18,72],"simultaneously":[19],"large":[20],"and":[21,38],"numerous":[22],"Gaussian":[23],"mixture":[24],"modelled":[25],"data.":[26],"We":[27],"first":[28],"provide":[29],"theoretical":[30,50],"bounds":[31],"on":[32,52],"minimally":[34],"discriminable":[35],"class":[36],"means":[37],"covariances":[39],"under":[40],"an":[41],"oracle":[42],"setting,":[43],"which":[44,63],"are":[45,60],"then":[46],"compared":[47],"recent":[49],"findings":[51],"learning.":[57],"Non-obvious":[58],"phenomena":[59],"discussed,":[61],"among":[62],"surprising":[64],"phase":[65],"transitions":[66],"in":[67],"optimal":[69],"rates":[71],"specific":[73],"hyperparameter":[74],"settings.":[75]},"counts_by_year":[{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
