{"id":"https://openalex.org/W3009533209","doi":"https://doi.org/10.1109/tit.2021.3075137","title":"Multiclass Classification by Sparse Multinomial Logistic Regression","display_name":"Multiclass Classification by Sparse Multinomial Logistic Regression","publication_year":2021,"publication_date":"2021-04-22","ids":{"openalex":"https://openalex.org/W3009533209","doi":"https://doi.org/10.1109/tit.2021.3075137","mag":"3009533209"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2021.3075137","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2021.3075137","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2003.01951","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002404593","display_name":"Felix Abramovich","orcid":"https://orcid.org/0000-0001-7313-1050"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Felix Abramovich","raw_affiliation_strings":["Department of Statistics and Operations Research, Tel Aviv University, Tel Aviv, Israel","Tel Aviv University *"],"raw_orcid":"https://orcid.org/0000-0001-7313-1050","affiliations":[{"raw_affiliation_string":"Department of Statistics and Operations Research, Tel Aviv University, Tel Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]},{"raw_affiliation_string":"Tel Aviv University *","institution_ids":["https://openalex.org/I16391192"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016582623","display_name":"Vadim Grinshtein","orcid":"https://orcid.org/0000-0002-4600-6892"},"institutions":[{"id":"https://openalex.org/I164950643","display_name":"Open University of Israel","ror":"https://ror.org/027z64205","country_code":"IL","type":"education","lineage":["https://openalex.org/I164950643"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Vadim Grinshtein","raw_affiliation_strings":["Department of Mathematics and Computer Science, The Open University of Israel, Ra\u2019anana, Israel","Open University of Israel"],"raw_orcid":"https://orcid.org/0000-0002-4600-6892","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, The Open University of Israel, Ra\u2019anana, Israel","institution_ids":["https://openalex.org/I164950643"]},{"raw_affiliation_string":"Open University of Israel","institution_ids":["https://openalex.org/I164950643"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012110624","display_name":"Tomer Levy","orcid":"https://orcid.org/0000-0002-1976-6781"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Tomer Levy","raw_affiliation_strings":["Department of Statistics and Operations Research, Tel Aviv University, Tel Aviv, Israel","Department of Statistics and Operations Research, Tel Aviv University, Tel-Aviv, Israel"],"raw_orcid":"https://orcid.org/0000-0002-1976-6781","affiliations":[{"raw_affiliation_string":"Department of Statistics and Operations Research, Tel Aviv University, Tel Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]},{"raw_affiliation_string":"Department of Statistics and Operations Research, Tel Aviv University, Tel-Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5002404593"],"corresponding_institution_ids":["https://openalex.org/I16391192"],"apc_list":null,"apc_paid":null,"fwci":0.7097,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.70551821,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"67","issue":"7","first_page":"4637","last_page":"4646"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.9987000226974487,"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"}},"topics":[{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.9987000226974487,"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/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9825999736785889,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9804999828338623,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/multinomial-logistic-regression","display_name":"Multinomial logistic regression","score":0.8447250127792358},{"id":"https://openalex.org/keywords/minimax","display_name":"Minimax","score":0.7416999340057373},{"id":"https://openalex.org/keywords/feature-selection","display_name":"Feature selection","score":0.7341341972351074},{"id":"https://openalex.org/keywords/multinomial-distribution","display_name":"Multinomial distribution","score":0.611606240272522},{"id":"https://openalex.org/keywords/classifier","display_name":"Classifier (UML)","score":0.5880789756774902},{"id":"https://openalex.org/keywords/logistic-regression","display_name":"Logistic regression","score":0.5752352476119995},{"id":"https://openalex.org/keywords/lasso","display_name":"Lasso (programming language)","score":0.551123857498169},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.5092026591300964},{"id":"https://openalex.org/keywords/multiclass-classification","display_name":"Multiclass classification","score":0.48133406043052673},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4755246937274933},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.444196492433548},{"id":"https://openalex.org/keywords/feature","display_name":"Feature (linguistics)","score":0.42965441942214966},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4278068542480469},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4255255162715912},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.3818361759185791},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.35397759079933167},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.28656432032585144},{"id":"https://openalex.org/keywords/support-vector-machine","display_name":"Support vector machine","score":0.19329530000686646}],"concepts":[{"id":"https://openalex.org/C117568660","wikidata":"https://www.wikidata.org/wiki/Q1650843","display_name":"Multinomial logistic regression","level":2,"score":0.8447250127792358},{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.7416999340057373},{"id":"https://openalex.org/C148483581","wikidata":"https://www.wikidata.org/wiki/Q446488","display_name":"Feature selection","level":2,"score":0.7341341972351074},{"id":"https://openalex.org/C192065140","wikidata":"https://www.wikidata.org/wiki/Q1147928","display_name":"Multinomial distribution","level":2,"score":0.611606240272522},{"id":"https://openalex.org/C95623464","wikidata":"https://www.wikidata.org/wiki/Q1096149","display_name":"Classifier (UML)","level":2,"score":0.5880789756774902},{"id":"https://openalex.org/C151956035","wikidata":"https://www.wikidata.org/wiki/Q1132755","display_name":"Logistic regression","level":2,"score":0.5752352476119995},{"id":"https://openalex.org/C37616216","wikidata":"https://www.wikidata.org/wiki/Q3218363","display_name":"Lasso (programming language)","level":2,"score":0.551123857498169},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.5092026591300964},{"id":"https://openalex.org/C123860398","wikidata":"https://www.wikidata.org/wiki/Q6934605","display_name":"Multiclass classification","level":3,"score":0.48133406043052673},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4755246937274933},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.444196492433548},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.42965441942214966},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4278068542480469},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4255255162715912},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3818361759185791},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35397759079933167},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.28656432032585144},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.19329530000686646},{"id":"https://openalex.org/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tit.2021.3075137","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2021.3075137","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2003.01951","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2003.01951","pdf_url":"https://arxiv.org/pdf/2003.01951","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":"mag:3009533209","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2003.01951.pdf","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2003.01951","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2003.01951","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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2003.01951","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2003.01951","pdf_url":"https://arxiv.org/pdf/2003.01951","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/G7781875573","display_name":null,"funder_award_id":"ISF-589/18","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320322252","display_name":"Israel Science Foundation","ror":"https://ror.org/04sazxf24"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3009533209.pdf"},"referenced_works_count":53,"referenced_works":["https://openalex.org/W1564947197","https://openalex.org/W1569616332","https://openalex.org/W1573195610","https://openalex.org/W1916786071","https://openalex.org/W1982032418","https://openalex.org/W1984876737","https://openalex.org/W1995771589","https://openalex.org/W1996437515","https://openalex.org/W2004686034","https://openalex.org/W2014902932","https://openalex.org/W2020247811","https://openalex.org/W2023163512","https://openalex.org/W2032291279","https://openalex.org/W2033868481","https://openalex.org/W2035983506","https://openalex.org/W2043919728","https://openalex.org/W2049393399","https://openalex.org/W2049701820","https://openalex.org/W2089075540","https://openalex.org/W2097360283","https://openalex.org/W2116581043","https://openalex.org/W2118250684","https://openalex.org/W2119851445","https://openalex.org/W2142246398","https://openalex.org/W2179504854","https://openalex.org/W2268245722","https://openalex.org/W2472087060","https://openalex.org/W2523051598","https://openalex.org/W2598989315","https://openalex.org/W2952817049","https://openalex.org/W2962708723","https://openalex.org/W2962710557","https://openalex.org/W2962989869","https://openalex.org/W2963156524","https://openalex.org/W2963548292","https://openalex.org/W2963943067","https://openalex.org/W2963991711","https://openalex.org/W2964044289","https://openalex.org/W3024609689","https://openalex.org/W3102942031","https://openalex.org/W3106224380","https://openalex.org/W4211030719","https://openalex.org/W4213201446","https://openalex.org/W4230674625","https://openalex.org/W4301861531","https://openalex.org/W6628642759","https://openalex.org/W6634146089","https://openalex.org/W6674516588","https://openalex.org/W6677331607","https://openalex.org/W6678048025","https://openalex.org/W6680020180","https://openalex.org/W6686827794","https://openalex.org/W6727211380"],"related_works":["https://openalex.org/W3008489523","https://openalex.org/W822005603","https://openalex.org/W2892674788","https://openalex.org/W2093071370","https://openalex.org/W2291342904","https://openalex.org/W2951575892","https://openalex.org/W2951709445","https://openalex.org/W3197144487","https://openalex.org/W3201515136","https://openalex.org/W72116547","https://openalex.org/W2990661983","https://openalex.org/W2146666958","https://openalex.org/W2052352764","https://openalex.org/W2970267318","https://openalex.org/W2798659456","https://openalex.org/W2804662772","https://openalex.org/W2034370748","https://openalex.org/W2106485032","https://openalex.org/W2061512147","https://openalex.org/W2787924355"],"abstract_inverted_index":{"In":[0,58],"this":[1],"paper":[2],"we":[3,60,117],"consider":[4],"high-dimensional":[5,115],"multiclass":[6],"classification":[7],"by":[8,51],"sparse":[9],"multinomial":[10,119],"logistic":[11,120],"regression.":[12],"We":[13,46],"propose":[14,118],"first":[15],"a":[16,26,65,88,94,99,108],"feature":[17,109],"selection":[18,110],"procedure":[19,111],"based":[20],"on":[21,29],"penalized":[22,89],"maximum":[23,90],"likelihood":[24,91],"with":[25,93],"complexity":[27,95],"penalty":[28,96],"the":[30,35,43,53,81,132],"model":[31],"size":[32],"and":[33,70,123,126],"derive":[34],"nonasymptotic":[36],"bounds":[37,76],"for":[38,114],"misclassification":[39],"excess":[40],"risk":[41],"of":[42,73],"resulting":[44],"classifier.":[45],"establish":[47],"also":[48,130],"their":[49],"tightness":[50],"deriving":[52],"corresponding":[54],"minimax":[55,133],"lower":[56],"bounds.":[57],"particular,":[59],"show":[61,127],"that":[62,128],"there":[63],"is":[64],"phase":[66],"transition":[67],"between":[68],"small":[69],"large":[71],"number":[72],"classes.":[74],"The":[75],"can":[77],"be":[78],"reduced":[79],"under":[80],"additional":[82],"low":[83],"noise":[84],"condition.":[85],"To":[86,106],"find":[87],"solution":[92],"requires,":[97],"however,":[98],"combinatorial":[100],"search":[101],"over":[102],"all":[103],"possible":[104],"models.":[105],"design":[107],"computationally":[112],"feasible":[113],"data,":[116],"group":[121],"Lasso":[122],"Slope":[124],"classifiers":[125],"they":[129],"achieve":[131],"order.":[134]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}