{"id":"https://openalex.org/W4410153303","doi":"https://doi.org/10.1109/tit.2025.3565706","title":"Asymmetry of the Relative Entropy in the Regularization of Empirical Risk Minimization","display_name":"Asymmetry of the Relative Entropy in the Regularization of Empirical Risk Minimization","publication_year":2025,"publication_date":"2025-05-07","ids":{"openalex":"https://openalex.org/W4410153303","doi":"https://doi.org/10.1109/tit.2025.3565706"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2025.3565706","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2025.3565706","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":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://inria.hal.science/hal-04719783v3/document","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5092160897","display_name":"Francisco Daunas","orcid":"https://orcid.org/0009-0009-2038-9985"},"institutions":[{"id":"https://openalex.org/I91136226","display_name":"University of Sheffield","ror":"https://ror.org/05krs5044","country_code":"GB","type":"education","lineage":["https://openalex.org/I91136226"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Francisco Daunas","raw_affiliation_strings":["School of Electrical and Electronic Engineering, University of Sheffield, Sheffield, U.K"],"raw_orcid":"https://orcid.org/0009-0009-2038-9985","affiliations":[{"raw_affiliation_string":"School of Electrical and Electronic Engineering, University of Sheffield, Sheffield, U.K","institution_ids":["https://openalex.org/I91136226"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059775092","display_name":"I\u00f1aki Esnaola","orcid":"https://orcid.org/0000-0001-5597-1718"},"institutions":[{"id":"https://openalex.org/I91136226","display_name":"University of Sheffield","ror":"https://ror.org/05krs5044","country_code":"GB","type":"education","lineage":["https://openalex.org/I91136226"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"I\u00f1aki Esnaola","raw_affiliation_strings":["School of Electrical and Electronic Engineering, University of Sheffield, Sheffield, U.K"],"raw_orcid":"https://orcid.org/0000-0001-5597-1718","affiliations":[{"raw_affiliation_string":"School of Electrical and Electronic Engineering, University of Sheffield, Sheffield, U.K","institution_ids":["https://openalex.org/I91136226"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067353369","display_name":"Samir M. Perlaza","orcid":"https://orcid.org/0000-0002-1887-9215"},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Samir M. Perlaza","raw_affiliation_strings":["INRIA, Centre Inria d&#x2019;Universit&#x00E9; C&#x00F4;te d&#x2019;Azur, Sophia Antipolis, France","Centre Inria d&#x2019;Universit&#x00E9; C&#x00F4;te d&#x2019;Azur, INRIA, Sophia Antipolis, France"],"raw_orcid":"https://orcid.org/0000-0002-1887-9215","affiliations":[{"raw_affiliation_string":"INRIA, Centre Inria d&#x2019;Universit&#x00E9; C&#x00F4;te d&#x2019;Azur, Sophia Antipolis, France","institution_ids":["https://openalex.org/I1326498283"]},{"raw_affiliation_string":"Centre Inria d&#x2019;Universit&#x00E9; C&#x00F4;te d&#x2019;Azur, INRIA, Sophia Antipolis, France","institution_ids":["https://openalex.org/I1326498283"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042307561","display_name":"H. Vincent Poor","orcid":"https://orcid.org/0000-0002-2062-131X"},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"H. Vincent Poor","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Princeton University, Princeton, NJ, USA"],"raw_orcid":"https://orcid.org/0000-0002-2062-131X","affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Princeton University, Princeton, NJ, USA","institution_ids":["https://openalex.org/I20089843"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.09965013,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"71","issue":"8","first_page":"6198","last_page":"6226"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.5985000133514404,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.5985000133514404,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/asymmetry","display_name":"Asymmetry","score":0.5836312174797058},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.5030443072319031},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.489022821187973},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.48427408933639526},{"id":"https://openalex.org/keywords/kullback\u2013leibler-divergence","display_name":"Kullback\u2013Leibler divergence","score":0.44738391041755676},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.43444114923477173},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3482772707939148},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.33424112200737},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2964487671852112},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.288768470287323},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.28441157937049866},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1839953362941742},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.16465938091278076},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.09562751650810242}],"concepts":[{"id":"https://openalex.org/C38976095","wikidata":"https://www.wikidata.org/wiki/Q752641","display_name":"Asymmetry","level":2,"score":0.5836312174797058},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.5030443072319031},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.489022821187973},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48427408933639526},{"id":"https://openalex.org/C171752962","wikidata":"https://www.wikidata.org/wiki/Q255166","display_name":"Kullback\u2013Leibler divergence","level":2,"score":0.44738391041755676},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.43444114923477173},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3482772707939148},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.33424112200737},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2964487671852112},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.288768470287323},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28441157937049866},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1839953362941742},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.16465938091278076},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.09562751650810242},{"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:10.1109/tit.2025.3565706","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2025.3565706","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:HAL:hal-04719783v3","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-04719783v3/file/V2_TIT2023_Journal_CR.pdf","pdf_url":"https://inria.hal.science/hal-04719783v3/document","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Information Theory, 2025, 71 (8), pp.6198 - 6226. &#x27E8;10.1109/TIT.2025.3565706&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-04719783v3","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-04719783v3/file/V2_TIT2023_Journal_CR.pdf","pdf_url":"https://inria.hal.science/hal-04719783v3/document","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Information Theory, 2025, 71 (8), pp.6198 - 6226. &#x27E8;10.1109/TIT.2025.3565706&#x27E9;","raw_type":"Journal articles"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1389156122","display_name":null,"funder_award_id":"872172","funder_id":"https://openalex.org/F4320332999","funder_display_name":"Horizon 2020 Framework Programme"},{"id":"https://openalex.org/G2012084898","display_name":null,"funder_award_id":"2335876","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2053461272","display_name":null,"funder_award_id":"872172","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G213964246","display_name":null,"funder_award_id":"H2020-MSCA-RISE","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G2860730260","display_name":null,"funder_award_id":"ANR-22-PEFT-0010","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G2928114056","display_name":null,"funder_award_id":"MSCA-RISE-2019","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G3345895242","display_name":null,"funder_award_id":"H2020-MSCA","funder_id":"https://openalex.org/F4320332999","funder_display_name":"Horizon 2020 Framework Programme"},{"id":"https://openalex.org/G3477743816","display_name":null,"funder_award_id":"H2020-MSCA-RISE","funder_id":"https://openalex.org/F4320332999","funder_display_name":"Horizon 2020 Framework Programme"},{"id":"https://openalex.org/G4162724171","display_name":null,"funder_award_id":"ECCS-2335876","funder_id":"https://openalex.org/F4320337392","funder_display_name":"Division of Electrical, Communications and Cyber Systems"},{"id":"https://openalex.org/G481716612","display_name":null,"funder_award_id":"ECCS-2335876","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4937468798","display_name":null,"funder_award_id":"H2020","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G6612625481","display_name":null,"funder_award_id":"France 2030","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G8152684609","display_name":null,"funder_award_id":"H2020-MSCA-RISE-2019","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8367957132","display_name":null,"funder_award_id":"MSCA-RISE-2019","funder_id":"https://openalex.org/F4320332999","funder_display_name":"Horizon 2020 Framework Programme"},{"id":"https://openalex.org/G8512683158","display_name":null,"funder_award_id":"H2020-MSCA","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8859643717","display_name":null,"funder_award_id":"ANR-21-CE25-0013","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320332999","display_name":"Horizon 2020 Framework Programme","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320336678","display_name":"Agence de l'innovation de D\u00e9fense","ror":null},{"id":"https://openalex.org/F4320337392","display_name":"Division of Electrical, Communications and Cyber Systems","ror":"https://ror.org/01krpsy48"},{"id":"https://openalex.org/F4320338463","display_name":"CHIST-ERA","ror":"https://ror.org/00rbzpz17"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4410153303.pdf","grobid_xml":"https://content.openalex.org/works/W4410153303.grobid-xml"},"referenced_works_count":54,"referenced_works":["https://openalex.org/W1554922784","https://openalex.org/W2006681603","https://openalex.org/W2009274429","https://openalex.org/W2014384147","https://openalex.org/W2016384870","https://openalex.org/W2029538739","https://openalex.org/W2039252615","https://openalex.org/W2058402854","https://openalex.org/W2062714872","https://openalex.org/W2099111195","https://openalex.org/W2099579348","https://openalex.org/W2112796928","https://openalex.org/W2119818606","https://openalex.org/W2131771566","https://openalex.org/W2149298154","https://openalex.org/W2154852616","https://openalex.org/W2154952480","https://openalex.org/W2161969291","https://openalex.org/W2163786124","https://openalex.org/W2169502938","https://openalex.org/W2541283300","https://openalex.org/W2566505556","https://openalex.org/W2805329953","https://openalex.org/W2963433607","https://openalex.org/W2976697791","https://openalex.org/W2979452771","https://openalex.org/W3215049250","https://openalex.org/W4206043711","https://openalex.org/W4211030719","https://openalex.org/W4220922755","https://openalex.org/W4234067117","https://openalex.org/W4238893454","https://openalex.org/W4242471985","https://openalex.org/W4250954493","https://openalex.org/W4283783871","https://openalex.org/W4289655190","https://openalex.org/W4309129783","https://openalex.org/W4386047747","https://openalex.org/W4386075091","https://openalex.org/W4388240183","https://openalex.org/W4391591286","https://openalex.org/W4393147167","https://openalex.org/W4401567990","https://openalex.org/W4402701019","https://openalex.org/W4406780284","https://openalex.org/W6682891771","https://openalex.org/W6684562015","https://openalex.org/W6740005241","https://openalex.org/W6754848437","https://openalex.org/W6782924552","https://openalex.org/W6804346497","https://openalex.org/W6846553139","https://openalex.org/W6873921372","https://openalex.org/W7034108470"],"related_works":["https://openalex.org/W1980563100","https://openalex.org/W1644661642","https://openalex.org/W4297670902","https://openalex.org/W2035154026","https://openalex.org/W2065779551","https://openalex.org/W2050217822","https://openalex.org/W2163103544","https://openalex.org/W2350826920","https://openalex.org/W2551182807","https://openalex.org/W3033899355"],"abstract_inverted_index":{"The":[0,66,100],"effect":[1],"of":[2,11,31,52,72,95,114,122,156],"relative":[3,17,29,50,109],"entropy":[4,18,30,51,96,110],"asymmetry":[5,97],"is":[6,69,142,147],"analyzed":[7],"in":[8,104],"the":[9,28,32,49,53,59,70,73,76,86,93,112,115,120,123,133,137,157],"context":[10],"empirical":[12,158],"risk":[13,159],"minimization":[14],"(ERM)":[15],"with":[16,37,56,90,152],"regularization":[19,107,146,151],"(ERM-RER).":[20],"Two":[21],"regularizations":[22],"are":[23,98],"considered:":[24],"(<italic":[25,46],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[26,47],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">a</i>)":[27],"measure":[33,42,55,60],"to":[34,39,58,61,75,117,149],"be":[35,62],"optimized":[36,63],"respect":[38,57],"a":[40,127],"reference":[41,54,124],"(Type-I":[43],"ERM-RER);":[44],"and":[45,80],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">b</i>)":[48],"(Type-II":[64],"ERM-RER).":[65],"main":[67],"result":[68],"characterization":[71],"solution":[74,116],"Type-II":[77,91,145],"ERM-RER":[78,89],"problem":[79],"its":[81],"key":[82],"properties.":[83],"By":[84],"comparing":[85],"well-understood":[87],"Type-I":[88,150],"ERM-RER,":[92],"effects":[94],"highlighted.":[99],"analysis":[101],"shows":[102],"that":[103,131,144],"both":[105],"cases,":[106],"by":[108,136],"forces":[111],"support":[113,121],"collapse":[118],"into":[119],"measure,":[125],"introducing":[126],"strong":[128],"inductive":[129],"bias":[130],"negates":[132],"evidence":[134],"provided":[135],"training":[138],"data.":[139],"Finally,":[140],"it":[141],"shown":[143],"equivalent":[148],"an":[153],"appropriate":[154],"transformation":[155],"function.":[160]},"counts_by_year":[],"updated_date":"2026-06-17T08:01:34.144755","created_date":"2025-10-10T00:00:00"}
