{"id":"https://openalex.org/W4385838931","doi":"https://doi.org/10.1088/2632-2153/acf041","title":"Error scaling laws for kernel classification under source and capacity conditions","display_name":"Error scaling laws for kernel classification under source and capacity conditions","publication_year":2023,"publication_date":"2023-08-15","ids":{"openalex":"https://openalex.org/W4385838931","doi":"https://doi.org/10.1088/2632-2153/acf041"},"language":"en","primary_location":{"id":"doi:10.1088/2632-2153/acf041","is_oa":true,"landing_page_url":"https://doi.org/10.1088/2632-2153/acf041","pdf_url":"https://iopscience.iop.org/article/10.1088/2632-2153/acf041/pdf","source":{"id":"https://openalex.org/S4210200687","display_name":"Machine Learning Science and Technology","issn_l":"2632-2153","issn":["2632-2153"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320083","host_organization_name":"IOP Publishing","host_organization_lineage":["https://openalex.org/P4310320083","https://openalex.org/P4310311669"],"host_organization_lineage_names":["IOP Publishing","Institute of Physics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Machine Learning: Science and Technology","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://iopscience.iop.org/article/10.1088/2632-2153/acf041/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5059765426","display_name":"Hugo Cui","orcid":"https://orcid.org/0000-0003-4648-244X"},"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":true,"raw_author_name":"Hugo Cui","raw_affiliation_strings":["Physics, EPFL, EPFL SB SPOC, Lausanne, 1015, SWITZERLAND"],"affiliations":[{"raw_affiliation_string":"Physics, EPFL, EPFL SB SPOC, Lausanne, 1015, SWITZERLAND","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083837327","display_name":"Bruno Loureiro","orcid":"https://orcid.org/0000-0002-6327-4688"},"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":"Bruno Loureiro","raw_affiliation_strings":["Electrical Engineering, EPFL, EPFL STI IEM IDEPHICS, ELD 330 (B\u00e2timent ELD), Station 11, Lausanne, Vaud, 1015, SWITZERLAND"],"affiliations":[{"raw_affiliation_string":"Electrical Engineering, EPFL, EPFL STI IEM IDEPHICS, ELD 330 (B\u00e2timent ELD), Station 11, Lausanne, Vaud, 1015, SWITZERLAND","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068236230","display_name":"Florent Krz\u0105ka\u0142a","orcid":"https://orcid.org/0000-0003-2313-2578"},"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":"Florent Krzakala","raw_affiliation_strings":["Electrical Engineering, EPFL, EPFL STI IEM IDEPHICS, Lausanne, VD, 1015, SWITZERLAND"],"affiliations":[{"raw_affiliation_string":"Electrical Engineering, EPFL, EPFL STI IEM IDEPHICS, Lausanne, VD, 1015, SWITZERLAND","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089268172","display_name":"Lenka Zdeborov\u00e1","orcid":"https://orcid.org/0000-0002-8377-3978"},"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":"Lenka Zdeborov\u00e1","raw_affiliation_strings":["Physics, Computer Science, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL), EPFL SB SPOC, Lausanne, 1015, SWITZERLAND"],"affiliations":[{"raw_affiliation_string":"Physics, Computer Science, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL), EPFL SB SPOC, Lausanne, 1015, SWITZERLAND","institution_ids":["https://openalex.org/I5124864"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5059765426"],"corresponding_institution_ids":["https://openalex.org/I5124864"],"apc_list":{"value":1600,"currency":"GBP","value_usd":1962},"apc_paid":{"value":1600,"currency":"GBP","value_usd":1962},"fwci":0.69,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.75693941,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"4","issue":"3","first_page":"035033","last_page":"035033"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12535","display_name":"Machine Learning and Data Classification","score":0.9977999925613403,"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/T12535","display_name":"Machine Learning and Data Classification","score":0.9977999925613403,"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/T12761","display_name":"Data Stream Mining Techniques","score":0.9961000084877014,"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.9954000115394592,"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/kernel","display_name":"Kernel (algebra)","score":0.6299538016319275},{"id":"https://openalex.org/keywords/margin","display_name":"Margin (machine learning)","score":0.5578693151473999},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5503008365631104},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.5326278805732727},{"id":"https://openalex.org/keywords/gaussian-function","display_name":"Gaussian function","score":0.527062177658081},{"id":"https://openalex.org/keywords/support-vector-machine","display_name":"Support vector machine","score":0.5024969577789307},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5013489723205566},{"id":"https://openalex.org/keywords/hinge-loss","display_name":"Hinge loss","score":0.48379844427108765},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4835098087787628},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4477074146270752},{"id":"https://openalex.org/keywords/kernel-method","display_name":"Kernel method","score":0.4344247579574585},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.39719265699386597},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.3680265545845032},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3569512963294983},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.3011828064918518},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.11778819561004639}],"concepts":[{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.6299538016319275},{"id":"https://openalex.org/C774472","wikidata":"https://www.wikidata.org/wiki/Q6760393","display_name":"Margin (machine learning)","level":2,"score":0.5578693151473999},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5503008365631104},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.5326278805732727},{"id":"https://openalex.org/C7218915","wikidata":"https://www.wikidata.org/wiki/Q1054475","display_name":"Gaussian function","level":3,"score":0.527062177658081},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.5024969577789307},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5013489723205566},{"id":"https://openalex.org/C39891107","wikidata":"https://www.wikidata.org/wiki/Q5767098","display_name":"Hinge loss","level":3,"score":0.48379844427108765},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4835098087787628},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4477074146270752},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.4344247579574585},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39719265699386597},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.3680265545845032},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3569512963294983},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3011828064918518},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.11778819561004639},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1088/2632-2153/acf041","is_oa":true,"landing_page_url":"https://doi.org/10.1088/2632-2153/acf041","pdf_url":"https://iopscience.iop.org/article/10.1088/2632-2153/acf041/pdf","source":{"id":"https://openalex.org/S4210200687","display_name":"Machine Learning Science and Technology","issn_l":"2632-2153","issn":["2632-2153"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320083","host_organization_name":"IOP Publishing","host_organization_lineage":["https://openalex.org/P4310320083","https://openalex.org/P4310311669"],"host_organization_lineage_names":["IOP Publishing","Institute of Physics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Machine Learning: Science and Technology","raw_type":"journal-article"},{"id":"pmh:oai:infoscience.epfl.ch:304752","is_oa":true,"landing_page_url":"https://infoscience.epfl.ch/handle/20.500.14299/200389","pdf_url":"https://infoscience.epfl.ch/bitstreams/46b422db-9a9e-4dd8-bf76-74e81547af24/download","source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"research article"},{"id":"pmh:oai:HAL:hal-05526430v1","is_oa":true,"landing_page_url":"https://hal.science/hal-05526430","pdf_url":null,"source":{"id":"https://openalex.org/S4406922466","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":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Machine Learning: Science and Technology, 2023, 4 (3), pp.035033. &#x27E8;10.1088/2632-2153/acf041&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:doaj.org/article:42957d087507457e8ac4fe235786ff15","is_oa":true,"landing_page_url":"https://doaj.org/article/42957d087507457e8ac4fe235786ff15","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Machine Learning: Science and Technology, Vol 4, Iss 3, p 035033 (2023)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1088/2632-2153/acf041","is_oa":true,"landing_page_url":"https://doi.org/10.1088/2632-2153/acf041","pdf_url":"https://iopscience.iop.org/article/10.1088/2632-2153/acf041/pdf","source":{"id":"https://openalex.org/S4210200687","display_name":"Machine Learning Science and Technology","issn_l":"2632-2153","issn":["2632-2153"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320083","host_organization_name":"IOP Publishing","host_organization_lineage":["https://openalex.org/P4310320083","https://openalex.org/P4310311669"],"host_organization_lineage_names":["IOP Publishing","Institute of Physics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Machine Learning: Science and Technology","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.7799999713897705}],"awards":[{"id":"https://openalex.org/G3694363619","display_name":"Statistical Mechanics of Learning","funder_award_id":"714608","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G5790682227","display_name":null,"funder_award_id":"714608-SMiLe","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8051717526","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8318064016","display_name":null,"funder_award_id":"Horizon","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4385838931.pdf"},"referenced_works_count":43,"referenced_works":["https://openalex.org/W194417083","https://openalex.org/W1860574113","https://openalex.org/W1996437515","https://openalex.org/W2003585400","https://openalex.org/W2012501405","https://openalex.org/W2014902932","https://openalex.org/W2089880431","https://openalex.org/W2103376147","https://openalex.org/W2112796928","https://openalex.org/W2396213570","https://openalex.org/W2895466035","https://openalex.org/W2945765717","https://openalex.org/W2945975513","https://openalex.org/W2963094815","https://openalex.org/W2997591727","https://openalex.org/W3018252856","https://openalex.org/W3034708079","https://openalex.org/W3083720136","https://openalex.org/W3089321292","https://openalex.org/W3096003755","https://openalex.org/W3099978158","https://openalex.org/W3104165014","https://openalex.org/W3105622673","https://openalex.org/W3105792944","https://openalex.org/W3111154923","https://openalex.org/W3117575511","https://openalex.org/W3118608800","https://openalex.org/W3162003518","https://openalex.org/W3198964499","https://openalex.org/W3209248780","https://openalex.org/W4288324537","https://openalex.org/W4321226558","https://openalex.org/W4366084840","https://openalex.org/W6607883127","https://openalex.org/W6664076635","https://openalex.org/W6751828895","https://openalex.org/W6759134080","https://openalex.org/W6762667689","https://openalex.org/W6773742229","https://openalex.org/W6779356556","https://openalex.org/W6783911279","https://openalex.org/W6787972765","https://openalex.org/W6803389437"],"related_works":["https://openalex.org/W2558935147","https://openalex.org/W2605627527","https://openalex.org/W3099699208","https://openalex.org/W1973746459","https://openalex.org/W2089892314","https://openalex.org/W2995405785","https://openalex.org/W2095626363","https://openalex.org/W2169565408","https://openalex.org/W2375370983","https://openalex.org/W2011212036"],"abstract_inverted_index":{"Abstract":[0],"In":[1,45],"this":[2,46,130],"manuscript":[3],"we":[4,48,71,78],"consider":[5,49],"the":[6,15,19,23,38,50,57,75,80,84,92,116,126,153],"problem":[7],"of":[8,18,25,41,53,66,91,132,152,155],"kernel":[9,103,160],"classification.":[10],"While":[11],"worst-case":[12],"bounds":[13],"on":[14,139,165],"decay":[16,81],"rate":[17],"prediction":[20,151],"error":[21,87],"with":[22],"number":[24,65],"samples":[26],"are":[27,136],"known":[28],"for":[29,83,100,129,159],"some":[30,166],"classifiers,":[31],"they":[32],"often":[33],"fail":[34],"to":[35],"accurately":[36],"describe":[37,125],"learning":[39,127],"curves":[40,128],"real":[42,67,140,167],"data":[43,54,68,133],"sets.":[44],"work,":[47],"important":[51],"class":[52,131],"sets":[55,69],"satisfying":[56],"standard":[58,102],"source":[59,93],"and":[60,94,111,114,135],"capacity":[61,95],"conditions,":[62],"comprising":[63],"a":[64,89,156],"as":[70,88,148],"show":[72],"numerically.":[73],"Under":[74],"Gaussian":[76],"design,":[77],"derive":[79],"rates":[82,123],"misclassification":[85],"(prediction)":[86],"function":[90],"coefficients.":[96],"We":[97,119],"do":[98],"so":[99],"two":[101,117],"classification":[104,161],"settings,":[105],"namely":[106],"margin-maximizing":[107],"support":[108],"vector":[109],"machines":[110],"ridge":[112],"classification,":[113],"contrast":[115],"methods.":[118],"find":[120],"that":[121,162],"our":[122],"tightly":[124],"sets,":[134],"also":[137,145],"observed":[138],"data.":[141],"Our":[142],"results":[143],"can":[144],"be":[146],"seen":[147],"an":[149],"explicit":[150],"exponents":[154],"scaling":[157],"law":[158],"is":[163],"accurate":[164],"datasets.":[168]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-04-13T07:58:08.660418","created_date":"2025-10-10T00:00:00"}
