{"id":"https://openalex.org/W2115390216","doi":"https://doi.org/10.1162/neco_a_00028","title":"Rademacher Chaos Complexities for Learning the Kernel Problem","display_name":"Rademacher Chaos Complexities for Learning the Kernel Problem","publication_year":2010,"publication_date":"2010-08-30","ids":{"openalex":"https://openalex.org/W2115390216","doi":"https://doi.org/10.1162/neco_a_00028","mag":"2115390216","pmid":"https://pubmed.ncbi.nlm.nih.gov/20804384"},"language":"en","primary_location":{"id":"doi:10.1162/neco_a_00028","is_oa":false,"landing_page_url":"https://doi.org/10.1162/neco_a_00028","pdf_url":null,"source":{"id":"https://openalex.org/S207023548","display_name":"Neural Computation","issn_l":"0899-7667","issn":["0899-7667","1530-888X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048960543","display_name":"Yiming Ying","orcid":null},"institutions":[{"id":"https://openalex.org/I23923803","display_name":"University of Exeter","ror":"https://ror.org/03yghzc09","country_code":"GB","type":"education","lineage":["https://openalex.org/I23923803"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Yiming Ying","raw_affiliation_strings":["College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, EX4 4QF, U.K","[College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter EX4 4QF, U.K..]"],"affiliations":[{"raw_affiliation_string":"College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, EX4 4QF, U.K","institution_ids":["https://openalex.org/I23923803"]},{"raw_affiliation_string":"[College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter EX4 4QF, U.K..]","institution_ids":["https://openalex.org/I23923803"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079342653","display_name":"Colin Campbell","orcid":"https://orcid.org/0000-0002-4775-9802"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Colin Campbell","raw_affiliation_strings":["Department of Engineering Mathematics, University of Bristol, Bristol, BS8 1TR, U.K"],"affiliations":[{"raw_affiliation_string":"Department of Engineering Mathematics, University of Bristol, Bristol, BS8 1TR, U.K","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5048960543"],"corresponding_institution_ids":["https://openalex.org/I23923803"],"apc_list":null,"apc_paid":null,"fwci":2.9161,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.91889854,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"22","issue":"11","first_page":"2858","last_page":"2886"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.9890000224113464,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.9890000224113464,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9814000129699707,"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/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/mathematics","display_name":"Mathematics","score":0.6843565106391907},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.6631407737731934},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.4859846532344818},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.4845515787601471},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.46042490005493164},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.42215168476104736},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4187832772731781},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3245173692703247},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.27903756499290466},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.23351308703422546},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.0886831283569336}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6843565106391907},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6631407737731934},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.4859846532344818},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.4845515787601471},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.46042490005493164},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42215168476104736},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4187832772731781},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3245173692703247},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27903756499290466},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.23351308703422546},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0886831283569336},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","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},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D007858","descriptor_name":"Learning","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D007858","descriptor_name":"Learning","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D007858","descriptor_name":"Learning","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true}],"locations_count":8,"locations":[{"id":"doi:10.1162/neco_a_00028","is_oa":false,"landing_page_url":"https://doi.org/10.1162/neco_a_00028","pdf_url":null,"source":{"id":"https://openalex.org/S207023548","display_name":"Neural Computation","issn_l":"0899-7667","issn":["0899-7667","1530-888X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Computation","raw_type":"journal-article"},{"id":"pmid:20804384","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/20804384","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural computation","raw_type":null},{"id":"pmh:oai:research-information.bris.ac.uk:openaire_cris_publications/034d7642-f60b-4a3c-9c26-ede352101189","is_oa":false,"landing_page_url":"https://research-information.bris.ac.uk/en/publications/034d7642-f60b-4a3c-9c26-ede352101189","pdf_url":null,"source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Ying, Y & Campbell, ICG 2010, 'Rademacher chaos complexities for learning the kernel', Neural Computation, vol. 22, no. 11, pp. 2858 - 2886. https://doi.org/10.1162/NECO_a_00028","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:research-information.bris.ac.uk:publications/034d7642-f60b-4a3c-9c26-ede352101189","is_oa":false,"landing_page_url":"https://direct.mit.edu/neco/article-pdf/22/11/2858/1064356/neco_a_00028.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S7407055359","display_name":"Explore Bristol Research","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":"Ying, Y & Campbell, ICG 2010, 'Rademacher chaos complexities for learning the kernel', Neural Computation, vol. 22, no. 11, pp. 2858 - 2886. https://doi.org/10.1162/NECO_a_00028","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.374.6616","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.374.6616","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://empslocal.ex.ac.uk/people/staff/yy267/KLbound-version3.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.720.7902","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.720.7902","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://seis.bris.ac.uk/%7Eenicgc/pubs/2010/KLbound-version3.pdf","raw_type":"text"},{"id":"pmh:oai:figshare.com:article/29699474","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Journal contribution"},{"id":"pmh:oai:ore.exeter.ac.uk:10871/11962","is_oa":false,"landing_page_url":"http://hdl.handle.net/10871/11962","pdf_url":null,"source":{"id":"https://openalex.org/S4306401998","display_name":"Open Research Exeter (University of Exeter)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I23923803","host_organization_name":"University of Exeter","host_organization_lineage":["https://openalex.org/I23923803"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:figshare.com:article/29699474","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Journal contribution"},"sustainable_development_goals":[{"score":0.4399999976158142,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G6471336651","display_name":null,"funder_award_id":"EP/E027296/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":57,"referenced_works":["https://openalex.org/W93885277","https://openalex.org/W102835753","https://openalex.org/W597932189","https://openalex.org/W1510073064","https://openalex.org/W1519789693","https://openalex.org/W1542886316","https://openalex.org/W1544839292","https://openalex.org/W1559159361","https://openalex.org/W1564947197","https://openalex.org/W1608733719","https://openalex.org/W1698155719","https://openalex.org/W1827175191","https://openalex.org/W1971402309","https://openalex.org/W1978810924","https://openalex.org/W1982032418","https://openalex.org/W2000021956","https://openalex.org/W2003585400","https://openalex.org/W2010353172","https://openalex.org/W2012501405","https://openalex.org/W2017753243","https://openalex.org/W2023163512","https://openalex.org/W2048896634","https://openalex.org/W2063368770","https://openalex.org/W2082100828","https://openalex.org/W2083575259","https://openalex.org/W2087258353","https://openalex.org/W2095692770","https://openalex.org/W2099210314","https://openalex.org/W2103972570","https://openalex.org/W2108198948","https://openalex.org/W2112528242","https://openalex.org/W2116589987","https://openalex.org/W2121033924","https://openalex.org/W2123068691","https://openalex.org/W2128345262","https://openalex.org/W2131804466","https://openalex.org/W2135498906","https://openalex.org/W2140348539","https://openalex.org/W2145295623","https://openalex.org/W2154462399","https://openalex.org/W2158001550","https://openalex.org/W2170356051","https://openalex.org/W2171798319","https://openalex.org/W2501948295","https://openalex.org/W2527802255","https://openalex.org/W2579923771","https://openalex.org/W2950740915","https://openalex.org/W2999905431","https://openalex.org/W3023786531","https://openalex.org/W3099978158","https://openalex.org/W3100743579","https://openalex.org/W4242534643","https://openalex.org/W4245558064","https://openalex.org/W4246350460","https://openalex.org/W4249716558","https://openalex.org/W4251115686","https://openalex.org/W4253712714"],"related_works":["https://openalex.org/W2034881304","https://openalex.org/W2055191027","https://openalex.org/W2061937439","https://openalex.org/W1971753667","https://openalex.org/W2167683897","https://openalex.org/W2052275678","https://openalex.org/W1997271576","https://openalex.org/W2370854018","https://openalex.org/W2559473971","https://openalex.org/W2068208308"],"abstract_inverted_index":{"We":[0],"develop":[1],"a":[2],"novel":[3],"generalization":[4,16,91],"bound":[5],"for":[6,97],"learning":[7,21,98],"the":[8,15,19,27,30,54,67,78],"kernel":[9,20],"problem.":[10],"First,":[11],"we":[12,41,49,87],"show":[13,50],"that":[14],"analysis":[17],"of":[18,26,29,34,66,69,81],"problem":[22],"reduces":[23],"to":[24,43,52],"investigation":[25],"suprema":[28],"Rademacher":[31,45,56],"chaos":[32,46,57],"process":[33],"order":[35],"2":[36],"over":[37],"candidate":[38,70],"kernels,":[39],"which":[40],"refer":[42],"as":[44],"complexity.":[47],"Next,":[48],"how":[51],"estimate":[53],"empirical":[55],"complexity":[58],"by":[59],"well-established":[60],"metric":[61],"entropy":[62,84],"integrals":[63],"and":[64,83,93,101],"pseudo-dimension":[65],"set":[68],"kernels.":[71,105],"Our":[72],"new":[73],"methodology":[74],"mainly":[75],"depends":[76],"on":[77],"principal":[79],"theory":[80],"U-processes":[82],"integrals.":[85],"Finally,":[86],"establish":[88],"satisfactory":[89],"excess":[90],"bounds":[92],"misclassification":[94],"error":[95],"rates":[96],"gaussian":[99],"kernels":[100],"general":[102],"radial":[103],"basis":[104]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}