{"id":"https://openalex.org/W2156230286","doi":"https://doi.org/10.1162/neco_a_00566","title":"Refined Rademacher Chaos Complexity Bounds with Applications to the Multikernel Learning Problem","display_name":"Refined Rademacher Chaos Complexity Bounds with Applications to the Multikernel Learning Problem","publication_year":2014,"publication_date":"2014-01-30","ids":{"openalex":"https://openalex.org/W2156230286","doi":"https://doi.org/10.1162/neco_a_00566","mag":"2156230286","pmid":"https://pubmed.ncbi.nlm.nih.gov/24479777"},"language":"en","primary_location":{"id":"doi:10.1162/neco_a_00566","is_oa":false,"landing_page_url":"https://doi.org/10.1162/neco_a_00566","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046468616","display_name":"Yunwen Lei","orcid":"https://orcid.org/0000-0002-5383-467X"},"institutions":[{"id":"https://openalex.org/I37461747","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17","country_code":"CN","type":"education","lineage":["https://openalex.org/I37461747"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yunwen Lei","raw_affiliation_strings":["State Key Lab of Software Engineering, School of Computer, Wuhan University, Wuhan 430072, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State Key Lab of Software Engineering, School of Computer, Wuhan University, Wuhan 430072, China","institution_ids":["https://openalex.org/I37461747"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100829152","display_name":"Lixin Ding","orcid":null},"institutions":[{"id":"https://openalex.org/I37461747","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17","country_code":"CN","type":"education","lineage":["https://openalex.org/I37461747"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Lixin Ding","raw_affiliation_strings":["State Key Lab of Software Engineering, School of Computer, Wuhan University, Wuhan 430072, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State Key Lab of Software Engineering, School of Computer, Wuhan University, Wuhan 430072, China","institution_ids":["https://openalex.org/I37461747"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5046468616","https://openalex.org/A5100829152"],"corresponding_institution_ids":["https://openalex.org/I37461747"],"apc_list":null,"apc_paid":null,"fwci":1.6567,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.87978717,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"26","issue":"4","first_page":"739","last_page":"760"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.9959999918937683,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9959999918937683,"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/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9684000015258789,"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/T10057","display_name":"Face and Expression Recognition","score":0.9607999920845032,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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":0.5726081728935242},{"id":"https://openalex.org/keywords/chaos","display_name":"CHAOS (operating system)","score":0.5504699945449829},{"id":"https://openalex.org/keywords/divergence","display_name":"Divergence (linguistics)","score":0.529224157333374},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.43853485584259033},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.4372010827064514},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.360162615776062},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.35607224702835083},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.32783663272857666}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5726081728935242},{"id":"https://openalex.org/C2779374083","wikidata":"https://www.wikidata.org/wiki/Q5011038","display_name":"CHAOS (operating system)","level":2,"score":0.5504699945449829},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.529224157333374},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.43853485584259033},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.4372010827064514},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.360162615776062},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.35607224702835083},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32783663272857666},{"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0}],"mesh":[{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D001185","descriptor_name":"Artificial Intelligence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D001185","descriptor_name":"Artificial Intelligence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D001185","descriptor_name":"Artificial Intelligence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D007858","descriptor_name":"Learning","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D007858","descriptor_name":"Learning","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D007858","descriptor_name":"Learning","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D010363","descriptor_name":"Pattern Recognition, Automated","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D010363","descriptor_name":"Pattern Recognition, Automated","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D010363","descriptor_name":"Pattern Recognition, Automated","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D017711","descriptor_name":"Nonlinear Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D017711","descriptor_name":"Nonlinear Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D017711","descriptor_name":"Nonlinear Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true}],"locations_count":2,"locations":[{"id":"doi:10.1162/neco_a_00566","is_oa":false,"landing_page_url":"https://doi.org/10.1162/neco_a_00566","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:24479777","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/24479777","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}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W93885277","https://openalex.org/W597932189","https://openalex.org/W1507545330","https://openalex.org/W1509689762","https://openalex.org/W1510073064","https://openalex.org/W1519789693","https://openalex.org/W1542886316","https://openalex.org/W1544839292","https://openalex.org/W1559159361","https://openalex.org/W1560724230","https://openalex.org/W1572386387","https://openalex.org/W1968436459","https://openalex.org/W1982032418","https://openalex.org/W2003585400","https://openalex.org/W2010353172","https://openalex.org/W2016852016","https://openalex.org/W2023163512","https://openalex.org/W2047278710","https://openalex.org/W2047709005","https://openalex.org/W2065976408","https://openalex.org/W2082174631","https://openalex.org/W2083575259","https://openalex.org/W2115390216","https://openalex.org/W2121033924","https://openalex.org/W2123068691","https://openalex.org/W2127069950","https://openalex.org/W2128345262","https://openalex.org/W2135498906","https://openalex.org/W2145295623","https://openalex.org/W2150772522","https://openalex.org/W2154630456","https://openalex.org/W2170356051","https://openalex.org/W2171798319","https://openalex.org/W2527802255","https://openalex.org/W2579923771","https://openalex.org/W2596585349","https://openalex.org/W2990138404","https://openalex.org/W2999905431","https://openalex.org/W3013820469","https://openalex.org/W3099978158","https://openalex.org/W3144619878","https://openalex.org/W4245558064","https://openalex.org/W4246350460","https://openalex.org/W4249716558","https://openalex.org/W4254362479","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2320196587","https://openalex.org/W3208095355","https://openalex.org/W2177370417","https://openalex.org/W4243901518","https://openalex.org/W2052507016","https://openalex.org/W2180461068","https://openalex.org/W4383267773","https://openalex.org/W3110439525","https://openalex.org/W2051816080","https://openalex.org/W4251075027"],"abstract_inverted_index":{"Estimating":[0],"the":[1,12,35,53,56,60,63,80],"Rademacher":[2,29,75],"chaos":[3,30,76],"complexity":[4,77],"of":[5,14,55,62],"order":[6],"two":[7],"is":[8,40],"important":[9],"for":[10,28],"understanding":[11],"performance":[13],"multikernel":[15],"learning":[16,86],"(MKL)":[17],"machines.":[18],"In":[19],"this":[20],"letter,":[21],"we":[22,71],"develop":[23],"a":[24],"novel":[25],"entropy":[26],"integral":[27],"complexities.":[31],"As":[32],"compared":[33],"to":[34,51,79],"previous":[36],"bounds,":[37],"our":[38,74],"result":[39],"much":[41],"improved":[42],"in":[43,66],"that":[44],"it":[45],"introduces":[46],"an":[47],"adjustable":[48],"parameter":[49],"\u03b5":[50],"prohibit":[52],"divergence":[54],"involved":[57],"integral.":[58],"With":[59],"use":[61],"iteration":[64],"technique":[65],"Steinwart":[67],"and":[68,83],"Scovel":[69],"(2007),":[70],"also":[72],"apply":[73],"bound":[78],"MKL":[81],"problems":[82],"improve":[84],"existing":[85],"rates.":[87]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2013,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
