{"id":"https://openalex.org/W2016865000","doi":"https://doi.org/10.1162/neco_a_00178","title":"Reproducing Kernel Banach Spaces with the \u2113<sup>1</sup>Norm II: Error Analysis for Regularized Least Square Regression","display_name":"Reproducing Kernel Banach Spaces with the \u2113<sup>1</sup>Norm II: Error Analysis for Regularized Least Square Regression","publication_year":2011,"publication_date":"2011-07-07","ids":{"openalex":"https://openalex.org/W2016865000","doi":"https://doi.org/10.1162/neco_a_00178","mag":"2016865000"},"language":"en","primary_location":{"id":"doi:10.1162/neco_a_00178","is_oa":false,"landing_page_url":"https://doi.org/10.1162/neco_a_00178","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"],"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/A5102759381","display_name":"Guohui Song","orcid":"https://orcid.org/0000-0002-6811-9089"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Guohui Song","raw_affiliation_strings":["School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287, U.S.A"],"affiliations":[{"raw_affiliation_string":"School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287, U.S.A","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023682610","display_name":"Haizhang Zhang","orcid":"https://orcid.org/0000-0002-8241-3145"},"institutions":[{"id":"https://openalex.org/I157773358","display_name":"Sun Yat-sen University","ror":"https://ror.org/0064kty71","country_code":"CN","type":"education","lineage":["https://openalex.org/I157773358"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Haizhang Zhang","raw_affiliation_strings":["School of Mathematics and Computational Science and Guangdong Province Key Laboratory of Computational Science, Sun Yat-sen University, Guangzhou 510275, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computational Science and Guangdong Province Key Laboratory of Computational Science, Sun Yat-sen University, Guangzhou 510275, China","institution_ids":["https://openalex.org/I157773358"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5102759381"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.8233,"has_fulltext":false,"cited_by_count":41,"citation_normalized_percentile":{"value":0.9511722,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"23","issue":"10","first_page":"2713","last_page":"2729"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9994000196456909,"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"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9994000196456909,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11236","display_name":"Control Systems and Identification","score":0.9915000200271606,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7388492226600647},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.6665198802947998},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.5765103101730347},{"id":"https://openalex.org/keywords/representer-theorem","display_name":"Representer theorem","score":0.5583869814872742},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.5454117655754089},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.47649019956588745},{"id":"https://openalex.org/keywords/mean-squared-error","display_name":"Mean squared error","score":0.4579869508743286},{"id":"https://openalex.org/keywords/kernel-method","display_name":"Kernel method","score":0.4439728260040283},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4393864870071411},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35142844915390015},{"id":"https://openalex.org/keywords/kernel-embedding-of-distributions","display_name":"Kernel embedding of distributions","score":0.20319673418998718},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.19804736971855164},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1964188516139984},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18079674243927002},{"id":"https://openalex.org/keywords/support-vector-machine","display_name":"Support vector machine","score":0.13823598623275757}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7388492226600647},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.6665198802947998},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.5765103101730347},{"id":"https://openalex.org/C172623408","wikidata":"https://www.wikidata.org/wiki/Q7314263","display_name":"Representer theorem","level":5,"score":0.5583869814872742},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.5454117655754089},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.47649019956588745},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.4579869508743286},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.4439728260040283},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4393864870071411},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35142844915390015},{"id":"https://openalex.org/C134517425","wikidata":"https://www.wikidata.org/wiki/Q16000131","display_name":"Kernel embedding of distributions","level":4,"score":0.20319673418998718},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.19804736971855164},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1964188516139984},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18079674243927002},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.13823598623275757},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1162/neco_a_00178","is_oa":false,"landing_page_url":"https://doi.org/10.1162/neco_a_00178","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321895","display_name":"Government of Jiangxi Province","ror":"https://ror.org/02fzqav45"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W93885277","https://openalex.org/W597932189","https://openalex.org/W1510073064","https://openalex.org/W1560724230","https://openalex.org/W1572636854","https://openalex.org/W1970781863","https://openalex.org/W1972267660","https://openalex.org/W1982296049","https://openalex.org/W1986931325","https://openalex.org/W1988936067","https://openalex.org/W1994642189","https://openalex.org/W2010916095","https://openalex.org/W2015904350","https://openalex.org/W2032882463","https://openalex.org/W2033603511","https://openalex.org/W2044421224","https://openalex.org/W2045386260","https://openalex.org/W2047278710","https://openalex.org/W2110652811","https://openalex.org/W2112531253","https://openalex.org/W2113075591","https://openalex.org/W2125085449","https://openalex.org/W2135046866","https://openalex.org/W2145096794","https://openalex.org/W2148603752","https://openalex.org/W4245558064","https://openalex.org/W4250071731","https://openalex.org/W4254721730"],"related_works":["https://openalex.org/W2931773519","https://openalex.org/W1847580023","https://openalex.org/W4247446331","https://openalex.org/W4243330733","https://openalex.org/W2170356051","https://openalex.org/W1836142315","https://openalex.org/W2172290429","https://openalex.org/W177392165","https://openalex.org/W4294351650","https://openalex.org/W2122925131"],"abstract_inverted_index":{"A":[0],"typical":[1],"approach":[2],"in":[3,84],"estimating":[4],"the":[5,16,20,23,26,30,40,45,49,53,67,76],"learning":[6,11,77],"rate":[7,78],"of":[8,22,47,80],"a":[9,34],"regularized":[10],"scheme":[12],"is":[13],"to":[14,74],"bound":[15],"approximation":[17],"error":[18,51],"by":[19],"sum":[21,54],"sampling":[24],"error,":[25,28],"hypothesis":[27,50],"and":[29],"regularization":[31],"error.":[32],"Using":[33],"reproducing":[35,62],"kernel":[36,63],"space":[37],"that":[38],"satisfies":[39],"linear":[41],"representer":[42],"theorem":[43],"brings":[44],"advantage":[46],"discarding":[48],"from":[52],"automatically.":[55],"Following":[56],"this":[57],"direction,":[58],"we":[59],"illustrate":[60],"how":[61],"Banach":[64],"spaces":[65],"with":[66],"\u2113":[68,81],"1":[69,82],"norm":[70],"can":[71],"be":[72],"applied":[73],"improve":[75],"estimate":[79],"-regularization":[83],"machine":[85],"learning.":[86]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}