{"id":"https://openalex.org/W2963193705","doi":"https://doi.org/10.1007/s10208-018-09407-7","title":"Convergence Analysis of Deterministic Kernel-Based Quadrature Rules in Misspecified Settings","display_name":"Convergence Analysis of Deterministic Kernel-Based Quadrature Rules in Misspecified Settings","publication_year":2019,"publication_date":"2019-01-07","ids":{"openalex":"https://openalex.org/W2963193705","doi":"https://doi.org/10.1007/s10208-018-09407-7","mag":"2963193705"},"language":"en","primary_location":{"id":"doi:10.1007/s10208-018-09407-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10208-018-09407-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10208-018-09407-7.pdf","source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10208-018-09407-7.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014758363","display_name":"Motonobu Kanagawa","orcid":"https://orcid.org/0000-0002-3948-8053"},"institutions":[{"id":"https://openalex.org/I4210135521","display_name":"Max Planck Institute for Intelligent Systems","ror":"https://ror.org/04fq9j139","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210135521"]},{"id":"https://openalex.org/I8087733","display_name":"University of T\u00fcbingen","ror":"https://ror.org/03a1kwz48","country_code":"DE","type":"education","lineage":["https://openalex.org/I8087733"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Motonobu Kanagawa","raw_affiliation_strings":["University of T\u00fcbingen and Max Planck Institute for Intelligent Systems, Max-Planck-Ring 4, 72076, T\u00fcbingen, Germany"],"affiliations":[{"raw_affiliation_string":"University of T\u00fcbingen and Max Planck Institute for Intelligent Systems, Max-Planck-Ring 4, 72076, T\u00fcbingen, Germany","institution_ids":["https://openalex.org/I4210135521","https://openalex.org/I8087733"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109582233","display_name":"Bharath K. Sriperumbudur","orcid":null},"institutions":[{"id":"https://openalex.org/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Bharath K. Sriperumbudur","raw_affiliation_strings":["Department of Statistics, Pennsylvania State University, University Park, PA, 16802, USA"],"affiliations":[{"raw_affiliation_string":"Department of Statistics, Pennsylvania State University, University Park, PA, 16802, USA","institution_ids":["https://openalex.org/I130769515"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012922872","display_name":"Kenji Fukumizu","orcid":"https://orcid.org/0000-0002-3488-2625"},"institutions":[{"id":"https://openalex.org/I4210134673","display_name":"The Institute of Statistical Mathematics","ror":"https://ror.org/03jcejr58","country_code":"JP","type":"facility","lineage":["https://openalex.org/I1319490839","https://openalex.org/I4210134673","https://openalex.org/I4210158934"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Kenji Fukumizu","raw_affiliation_strings":["The Institute of Statistical Mathematics, 10-3 Midori-cho, Tachikawa, Tokyo, 190-8562, Japan"],"affiliations":[{"raw_affiliation_string":"The Institute of Statistical Mathematics, 10-3 Midori-cho, Tachikawa, Tokyo, 190-8562, Japan","institution_ids":["https://openalex.org/I4210134673"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5014758363"],"corresponding_institution_ids":["https://openalex.org/I4210135521","https://openalex.org/I8087733"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":4.542,"has_fulltext":true,"cited_by_count":19,"citation_normalized_percentile":{"value":0.95055198,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"20","issue":"1","first_page":"155","last_page":"194"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9959999918937683,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9929999709129333,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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":0.8003289699554443},{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.6497739553451538},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6139616966247559},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5823653340339661},{"id":"https://openalex.org/keywords/numerical-integration","display_name":"Numerical integration","score":0.5422937870025635},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5411279797554016},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.4301379919052124},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.38755881786346436},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.33934301137924194},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2877443730831146},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.15245074033737183}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8003289699554443},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.6497739553451538},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6139616966247559},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5823653340339661},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.5422937870025635},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5411279797554016},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.4301379919052124},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.38755881786346436},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33934301137924194},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2877443730831146},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.15245074033737183},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10208-018-09407-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10208-018-09407-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10208-018-09407-7.pdf","source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s10208-018-09407-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10208-018-09407-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10208-018-09407-7.pdf","source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2028714080","display_name":null,"funder_award_id":"25120012","funder_id":"https://openalex.org/F4320320912","funder_display_name":"Ministry of Education, Culture, Sports, Science and Technology"},{"id":"https://openalex.org/G3204869063","display_name":null,"funder_award_id":"25120012","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G3236194794","display_name":null,"funder_award_id":"Grant-in-Aid","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G3857676562","display_name":null,"funder_award_id":"Grant-in-Aid for Scientific Research on Innovative","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G5755530080","display_name":null,"funder_award_id":"Scientific Research on Innovative A","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G6267471473","display_name":null,"funder_award_id":"Grant-in-Aid","funder_id":"https://openalex.org/F4320320912","funder_display_name":"Ministry of Education, Culture, Sports, Science and Technology"},{"id":"https://openalex.org/G6504706879","display_name":"\u8133\u306e\u7d71\u5fa1\u6a5f\u80fd","funder_award_id":"512001","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G7167128334","display_name":null,"funder_award_id":"Grant-in-Aid for Scientific Researc","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G7290979651","display_name":"Reproducing Kernel Hilbert Space Embedding of Measures: Theory and Applications to Statistical Learning","funder_award_id":"1713011","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7311877988","display_name":"\u30d9\u30a4\u30ba\u7684\u6570\u5024\u89e3\u6790\u306b\u3088\u308b\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u8aa4\u5dee\u306e\u5b9a\u91cf\u5316\uff1a\u65b0\u5c55\u958b\u3068\u30c7\u30fc\u30bf\u540c\u5316\u3078\u306e\u5fdc\u7528","funder_award_id":"17K12654","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G7337825077","display_name":null,"funder_award_id":"Grant-in-Aid for Sc","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G733985567","display_name":"\u938c\u5009\u6642\u4ee3\u306b\u767a\u751f\u3057\u305f\u308b\u6587\u5b66\u8a55\u66f2(\u8a9e\u308a\u7269)\u306e\u79d1\u5b66\u7684\u306a\u308b\u5b9f\u4f53\u306e\u7814\u7a76(\u58f0\u660e\u3068\u5e73\u66f2\u3068\u5f8c\u4e16\u90a6\u697d\u3068\u306e\u95a2\u4fc2)","funder_award_id":"12001","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G7748302082","display_name":null,"funder_award_id":"Scientific Research on Innovative Areas","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G805358627","display_name":"\u30e1\u30c0\u30ab\u306b\u304a\u3051\u308b\u904a\u96e2\u80da\u7d30\u80de\u306b\u95a2\u3059\u308b\u7814\u7a76","funder_award_id":"25120","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G8759943101","display_name":null,"funder_award_id":"rant-in-Aid for Scientific Research","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G878694594","display_name":"\u4fe1\u98db\u56fd\u5883\u5730\u5e2f\u306e\u65b9\u8a00\u5206\u5e03\u3068\u305d\u306e\u63a8\u79fb","funder_award_id":"13011","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320912","display_name":"Ministry of Education, Culture, Sports, Science and Technology","ror":"https://ror.org/048rj2z13"},{"id":"https://openalex.org/F4320322434","display_name":"Max-Planck-Gesellschaft","ror":"https://ror.org/01hhn8329"},{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2963193705.pdf","grobid_xml":"https://content.openalex.org/works/W2963193705.grobid-xml"},"referenced_works_count":70,"referenced_works":["https://openalex.org/W93885277","https://openalex.org/W162854683","https://openalex.org/W561317618","https://openalex.org/W654435104","https://openalex.org/W1486164486","https://openalex.org/W1488877410","https://openalex.org/W1492326914","https://openalex.org/W1530226021","https://openalex.org/W1554388601","https://openalex.org/W1632550705","https://openalex.org/W1698155719","https://openalex.org/W1731081199","https://openalex.org/W1810147435","https://openalex.org/W1933639893","https://openalex.org/W1978501336","https://openalex.org/W1981743146","https://openalex.org/W1986280275","https://openalex.org/W1988473367","https://openalex.org/W1988793248","https://openalex.org/W2008056655","https://openalex.org/W2014551121","https://openalex.org/W2030404880","https://openalex.org/W2038461951","https://openalex.org/W2040396531","https://openalex.org/W2052524535","https://openalex.org/W2056251976","https://openalex.org/W2072216330","https://openalex.org/W2080679139","https://openalex.org/W2089245375","https://openalex.org/W2110720940","https://openalex.org/W2112459735","https://openalex.org/W2124331852","https://openalex.org/W2126272934","https://openalex.org/W2127689830","https://openalex.org/W2143772913","https://openalex.org/W2159977881","https://openalex.org/W2161591817","https://openalex.org/W2163255905","https://openalex.org/W2212660284","https://openalex.org/W2357479853","https://openalex.org/W2365455488","https://openalex.org/W2401419235","https://openalex.org/W2418306335","https://openalex.org/W2486824498","https://openalex.org/W2497677836","https://openalex.org/W2616566795","https://openalex.org/W2626041123","https://openalex.org/W2784010394","https://openalex.org/W2795812519","https://openalex.org/W2887152882","https://openalex.org/W2900617924","https://openalex.org/W2924199702","https://openalex.org/W2951392481","https://openalex.org/W2963135308","https://openalex.org/W2963169589","https://openalex.org/W2963249850","https://openalex.org/W2963709899","https://openalex.org/W2963945008","https://openalex.org/W2964061343","https://openalex.org/W2964202371","https://openalex.org/W2964204711","https://openalex.org/W2966734222","https://openalex.org/W3101183984","https://openalex.org/W3101300063","https://openalex.org/W3102328113","https://openalex.org/W3104531771","https://openalex.org/W3204708751","https://openalex.org/W4234721591","https://openalex.org/W4245558064","https://openalex.org/W4254115559"],"related_works":["https://openalex.org/W2035232447","https://openalex.org/W4237740072","https://openalex.org/W2056088350","https://openalex.org/W2144321310","https://openalex.org/W2001419904","https://openalex.org/W1982234448","https://openalex.org/W2560252838","https://openalex.org/W2024733137","https://openalex.org/W3158760621","https://openalex.org/W2358506996"],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"convergence":[3,47,73,118,153],"analysis":[4],"of":[5,82,109,117,152,158,163,167],"kernel-based":[6],"quadrature":[7,15,41,56,60,121,135],"rules":[8],"in":[9,16,122,154],"misspecified":[10,24,123],"settings,":[11],"focusing":[12],"on":[13,38,50,54,59,65,129,177],"deterministic":[14],"Sobolev":[17,35,156],"spaces.":[18],"In":[19],"particular,":[20],"we":[21,70,113],"deal":[22],"with":[23],"settings":[25],"where":[26],"a":[27,34,40,55,107,115,127,159,168,172],"test":[28,169],"integrand":[29],"is":[30,43],"less":[31],"smooth":[32],"than":[33],"RKHS":[36],"based":[37,49],"which":[39],"rule":[42],"constructed.":[44],"We":[45,125],"provide":[46],"guarantees":[48],"two":[51],"different":[52],"assumptions":[53],"rule:":[57],"one":[58],"weights":[61,84],"and":[62,139],"the":[63,80,95,110,149,155,164,178],"other":[64],"design":[66,99,130],"points.":[67],"More":[68],"precisely,":[69],"show":[71,140],"that":[72],"rates":[74],"can":[75],"be":[76],"derived":[77],"(i)":[78],"if":[79,94],"sum":[81],"absolute":[83],"remains":[85],"constant":[86],"(or":[87],"does":[88,101],"not":[89,102],"increase":[90],"quickly),":[91],"or":[92],"(ii)":[93],"minimum":[96],"distance":[97],"between":[98],"points":[100,131],"decrease":[103],"very":[104],"quickly.":[105],"As":[106],"consequence":[108],"latter":[111],"result,":[112],"derive":[114],"rate":[116,151],"for":[119],"Bayesian":[120,134],"settings.":[124],"reveal":[126],"condition":[128,176],"to":[132,137],"make":[133],"robust":[136],"misspecification,":[138],"that,":[141],"under":[142,171],"this":[143],"condition,":[144],"it":[145],"may":[146],"adaptively":[147],"achieve":[148],"optimal":[150],"space":[157],"lesser":[160],"order":[161],"(i.e.,":[162],"unknown":[165],"smoothness":[166],"integrand),":[170],"slightly":[173],"stronger":[174],"regularity":[175],"integrand.":[179]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":1}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}
