{"id":"https://openalex.org/W2027016402","doi":"https://doi.org/10.1016/s0893-6080(01)00122-8","title":"Upper bound of the expected training error of neural network regression for a Gaussian noise sequence","display_name":"Upper bound of the expected training error of neural network regression for a Gaussian noise sequence","publication_year":2001,"publication_date":"2001-12-01","ids":{"openalex":"https://openalex.org/W2027016402","doi":"https://doi.org/10.1016/s0893-6080(01)00122-8","mag":"2027016402","pmid":"https://pubmed.ncbi.nlm.nih.gov/11771721"},"language":"en","primary_location":{"id":"doi:10.1016/s0893-6080(01)00122-8","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0893-6080(01)00122-8","pdf_url":null,"source":{"id":"https://openalex.org/S123019304","display_name":"Neural Networks","issn_l":"0893-6080","issn":["0893-6080","1879-2782"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Networks","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/A5108357188","display_name":"Katsuyuki Hagiwara","orcid":null},"institutions":[{"id":"https://openalex.org/I178574317","display_name":"Mie University","ror":"https://ror.org/01529vy56","country_code":"JP","type":"education","lineage":["https://openalex.org/I178574317"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Katsuyuki Hagiwara","raw_affiliation_strings":["Faculty of Physics Engineering, Mie University, Tsu, Japan. hagi@phen.mie-u.ac.jp","Faculty of Physics Engineering, Mie University, 1515 Kamihama, Tsu, 514-8507 Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Physics Engineering, Mie University, Tsu, Japan. hagi@phen.mie-u.ac.jp","institution_ids":["https://openalex.org/I178574317"]},{"raw_affiliation_string":"Faculty of Physics Engineering, Mie University, 1515 Kamihama, Tsu, 514-8507 Japan","institution_ids":["https://openalex.org/I178574317"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078962051","display_name":"Taichi Hayasaka","orcid":null},"institutions":[{"id":"https://openalex.org/I136259955","display_name":"Toyohashi University of Technology","ror":"https://ror.org/04ezg6d83","country_code":"JP","type":"education","lineage":["https://openalex.org/I136259955"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Taichi Hayasaka","raw_affiliation_strings":["Department of Information and Computer Sciences, Toyohashi University of Technology, 1-1 Tempaku, Toyohashi, 441-8580, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Information and Computer Sciences, Toyohashi University of Technology, 1-1 Tempaku, Toyohashi, 441-8580, Japan","institution_ids":["https://openalex.org/I136259955"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047185748","display_name":"Naohiro Toda","orcid":"https://orcid.org/0000-0002-8475-5827"},"institutions":[{"id":"https://openalex.org/I45205469","display_name":"Aichi Prefectural University","ror":"https://ror.org/047n0b268","country_code":"JP","type":"education","lineage":["https://openalex.org/I45205469"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Naohiro Toda","raw_affiliation_strings":["Faculty of Information Science and Technology, Aichi Prefectural University, 522-3 Nagakute-cho, Aichi-gun, 480-1198, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Information Science and Technology, Aichi Prefectural University, 522-3 Nagakute-cho, Aichi-gun, 480-1198, Japan","institution_ids":["https://openalex.org/I45205469"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109042215","display_name":"Shiro Usui","orcid":null},"institutions":[{"id":"https://openalex.org/I136259955","display_name":"Toyohashi University of Technology","ror":"https://ror.org/04ezg6d83","country_code":"JP","type":"education","lineage":["https://openalex.org/I136259955"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Shiro Usui","raw_affiliation_strings":["Department of Information and Computer Sciences, Toyohashi University of Technology, 1-1 Tempaku, Toyohashi, 441-8580, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Information and Computer Sciences, Toyohashi University of Technology, 1-1 Tempaku, Toyohashi, 441-8580, Japan","institution_ids":["https://openalex.org/I136259955"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110042777","display_name":"Kazuhiro Kuno","orcid":null},"institutions":[{"id":"https://openalex.org/I178574317","display_name":"Mie University","ror":"https://ror.org/01529vy56","country_code":"JP","type":"education","lineage":["https://openalex.org/I178574317"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Kazuhiro Kuno","raw_affiliation_strings":["Faculty of Physics Engineering, Mie University, 1515 Kamihama, Tsu, 514-8507 Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Physics Engineering, Mie University, 1515 Kamihama, Tsu, 514-8507 Japan","institution_ids":["https://openalex.org/I178574317"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":3350,"currency":"USD","value_usd":3350},"apc_paid":null,"fwci":4.3737,"has_fulltext":false,"cited_by_count":28,"citation_normalized_percentile":{"value":0.9417009,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"14","issue":"10","first_page":"1419","last_page":"1429"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9990000128746033,"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/T10320","display_name":"Neural Networks and Applications","score":0.9990000128746033,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9984999895095825,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9929999709129333,"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/akaike-information-criterion","display_name":"Akaike information criterion","score":0.7898746728897095},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6570830345153809},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.6227817535400391},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.5168726444244385},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.48658692836761475},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4801054298877716},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.47127267718315125},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.45966801047325134},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4558206796646118},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4556233882904053},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4177822172641754},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.4176986813545227},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.4164997339248657},{"id":"https://openalex.org/keywords/mean-squared-error","display_name":"Mean squared error","score":0.41486692428588867},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39159974455833435},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.31332331895828247},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2961345911026001}],"concepts":[{"id":"https://openalex.org/C126674687","wikidata":"https://www.wikidata.org/wiki/Q1662573","display_name":"Akaike information criterion","level":2,"score":0.7898746728897095},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6570830345153809},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6227817535400391},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.5168726444244385},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.48658692836761475},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4801054298877716},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.47127267718315125},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45966801047325134},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4558206796646118},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4556233882904053},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4177822172641754},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.4176986813545227},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4164997339248657},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.41486692428588867},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39159974455833435},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.31332331895828247},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2961345911026001},{"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/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[{"descriptor_ui":"D000704","descriptor_name":"Analysis of Variance","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000704","descriptor_name":"Analysis of Variance","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000704","descriptor_name":"Analysis of Variance","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D012044","descriptor_name":"Regression Analysis","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D012044","descriptor_name":"Regression Analysis","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D012044","descriptor_name":"Regression Analysis","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D012107","descriptor_name":"Research Design","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D012107","descriptor_name":"Research Design","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D012107","descriptor_name":"Research Design","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D016011","descriptor_name":"Normal Distribution","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016011","descriptor_name":"Normal Distribution","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016011","descriptor_name":"Normal Distribution","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016013","descriptor_name":"Likelihood Functions","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D016013","descriptor_name":"Likelihood Functions","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D016013","descriptor_name":"Likelihood Functions","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"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":2,"locations":[{"id":"doi:10.1016/s0893-6080(01)00122-8","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0893-6080(01)00122-8","pdf_url":null,"source":{"id":"https://openalex.org/S123019304","display_name":"Neural Networks","issn_l":"0893-6080","issn":["0893-6080","1879-2782"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Networks","raw_type":"journal-article"},{"id":"pmid:11771721","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/11771721","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 networks : the official journal of the International Neural Network Society","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W1562777741","https://openalex.org/W1564204854","https://openalex.org/W1586371159","https://openalex.org/W1770912791","https://openalex.org/W1968908999","https://openalex.org/W1973631422","https://openalex.org/W1980620433","https://openalex.org/W1981184437","https://openalex.org/W1997504163","https://openalex.org/W2058815839","https://openalex.org/W2070681743","https://openalex.org/W2076118331","https://openalex.org/W2077390566","https://openalex.org/W2098545770","https://openalex.org/W2125074013","https://openalex.org/W2142635246","https://openalex.org/W2145513251","https://openalex.org/W2147299889","https://openalex.org/W2168175751","https://openalex.org/W2169945273","https://openalex.org/W2598912124","https://openalex.org/W2791786448","https://openalex.org/W3016197797","https://openalex.org/W3042041538","https://openalex.org/W3210385956","https://openalex.org/W4212828114","https://openalex.org/W4236966694","https://openalex.org/W4242688646","https://openalex.org/W6665272994","https://openalex.org/W6681810819","https://openalex.org/W6780769872","https://openalex.org/W6803212681","https://openalex.org/W6803234019"],"related_works":["https://openalex.org/W1987464952","https://openalex.org/W2735932032","https://openalex.org/W1673329429","https://openalex.org/W2028169157","https://openalex.org/W2172884470","https://openalex.org/W2188061941","https://openalex.org/W2148077962","https://openalex.org/W4253044522","https://openalex.org/W1980950130","https://openalex.org/W1999109251"],"abstract_inverted_index":null,"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
