{"id":"https://openalex.org/W2013892587","doi":"https://doi.org/10.1142/s0129065796000245","title":"EMPIRICAL ERROR-CONFIDENCE CURVES FOR NEURAL NETWORK AND GAUSSIAN CLASSIFIERS","display_name":"EMPIRICAL ERROR-CONFIDENCE CURVES FOR NEURAL NETWORK AND GAUSSIAN CLASSIFIERS","publication_year":1996,"publication_date":"1996-07-01","ids":{"openalex":"https://openalex.org/W2013892587","doi":"https://doi.org/10.1142/s0129065796000245","mag":"2013892587","pmid":"https://pubmed.ncbi.nlm.nih.gov/8891842"},"language":"en","primary_location":{"id":"doi:10.1142/s0129065796000245","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129065796000245","pdf_url":null,"source":{"id":"https://openalex.org/S197665576","display_name":"International Journal of Neural Systems","issn_l":"0129-0657","issn":["0129-0657","1793-6462"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Neural Systems","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/A5081745213","display_name":"Gregory J. Wolff","orcid":null},"institutions":[{"id":"https://openalex.org/I4210109512","display_name":"Ricoh (United States)","ror":"https://ror.org/017q93w69","country_code":"US","type":"company","lineage":["https://openalex.org/I24193003","https://openalex.org/I4210109512"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"GREGORY J. WOLFF","raw_affiliation_strings":["Machine Learning & Perception Group, Ricoh California Research Center, 2882 Sand Hill Road Suite 115, Menlo Park, CA 94025, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Machine Learning & Perception Group, Ricoh California Research Center, 2882 Sand Hill Road Suite 115, Menlo Park, CA 94025, USA","institution_ids":["https://openalex.org/I4210109512"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051143560","display_name":"David G. Stork","orcid":"https://orcid.org/0000-0002-0135-2652"},"institutions":[{"id":"https://openalex.org/I4210109512","display_name":"Ricoh (United States)","ror":"https://ror.org/017q93w69","country_code":"US","type":"company","lineage":["https://openalex.org/I24193003","https://openalex.org/I4210109512"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"DAVID G. STORK","raw_affiliation_strings":["Machine Learning & Perception Group, Ricoh California Research Center, 2882 Sand Hill Road Suite 115, Menlo Park, CA 94025, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Machine Learning & Perception Group, Ricoh California Research Center, 2882 Sand Hill Road Suite 115, Menlo Park, CA 94025, USA","institution_ids":["https://openalex.org/I4210109512"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035543011","display_name":"Art B. Owen","orcid":"https://orcid.org/0000-0001-5860-3945"},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"ART OWEN","raw_affiliation_strings":["Department of Statistics, Stanford University, Stanford, CA 94305, USA","Department of Statistics, Stanford University Stanford, CA 94305, USA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics, Stanford University, Stanford, CA 94305, USA","institution_ids":["https://openalex.org/I97018004"]},{"raw_affiliation_string":"Department of Statistics, Stanford University Stanford, CA 94305, USA#TAB#","institution_ids":["https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.11864691,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"07","issue":"03","first_page":"263","last_page":"271"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.7365000247955322,"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":0.7365000247955322,"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/artificial-neural-network","display_name":"Artificial neural network","score":0.6443896293640137},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5569531321525574},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5465828776359558},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.5325794219970703},{"id":"https://openalex.org/keywords/confidence-interval","display_name":"Confidence interval","score":0.502260684967041},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.43935689330101013},{"id":"https://openalex.org/keywords/gaussian-process","display_name":"Gaussian process","score":0.41511741280555725},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.4034876823425293},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.34103280305862427},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.30469369888305664},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06809389591217041}],"concepts":[{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6443896293640137},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5569531321525574},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5465828776359558},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5325794219970703},{"id":"https://openalex.org/C44249647","wikidata":"https://www.wikidata.org/wiki/Q208498","display_name":"Confidence interval","level":2,"score":0.502260684967041},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.43935689330101013},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.41511741280555725},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.4034876823425293},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.34103280305862427},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.30469369888305664},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06809389591217041},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[{"descriptor_ui":"D001499","descriptor_name":"Bayes Theorem","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D001499","descriptor_name":"Bayes Theorem","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D001499","descriptor_name":"Bayes Theorem","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D011336","descriptor_name":"Probability","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D011336","descriptor_name":"Probability","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D011336","descriptor_name":"Probability","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D015203","descriptor_name":"Reproducibility of Results","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D015203","descriptor_name":"Reproducibility of Results","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D015203","descriptor_name":"Reproducibility of Results","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D016001","descriptor_name":"Confidence Intervals","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D016001","descriptor_name":"Confidence Intervals","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D016001","descriptor_name":"Confidence Intervals","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":false},{"descriptor_ui":"D016011","descriptor_name":"Normal Distribution","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":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:10.1142/s0129065796000245","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129065796000245","pdf_url":null,"source":{"id":"https://openalex.org/S197665576","display_name":"International Journal of Neural Systems","issn_l":"0129-0657","issn":["0129-0657","1793-6462"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Neural Systems","raw_type":"journal-article"},{"id":"pmid:8891842","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/8891842","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":"International journal of neural systems","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6700000166893005,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2961085424","https://openalex.org/W2391251536","https://openalex.org/W2465918047","https://openalex.org/W2362198218","https://openalex.org/W2019521278","https://openalex.org/W1984922432","https://openalex.org/W1497739556","https://openalex.org/W2375008505","https://openalex.org/W2169866437","https://openalex.org/W1964286703"],"abstract_inverted_index":{"\"Error-Confidence\"":[0],"measures":[1],"the":[2,5,19,36,43,65,71,84,87,91,106,109,130,133,141,152],"probability":[3],"that":[4,70],"proportion":[6],"of":[7,17,38,52,86,93],"errors":[8],"made":[9],"by":[10,46],"a":[11,80,121,126,138,145],"classifier":[12,149],"will":[13],"be":[14],"within":[15],"epsilon":[16],"EB,":[18],"optimal":[20],"(Bayes)":[21],"error.":[22],"Probably":[23],"Almost":[24],"Bayes":[25,98,115],"(PAB)":[26],"theory":[27],"attempts":[28],"to":[29,158],"quantify":[30],"how":[31],"this":[32],"confidence":[33],"increases":[34],"with":[35,125],"number":[37,51,92],"training":[39,53,94],"samples.":[40],"We":[41],"investigate":[42],"relationship":[44,82],"empirically":[45],"comparing":[47],"average":[48,88],"error":[49,89,99,116],"versus":[50],"patterns":[54],"(m)":[55],"for":[56],"linear":[57,81,110,122,153],"and":[58,90,108,151],"neural":[59],"network":[60],"classifiers.":[61],"On":[62],"Gaussian":[63],"problems,":[64],"resulting":[66],"EC":[67,142],"curves":[68,143],"demonstrate":[69],"PAB":[72],"bounds":[73],"are":[74],"extremely":[75],"conservative.":[76],"Asymptotic":[77],"statistics":[78],"predicts":[79],"between":[83,105],"logarithms":[85],"patterns.":[95],"For":[96],"low":[97],"rates":[100,117],"we":[101,118],"found":[102,120],"excellent":[103],"agreement":[104],"prediction":[107],"discriminant":[111],"performance.":[112],"At":[113],"higher":[114],"still":[119],"relationship,":[123],"but":[124],"shallower":[127],"slope":[128],"than":[129],"predicted-1.":[131],"When":[132],"underlying":[134],"true":[135],"model":[136],"is":[137],"three-layer":[139],"network,":[140],"show":[144],"greater":[146],"dependence":[147],"on":[148],"capacity,":[150],"predictions":[154],"no":[155],"longer":[156],"seem":[157],"hold.":[159]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}