{"id":"https://openalex.org/W7153578315","doi":"https://doi.org/10.1016/j.cam.2026.117686","title":"Robust learning of minimum error entropy under heavy-tailed noise","display_name":"Robust learning of minimum error entropy under heavy-tailed noise","publication_year":2026,"publication_date":"2026-04-11","ids":{"openalex":"https://openalex.org/W7153578315","doi":"https://doi.org/10.1016/j.cam.2026.117686"},"language":"en","primary_location":{"id":"doi:10.1016/j.cam.2026.117686","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.cam.2026.117686","pdf_url":null,"source":{"id":"https://openalex.org/S165473669","display_name":"Journal of Computational and Applied Mathematics","issn_l":"0377-0427","issn":["0377-0427","1879-1778"],"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":"Journal of Computational and Applied Mathematics","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/A5128810209","display_name":"Siying Jiang","orcid":null},"institutions":[{"id":"https://openalex.org/I4210165606","display_name":"Hubei Normal University","ror":"https://ror.org/056y3dw16","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210165606"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Siying Jiang","raw_affiliation_strings":["organization=Department of Mathematics and Statistics, Hubei Normal University, state=Huangshi, postcode=435002, country=China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"organization=Department of Mathematics and Statistics, Hubei Normal University, state=Huangshi, postcode=435002, country=China","institution_ids":["https://openalex.org/I4210165606"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049783368","display_name":"Hongfei Xu","orcid":"https://orcid.org/0000-0001-8397-1459"},"institutions":[{"id":"https://openalex.org/I4210165606","display_name":"Hubei Normal University","ror":"https://ror.org/056y3dw16","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210165606"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Hongfei Xu","raw_affiliation_strings":["organization=Department of Mathematics and Statistics, Hubei Normal University, state=Huangshi, postcode=435002, country=China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"organization=Department of Mathematics and Statistics, Hubei Normal University, state=Huangshi, postcode=435002, country=China","institution_ids":["https://openalex.org/I4210165606"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042608294","display_name":"Qian Sun","orcid":"https://orcid.org/0000-0002-4926-2883"},"institutions":[{"id":"https://openalex.org/I4210165606","display_name":"Hubei Normal University","ror":"https://ror.org/056y3dw16","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210165606"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Qian Sun","raw_affiliation_strings":["organization=Department of Mathematics and Statistics, Hubei Normal University, state=Huangshi, postcode=435002, country=China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"organization=Department of Mathematics and Statistics, Hubei Normal University, state=Huangshi, postcode=435002, country=China","institution_ids":["https://openalex.org/I4210165606"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103764575","display_name":"ShouYou HUANG","orcid":null},"institutions":[{"id":"https://openalex.org/I4210165606","display_name":"Hubei Normal University","ror":"https://ror.org/056y3dw16","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210165606"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Shouyou Huang","raw_affiliation_strings":["organization=Department of Mathematics and Statistics, Hubei Normal University, state=Huangshi, postcode=435002, country=China"],"raw_orcid":"https://orcid.org/0000-0003-2705-5370","affiliations":[{"raw_affiliation_string":"organization=Department of Mathematics and Statistics, Hubei Normal University, state=Huangshi, postcode=435002, country=China","institution_ids":["https://openalex.org/I4210165606"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5042608294","https://openalex.org/A5049783368","https://openalex.org/A5103764575","https://openalex.org/A5128810209"],"corresponding_institution_ids":["https://openalex.org/I4210165606"],"apc_list":{"value":3040,"currency":"USD","value_usd":3040},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.8645919,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"487","issue":null,"first_page":"117686","last_page":"117686"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.6815000176429749,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T10136","display_name":"Statistical Methods and Inference","score":0.6815000176429749,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T12676","display_name":"Machine Learning and ELM","score":0.0357000008225441,"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":0.031099999323487282,"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/reproducing-kernel-hilbert-space","display_name":"Reproducing kernel Hilbert space","score":0.7325999736785889},{"id":"https://openalex.org/keywords/tikhonov-regularization","display_name":"Tikhonov regularization","score":0.6873000264167786},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.6746000051498413},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.6050999760627747},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5559999942779541},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5059000253677368},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.4408999979496002},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.42100000381469727},{"id":"https://openalex.org/keywords/representer-theorem","display_name":"Representer theorem","score":0.37929999828338623}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8766999840736389},{"id":"https://openalex.org/C80884492","wikidata":"https://www.wikidata.org/wiki/Q3345678","display_name":"Reproducing kernel Hilbert space","level":3,"score":0.7325999736785889},{"id":"https://openalex.org/C152442038","wikidata":"https://www.wikidata.org/wiki/Q2778212","display_name":"Tikhonov regularization","level":3,"score":0.6873000264167786},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6746000051498413},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.6050999760627747},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5559999942779541},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5526000261306763},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5059000253677368},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.4408999979496002},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.42100000381469727},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4090999960899353},{"id":"https://openalex.org/C172623408","wikidata":"https://www.wikidata.org/wiki/Q7314263","display_name":"Representer theorem","level":5,"score":0.37929999828338623},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37689998745918274},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.3490000069141388},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.34369999170303345},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.32280001044273376},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.3206000030040741},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.3107999861240387},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.30230000615119934},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.3003999888896942},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.2994999885559082},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.29919999837875366},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.28139999508857727},{"id":"https://openalex.org/C171752962","wikidata":"https://www.wikidata.org/wiki/Q255166","display_name":"Kullback\u2013Leibler divergence","level":2,"score":0.26910001039505005},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.2651999890804291},{"id":"https://openalex.org/C129848803","wikidata":"https://www.wikidata.org/wiki/Q2564360","display_name":"Sample size determination","level":2,"score":0.25850000977516174},{"id":"https://openalex.org/C117765406","wikidata":"https://www.wikidata.org/wiki/Q5362437","display_name":"Generalization error","level":3,"score":0.25600001215934753},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.2540000081062317}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/j.cam.2026.117686","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.cam.2026.117686","pdf_url":null,"source":{"id":"https://openalex.org/S165473669","display_name":"Journal of Computational and Applied Mathematics","issn_l":"0377-0427","issn":["0377-0427","1879-1778"],"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":"Journal of Computational and Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.5738810896873474}],"awards":[],"funders":[{"id":"https://openalex.org/F4320322186","display_name":"Natural Science Foundation of Hubei Province","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W1482673845","https://openalex.org/W1968436459","https://openalex.org/W1975027558","https://openalex.org/W1986280275","https://openalex.org/W1994642189","https://openalex.org/W2017332415","https://openalex.org/W2019359195","https://openalex.org/W2025199224","https://openalex.org/W2044289603","https://openalex.org/W2110810023","https://openalex.org/W2124572691","https://openalex.org/W2158781299","https://openalex.org/W2345904635","https://openalex.org/W2403797236","https://openalex.org/W2522471716","https://openalex.org/W2901373116","https://openalex.org/W2963604113","https://openalex.org/W2964248738","https://openalex.org/W3033779185","https://openalex.org/W3035624973","https://openalex.org/W3127795058","https://openalex.org/W3199829435","https://openalex.org/W3209695977","https://openalex.org/W4233413206","https://openalex.org/W4285013867","https://openalex.org/W4385173611","https://openalex.org/W4405184862","https://openalex.org/W4406235059","https://openalex.org/W4407399284","https://openalex.org/W4408414337"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-04-16T06:03:46.269776","created_date":"2026-04-12T00:00:00"}