{"id":"https://openalex.org/W3196413773","doi":"https://doi.org/10.1109/tnnls.2021.3105104","title":"A Probabilistic Formulation for Meta-Weight-Net","display_name":"A Probabilistic Formulation for Meta-Weight-Net","publication_year":2021,"publication_date":"2021-08-30","ids":{"openalex":"https://openalex.org/W3196413773","doi":"https://doi.org/10.1109/tnnls.2021.3105104","mag":"3196413773","pmid":"https://pubmed.ncbi.nlm.nih.gov/34460386"},"language":"en","primary_location":{"id":"doi:10.1109/tnnls.2021.3105104","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2021.3105104","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Neural Networks and Learning 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/A5078092645","display_name":"Qian Zhao","orcid":"https://orcid.org/0000-0001-9956-0064"},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qian Zhao","raw_affiliation_strings":["School of Mathematics and Statistics, Xi&#x2019;an Jiaotong University, Xi&#x2019;an, China","Key Laboratory for Intelligent Networks and Network Security, Ministry of Education, Xi'an Jiaotong University, Xi'an, China"],"raw_orcid":"https://orcid.org/0000-0001-9956-0064","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Xi&#x2019;an Jiaotong University, Xi&#x2019;an, China","institution_ids":["https://openalex.org/I87445476"]},{"raw_affiliation_string":"Key Laboratory for Intelligent Networks and Network Security, Ministry of Education, Xi'an Jiaotong University, Xi'an, China","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103221381","display_name":"Jun Shu","orcid":"https://orcid.org/0000-0001-9968-3048"},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jun Shu","raw_affiliation_strings":["School of Mathematics and Statistics, Xi&#x2019;an Jiaotong University, Xi&#x2019;an, China","Key Laboratory for Intelligent Networks and Network Security, Ministry of Education, Xi'an Jiaotong University, Xi'an, China"],"raw_orcid":"https://orcid.org/0000-0001-9968-3048","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Xi&#x2019;an Jiaotong University, Xi&#x2019;an, China","institution_ids":["https://openalex.org/I87445476"]},{"raw_affiliation_string":"Key Laboratory for Intelligent Networks and Network Security, Ministry of Education, Xi'an Jiaotong University, Xi'an, China","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044895531","display_name":"Xiang Yuan","orcid":"https://orcid.org/0009-0004-2687-8943"},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiang Yuan","raw_affiliation_strings":["School of Mathematics and Statistics, Xi&#x2019;an Jiaotong University, Xi&#x2019;an, China","Key Laboratory for Intelligent Networks and Network Security, Ministry of Education, Xi'an Jiaotong University, Xi'an, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Xi&#x2019;an Jiaotong University, Xi&#x2019;an, China","institution_ids":["https://openalex.org/I87445476"]},{"raw_affiliation_string":"Key Laboratory for Intelligent Networks and Network Security, Ministry of Education, Xi'an Jiaotong University, Xi'an, China","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101924541","display_name":"Ziming Liu","orcid":"https://orcid.org/0000-0002-7090-8853"},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ziming Liu","raw_affiliation_strings":["School of Mathematics and Statistics, Xi&#x2019;an Jiaotong University, Xi&#x2019;an, China","Key Laboratory for Intelligent Networks and Network Security, Ministry of Education, Xi'an Jiaotong University, Xi'an, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Xi&#x2019;an Jiaotong University, Xi&#x2019;an, China","institution_ids":["https://openalex.org/I87445476"]},{"raw_affiliation_string":"Key Laboratory for Intelligent Networks and Network Security, Ministry of Education, Xi'an Jiaotong University, Xi'an, China","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091017287","display_name":"Deyu Meng","orcid":"https://orcid.org/0000-0002-1294-8283"},"institutions":[{"id":"https://openalex.org/I111950717","display_name":"Macau University of Science and Technology","ror":"https://ror.org/03jqs2n27","country_code":"MO","type":"education","lineage":["https://openalex.org/I111950717","https://openalex.org/I4391767947"]},{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN","MO"],"is_corresponding":false,"raw_author_name":"Deyu Meng","raw_affiliation_strings":["School of Mathematics and Statistics, Xi&#x2019;an Jiaotong University, Xi&#x2019;an, China","Key Laboratory for Intelligent Networks and Network Security, Ministry of Education, Xi'an Jiaotong University, Xi'an, China","Faculty of Information Technology, Macau University of Science and Technology, Taipa, Macau, China"],"raw_orcid":"https://orcid.org/0000-0002-1294-8283","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Xi&#x2019;an Jiaotong University, Xi&#x2019;an, China","institution_ids":["https://openalex.org/I87445476"]},{"raw_affiliation_string":"Key Laboratory for Intelligent Networks and Network Security, Ministry of Education, Xi'an Jiaotong University, Xi'an, China","institution_ids":["https://openalex.org/I87445476"]},{"raw_affiliation_string":"Faculty of Information Technology, Macau University of Science and Technology, Taipa, Macau, China","institution_ids":["https://openalex.org/I111950717"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.1702,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.82730021,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"34","issue":"3","first_page":"1194","last_page":"1208"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12535","display_name":"Machine Learning and Data Classification","score":0.9998000264167786,"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/T12535","display_name":"Machine Learning and Data Classification","score":0.9998000264167786,"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/T11512","display_name":"Anomaly Detection Techniques and Applications","score":0.9980999827384949,"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/T10036","display_name":"Advanced Neural Network Applications","score":0.9951000213623047,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/computer-science","display_name":"Computer science","score":0.7183631062507629},{"id":"https://openalex.org/keywords/weighting","display_name":"Weighting","score":0.7165005207061768},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.6654211282730103},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.6095434427261353},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.5997003316879272},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.558380126953125},{"id":"https://openalex.org/keywords/overfitting","display_name":"Overfitting","score":0.5120669007301331},{"id":"https://openalex.org/keywords/net","display_name":"Net (polyhedron)","score":0.4294497072696686},{"id":"https://openalex.org/keywords/hyperparameter","display_name":"Hyperparameter","score":0.4258512258529663},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.313909649848938},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.21309301257133484}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7183631062507629},{"id":"https://openalex.org/C183115368","wikidata":"https://www.wikidata.org/wiki/Q856577","display_name":"Weighting","level":2,"score":0.7165005207061768},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.6654211282730103},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.6095434427261353},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5997003316879272},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.558380126953125},{"id":"https://openalex.org/C22019652","wikidata":"https://www.wikidata.org/wiki/Q331309","display_name":"Overfitting","level":3,"score":0.5120669007301331},{"id":"https://openalex.org/C14166107","wikidata":"https://www.wikidata.org/wiki/Q253829","display_name":"Net (polyhedron)","level":2,"score":0.4294497072696686},{"id":"https://openalex.org/C8642999","wikidata":"https://www.wikidata.org/wiki/Q4171168","display_name":"Hyperparameter","level":2,"score":0.4258512258529663},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.313909649848938},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.21309301257133484},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C126838900","wikidata":"https://www.wikidata.org/wiki/Q77604","display_name":"Radiology","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tnnls.2021.3105104","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2021.3105104","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Neural Networks and Learning Systems","raw_type":"journal-article"},{"id":"pmid:34460386","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/34460386","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":"IEEE transactions on neural networks and learning systems","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3720940119","display_name":null,"funder_award_id":"2020AAA0106300","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G5230869291","display_name":null,"funder_award_id":"061/2020/A2","funder_id":"https://openalex.org/F4320323893","funder_display_name":"Fundo para o Desenvolvimento das Ci\u00eancias e da Tecnologia"},{"id":"https://openalex.org/G5234250448","display_name":null,"funder_award_id":"11690011","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5372072380","display_name":null,"funder_award_id":"U1811461","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5709415372","display_name":null,"funder_award_id":"62076196","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6387986177","display_name":null,"funder_award_id":"61721002","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320323893","display_name":"Fundo para o Desenvolvimento das Ci\u00eancias e da Tecnologia","ror":"https://ror.org/05vna4324"},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":77,"referenced_works":["https://openalex.org/W189742998","https://openalex.org/W1513013675","https://openalex.org/W1921293667","https://openalex.org/W1988790447","https://openalex.org/W1989684337","https://openalex.org/W1995137594","https://openalex.org/W2024046085","https://openalex.org/W2032536435","https://openalex.org/W2034368206","https://openalex.org/W2090346540","https://openalex.org/W2095705004","https://openalex.org/W2099454382","https://openalex.org/W2113242816","https://openalex.org/W2117539524","https://openalex.org/W2118978333","https://openalex.org/W2164598857","https://openalex.org/W2194775991","https://openalex.org/W2256388387","https://openalex.org/W2296073425","https://openalex.org/W2486740305","https://openalex.org/W2557912764","https://openalex.org/W2620239873","https://openalex.org/W2767106145","https://openalex.org/W2775447965","https://openalex.org/W2798869704","https://openalex.org/W2884561390","https://openalex.org/W2905290040","https://openalex.org/W2936503027","https://openalex.org/W2963691377","https://openalex.org/W2964050365","https://openalex.org/W2964155802","https://openalex.org/W2964274690","https://openalex.org/W2964292098","https://openalex.org/W2978625989","https://openalex.org/W2981873476","https://openalex.org/W2982127418","https://openalex.org/W2990138404","https://openalex.org/W2990257819","https://openalex.org/W3038091703","https://openalex.org/W3112139896","https://openalex.org/W3118608800","https://openalex.org/W4213251304","https://openalex.org/W4214926090","https://openalex.org/W6607672814","https://openalex.org/W6631190155","https://openalex.org/W6640963894","https://openalex.org/W6674330103","https://openalex.org/W6675038308","https://openalex.org/W6678280073","https://openalex.org/W6679390333","https://openalex.org/W6682197734","https://openalex.org/W6711814783","https://openalex.org/W6732497821","https://openalex.org/W6735236233","https://openalex.org/W6736057607","https://openalex.org/W6740005241","https://openalex.org/W6740483536","https://openalex.org/W6741489220","https://openalex.org/W6743661861","https://openalex.org/W6745695344","https://openalex.org/W6746061758","https://openalex.org/W6747898760","https://openalex.org/W6748230616","https://openalex.org/W6750523955","https://openalex.org/W6751420435","https://openalex.org/W6752110675","https://openalex.org/W6753772092","https://openalex.org/W6754756046","https://openalex.org/W6757297395","https://openalex.org/W6763094270","https://openalex.org/W6763430915","https://openalex.org/W6763485134","https://openalex.org/W6765939562","https://openalex.org/W6766952621","https://openalex.org/W6781734511","https://openalex.org/W6785554234","https://openalex.org/W6787972765"],"related_works":["https://openalex.org/W4362597605","https://openalex.org/W1574414179","https://openalex.org/W4297676672","https://openalex.org/W3009056573","https://openalex.org/W2922073769","https://openalex.org/W4281702477","https://openalex.org/W2490526372","https://openalex.org/W4376166922","https://openalex.org/W4298369531","https://openalex.org/W3155135229"],"abstract_inverted_index":{"In":[0,112],"the":[1,58,78,92,129,139,155,158,178,182,185,189],"last":[2],"decade,":[3],"deep":[4],"neural":[5],"networks":[6],"(DNNs)":[7],"have":[8],"become":[9],"dominant":[10],"tools":[11],"for":[12,120],"various":[13],"of":[14,53,94,108,157,184],"supervised":[15],"learning":[16],"tasks,":[17],"especially":[18],"classification.":[19],"However,":[20],"it":[21],"is":[22,100,152],"demonstrated":[23],"that":[24,177],"they":[25],"can":[26,137,161,192],"easily":[27],"overfit":[28],"to":[29,75,197,201],"training":[30],"set":[31],"biases,":[32],"such":[33],"as":[34,61,63,142],"label":[35],"noise":[36],"and":[37,45,106,136,173],"class":[38],"imbalance.":[39],"Example":[40],"reweighting":[41],"algorithms":[42],"are":[43],"simple":[44],"effective":[46],"solutions":[47],"against":[48],"this":[49,113,147],"issue,":[50],"but":[51],"most":[52],"them":[54],"require":[55],"manually":[56],"specifying":[57],"weighting":[59,79,130,159],"functions":[60],"well":[62],"additional":[64,86,150],"hyperparameters.":[65],"Recently,":[66],"a":[67,103,117,133,143],"meta-learning-based":[68],"method":[69,180],"Meta-Weight-Net":[70],"(MW-Net)":[71],"has":[72],"been":[73],"proposed":[74,101,179,190],"automatically":[76],"learn":[77],"function":[80,131,160],"parameterized":[81],"by":[82],"an":[83],"MLP":[84],"via":[85],"unbiased":[87],"metadata,":[88],"which":[89,127],"significantly":[90],"improves":[91,181],"robustness":[93],"prior":[95],"arts.":[96],"The":[97],"method,":[98],"however,":[99],"in":[102,125,132],"deterministic":[104],"manner,":[105],"short":[107],"intrinsic":[109],"statistical":[110],"support.":[111],"work,":[114],"we":[115],"propose":[116],"probabilistic":[118,122,134,148],"formulation":[119],"MW-Net,":[121],"MW-Net":[123,141],"(PMW-Net)":[124],"short,":[126],"treats":[128],"way,":[135],"include":[138],"original":[140,186],"special":[144],"case.":[145],"By":[146],"formulation,":[149],"randomness":[151],"introduced":[153],"while":[154],"flexibility":[156],"be":[162,194],"further":[163,195],"controlled":[164],"during":[165],"learning.":[166],"Our":[167],"experimental":[168],"results":[169],"on":[170],"both":[171],"synthetic":[172],"real":[174],"datasets":[175],"show":[176],"performance":[183],"MW-Net.":[187],"Besides,":[188],"PMW-Net":[191],"also":[193],"extended":[196],"fully":[198],"Bayesian":[199],"models,":[200],"improve":[202],"their":[203],"robustness.":[204]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3}],"updated_date":"2026-07-25T15:57:00.446498","created_date":"2025-10-10T00:00:00"}
