{"id":"https://openalex.org/W4401607917","doi":"https://doi.org/10.1109/tnnls.2024.3406635","title":"Neural Operator Variational Inference Based on Regularized Stein Discrepancy for Deep Gaussian Processes","display_name":"Neural Operator Variational Inference Based on Regularized Stein Discrepancy for Deep Gaussian Processes","publication_year":2024,"publication_date":"2024-08-15","ids":{"openalex":"https://openalex.org/W4401607917","doi":"https://doi.org/10.1109/tnnls.2024.3406635","pmid":"https://pubmed.ncbi.nlm.nih.gov/39146176"},"language":"en","primary_location":{"id":"doi:10.1109/tnnls.2024.3406635","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2024.3406635","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/A5102559841","display_name":"Jian Xu","orcid":"https://orcid.org/0000-0002-0350-5528"},"institutions":[{"id":"https://openalex.org/I90610280","display_name":"South China University of Technology","ror":"https://ror.org/0530pts50","country_code":"CN","type":"education","lineage":["https://openalex.org/I90610280"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jian Xu","raw_affiliation_strings":["School of Mathematics, South China University of Technology, Guangzhou, China"],"raw_orcid":"https://orcid.org/0000-0002-0350-5528","affiliations":[{"raw_affiliation_string":"School of Mathematics, South China University of Technology, Guangzhou, China","institution_ids":["https://openalex.org/I90610280"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081399370","display_name":"Shian Du","orcid":"https://orcid.org/0000-0001-9392-6846"},"institutions":[{"id":"https://openalex.org/I3131625388","display_name":"University Town of Shenzhen","ror":"https://ror.org/05f5j6225","country_code":"CN","type":"education","lineage":["https://openalex.org/I3131625388"]},{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shian Du","raw_affiliation_strings":["Shenzhen International Graduate School, Tsinghua University, Shenzhen, China"],"raw_orcid":"https://orcid.org/0000-0001-9392-6846","affiliations":[{"raw_affiliation_string":"Shenzhen International Graduate School, Tsinghua University, Shenzhen, China","institution_ids":["https://openalex.org/I3131625388","https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101795525","display_name":"Junmei Yang","orcid":"https://orcid.org/0000-0002-9677-0768"},"institutions":[{"id":"https://openalex.org/I90610280","display_name":"South China University of Technology","ror":"https://ror.org/0530pts50","country_code":"CN","type":"education","lineage":["https://openalex.org/I90610280"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Junmei Yang","raw_affiliation_strings":["School of Electronic and Information Engineering, South China University of Technology, Guangzhou, China"],"raw_orcid":"https://orcid.org/0000-0002-9677-0768","affiliations":[{"raw_affiliation_string":"School of Electronic and Information Engineering, South China University of Technology, Guangzhou, China","institution_ids":["https://openalex.org/I90610280"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076609933","display_name":"Qianli Ma","orcid":"https://orcid.org/0000-0002-9356-2883"},"institutions":[{"id":"https://openalex.org/I90610280","display_name":"South China University of Technology","ror":"https://ror.org/0530pts50","country_code":"CN","type":"education","lineage":["https://openalex.org/I90610280"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qianli Ma","raw_affiliation_strings":["School of Computer Science and Engineering, South China University of Technology, Guangzhou, China"],"raw_orcid":"https://orcid.org/0000-0002-9356-2883","affiliations":[{"raw_affiliation_string":"School of Computer Science and Engineering, South China University of Technology, Guangzhou, China","institution_ids":["https://openalex.org/I90610280"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005221942","display_name":"Delu Zeng","orcid":"https://orcid.org/0000-0001-7322-1873"},"institutions":[{"id":"https://openalex.org/I90610280","display_name":"South China University of Technology","ror":"https://ror.org/0530pts50","country_code":"CN","type":"education","lineage":["https://openalex.org/I90610280"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Delu Zeng","raw_affiliation_strings":["School of Electronic and Information Engineering, South China University of Technology, Guangzhou, China"],"raw_orcid":"https://orcid.org/0000-0001-7322-1873","affiliations":[{"raw_affiliation_string":"School of Electronic and Information Engineering, South China University of Technology, Guangzhou, China","institution_ids":["https://openalex.org/I90610280"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0219,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.76962558,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"36","issue":"4","first_page":"6723","last_page":"6737"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.8985000252723694,"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"}},"topics":[{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.8985000252723694,"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"}},{"id":"https://openalex.org/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.8956000208854675,"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/inference","display_name":"Inference","score":0.67303466796875},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5445712804794312},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5162622928619385},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4942913055419922},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4855036735534668},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4815678596496582},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.47426140308380127},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3867989778518677},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.320418119430542},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.17234602570533752},{"id":"https://openalex.org/keywords/computational-chemistry","display_name":"Computational chemistry","score":0.08827072381973267}],"concepts":[{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.67303466796875},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5445712804794312},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5162622928619385},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4942913055419922},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4855036735534668},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4815678596496582},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.47426140308380127},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3867989778518677},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.320418119430542},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.17234602570533752},{"id":"https://openalex.org/C147597530","wikidata":"https://www.wikidata.org/wiki/Q369472","display_name":"Computational chemistry","level":1,"score":0.08827072381973267},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tnnls.2024.3406635","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2024.3406635","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:39146176","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/39146176","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":[{"score":0.49000000953674316,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G1800336020","display_name":null,"funder_award_id":"62272173","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5946461167","display_name":null,"funder_award_id":"2022A1515010179","funder_id":"https://openalex.org/F4320321921","funder_display_name":"Natural Science Foundation of Guangdong Province"},{"id":"https://openalex.org/G5967704285","display_name":null,"funder_award_id":"2024A1515010089","funder_id":"https://openalex.org/F4320321921","funder_display_name":"Natural Science Foundation of Guangdong Province"},{"id":"https://openalex.org/G7282001549","display_name":null,"funder_award_id":"61571005","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G774239774","display_name":null,"funder_award_id":"2023A1515011281","funder_id":"https://openalex.org/F4320321921","funder_display_name":"Natural Science Foundation of Guangdong Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321921","display_name":"Natural Science Foundation of Guangdong Province","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":77,"referenced_works":["https://openalex.org/W91088564","https://openalex.org/W1571870753","https://openalex.org/W2005089986","https://openalex.org/W2084238990","https://openalex.org/W2085330455","https://openalex.org/W2086234878","https://openalex.org/W2103496339","https://openalex.org/W2107152312","https://openalex.org/W2111698756","https://openalex.org/W2194775991","https://openalex.org/W2594374979","https://openalex.org/W2750001921","https://openalex.org/W2946547492","https://openalex.org/W2952353541","https://openalex.org/W2964322376","https://openalex.org/W2972938171","https://openalex.org/W3000508506","https://openalex.org/W3044676633","https://openalex.org/W3093985743","https://openalex.org/W3117074306","https://openalex.org/W3183787799","https://openalex.org/W3200364105","https://openalex.org/W3210682132","https://openalex.org/W3210956727","https://openalex.org/W4211049957","https://openalex.org/W4231458249","https://openalex.org/W4244155866","https://openalex.org/W4281561287","https://openalex.org/W6605566567","https://openalex.org/W6610566761","https://openalex.org/W6631190155","https://openalex.org/W6631732945","https://openalex.org/W6634880810","https://openalex.org/W6637968757","https://openalex.org/W6639216784","https://openalex.org/W6639524736","https://openalex.org/W6639732818","https://openalex.org/W6640000427","https://openalex.org/W6640963894","https://openalex.org/W6674989108","https://openalex.org/W6684109119","https://openalex.org/W6684578138","https://openalex.org/W6714644935","https://openalex.org/W6720558605","https://openalex.org/W6725708968","https://openalex.org/W6728823957","https://openalex.org/W6729403857","https://openalex.org/W6732430167","https://openalex.org/W6732943021","https://openalex.org/W6738492492","https://openalex.org/W6743688258","https://openalex.org/W6746977533","https://openalex.org/W6751975787","https://openalex.org/W6752195321","https://openalex.org/W6752691502","https://openalex.org/W6753361586","https://openalex.org/W6754635386","https://openalex.org/W6754704329","https://openalex.org/W6755056417","https://openalex.org/W6757672018","https://openalex.org/W6762985522","https://openalex.org/W6767283390","https://openalex.org/W6768529065","https://openalex.org/W6769658658","https://openalex.org/W6771556541","https://openalex.org/W6774449618","https://openalex.org/W6777869601","https://openalex.org/W6777943824","https://openalex.org/W6779823529","https://openalex.org/W6780100213","https://openalex.org/W6780201668","https://openalex.org/W6784193858","https://openalex.org/W6784987805","https://openalex.org/W6787972765","https://openalex.org/W6794453030","https://openalex.org/W6795164119","https://openalex.org/W7028669169"],"related_works":["https://openalex.org/W2055243143","https://openalex.org/W4321636575","https://openalex.org/W1986418932","https://openalex.org/W2357796999","https://openalex.org/W2045526782","https://openalex.org/W2741131631","https://openalex.org/W2156919374","https://openalex.org/W1984019423","https://openalex.org/W4280588203","https://openalex.org/W1483472507"],"abstract_inverted_index":{"Deep":[0],"Gaussian":[1,31,172],"process":[2,173],"(DGP)":[3],"models":[4,192],"offer":[5],"a":[6,63,68,120,160],"powerful":[7],"nonparametric":[8,191],"approach":[9],"for":[10,59,198],"Bayesian":[11,190],"inference,":[12],"but":[13],"exact":[14],"inference":[15,57],"is":[16],"typically":[17],"intractable,":[18],"motivating":[19],"the":[20,34,72,78,90,105,116,130,135,147,150,155,166,182,186],"use":[21],"of":[22,38,134,154,163,188],"various":[23,199],"approximations.":[24],"However,":[25],"existing":[26],"approaches,":[27],"such":[28],"as":[29],"mean-field":[30],"assumptions,":[32],"limit":[33],"expressiveness":[35],"and":[36,70,81,97,102,128,132,149,193],"efficacy":[37],"DGP":[39],"models,":[40],"while":[41],"stochastic":[42,99],"approximation":[43],"can":[44,111],"be":[45,112],"computationally":[46],"expensive.":[47],"To":[48],"tackle":[49],"these":[50],"challenges,":[51],"we":[52],"introduce":[53],"neural":[54,64],"operator":[55],"variational":[56],"(NOVI)":[58],"DGPs.":[60],"NOVI":[61,180],"uses":[62],"generator":[65],"to":[66,124,144,184],"obtain":[67],"sampler":[69],"minimizes":[71],"regularized":[73],"Stein":[74],"discrepancy":[75],"(RSD)":[76],"between":[77],"generated":[79],"distribution":[80],"true":[82],"posterior":[83],"in":[84],"$\\mathcal":[85],"{L}_{2}$":[86],"space.":[87],"We":[88,158,176],"solve":[89],"minimax":[91],"problem":[92],"using":[93],"Monte":[94],"Carlo":[95],"estimation":[96],"subsampling":[98],"optimization":[100],"techniques":[101],"demonstrate":[103,146],"that":[104,179],"bias":[106],"introduced":[107],"by":[108,114],"our":[109],"method":[110],"controlled":[113],"multiplying":[115],"Fisher":[117],"divergence":[118],"with":[119],"constant,":[121],"which":[122],"leads":[123],"robust":[125],"error":[126],"control":[127],"ensures":[129],"stability":[131],"precision":[133],"algorithm.":[136],"Our":[137],"experiments":[138],"on":[139,165],"datasets":[140],"ranging":[141],"from":[142],"hundreds":[143],"millions":[145],"effectiveness":[148],"faster":[151],"convergence":[152],"rate":[153],"proposed":[156],"method.":[157],"achieve":[159],"classification":[161],"accuracy":[162],"93.56":[164],"CIFAR10":[167],"dataset,":[168],"outperforming":[169],"state-of-the-art":[170],"(SOTA)":[171],"(GP)":[174],"methods.":[175],"are":[177],"optimistic":[178],"possesses":[181],"potential":[183],"enhance":[185],"performance":[187],"deep":[189],"could":[194],"have":[195],"significant":[196],"implications":[197],"practical":[200],"applications.":[201]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4}],"updated_date":"2025-12-22T23:10:17.713674","created_date":"2025-10-10T00:00:00"}