{"id":"https://openalex.org/W4408833864","doi":"https://doi.org/10.3390/e27040340","title":"Minimax Bayesian Neural Networks","display_name":"Minimax Bayesian Neural Networks","publication_year":2025,"publication_date":"2025-03-25","ids":{"openalex":"https://openalex.org/W4408833864","doi":"https://doi.org/10.3390/e27040340","pmid":"https://pubmed.ncbi.nlm.nih.gov/40282575"},"language":"en","primary_location":{"id":"doi:10.3390/e27040340","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e27040340","pdf_url":"https://www.mdpi.com/1099-4300/27/4/340/pdf?version=1742896552","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/27/4/340/pdf?version=1742896552","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035035593","display_name":"Junping Hong","orcid":"https://orcid.org/0000-0002-3341-7406"},"institutions":[{"id":"https://openalex.org/I4210114105","display_name":"Tsinghua\u2013Berkeley Shenzhen Institute","ror":"https://ror.org/02hhwwz98","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210114105","https://openalex.org/I95457486","https://openalex.org/I99065089"]},{"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":"Junping Hong","raw_affiliation_strings":["Tsinghua Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, China"],"raw_orcid":"https://orcid.org/0000-0002-3341-7406","affiliations":[{"raw_affiliation_string":"Tsinghua Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, China","institution_ids":["https://openalex.org/I4210114105","https://openalex.org/I99065089"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038228706","display_name":"Er\u00e7an E. Kuruo\u011flu","orcid":"https://orcid.org/0000-0002-2608-8034"},"institutions":[{"id":"https://openalex.org/I4210114105","display_name":"Tsinghua\u2013Berkeley Shenzhen Institute","ror":"https://ror.org/02hhwwz98","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210114105","https://openalex.org/I95457486","https://openalex.org/I99065089"]},{"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":true,"raw_author_name":"Ercan Engin Kuruoglu","raw_affiliation_strings":["Tsinghua Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, China"],"raw_orcid":"https://orcid.org/0000-0002-2608-8034","affiliations":[{"raw_affiliation_string":"Tsinghua Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, China","institution_ids":["https://openalex.org/I4210114105","https://openalex.org/I99065089"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5038228706"],"corresponding_institution_ids":["https://openalex.org/I4210114105","https://openalex.org/I99065089"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":3.8537,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.92678397,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"27","issue":"4","first_page":"340","last_page":"340"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.9998999834060669,"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/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.9998999834060669,"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":0.9990000128746033,"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/T10876","display_name":"Fault Detection and Control Systems","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/minimax","display_name":"Minimax","score":0.844042181968689},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.7827315330505371},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.7421373128890991},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6643285155296326},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.5168029069900513},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.5160362720489502},{"id":"https://openalex.org/keywords/stochastic-neural-network","display_name":"Stochastic neural network","score":0.46274760365486145},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.4564845561981201},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3553975224494934},{"id":"https://openalex.org/keywords/time-delay-neural-network","display_name":"Time delay neural network","score":0.2601025104522705},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.23137518763542175}],"concepts":[{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.844042181968689},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.7827315330505371},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.7421373128890991},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6643285155296326},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5168029069900513},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.5160362720489502},{"id":"https://openalex.org/C86582703","wikidata":"https://www.wikidata.org/wiki/Q7617824","display_name":"Stochastic neural network","level":4,"score":0.46274760365486145},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.4564845561981201},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3553975224494934},{"id":"https://openalex.org/C175202392","wikidata":"https://www.wikidata.org/wiki/Q2434543","display_name":"Time delay neural network","level":3,"score":0.2601025104522705},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.23137518763542175},{"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},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/e27040340","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e27040340","pdf_url":"https://www.mdpi.com/1099-4300/27/4/340/pdf?version=1742896552","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmid:40282575","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/40282575","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":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:doaj.org/article:bdd3c8ce9bf64dadb9dd40d4caf9466c","is_oa":true,"landing_page_url":"https://doaj.org/article/bdd3c8ce9bf64dadb9dd40d4caf9466c","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 27, Iss 4, p 340 (2025)","raw_type":"article"},{"id":"pmh:oai:pubmedcentral.nih.gov:12025800","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/12025800","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e27040340","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e27040340","pdf_url":"https://www.mdpi.com/1099-4300/27/4/340/pdf?version=1742896552","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8025701688","display_name":null,"funder_award_id":"JCYJ20220530143002005","funder_id":"https://openalex.org/F4320326705","funder_display_name":"Science, Technology and Innovation Commission of Shenzhen Municipality"}],"funders":[{"id":"https://openalex.org/F4320326705","display_name":"Science, Technology and Innovation Commission of Shenzhen Municipality","ror":null}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4408833864.pdf"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W1538131130","https://openalex.org/W2095705004","https://openalex.org/W2098137815","https://openalex.org/W2111051539","https://openalex.org/W2136132422","https://openalex.org/W2166767167","https://openalex.org/W2767471303","https://openalex.org/W2788907134","https://openalex.org/W2897083899","https://openalex.org/W2942454403","https://openalex.org/W2964059111","https://openalex.org/W3006315234","https://openalex.org/W3035664806","https://openalex.org/W3043426275","https://openalex.org/W3159054876","https://openalex.org/W4220862273","https://openalex.org/W4250024550","https://openalex.org/W4295312788","https://openalex.org/W4386065840","https://openalex.org/W6632100814","https://openalex.org/W6674330103","https://openalex.org/W6684488266","https://openalex.org/W6748865747","https://openalex.org/W6766978945","https://openalex.org/W6773684732","https://openalex.org/W6780322082"],"related_works":["https://openalex.org/W4200062060","https://openalex.org/W2378845890","https://openalex.org/W1584270863","https://openalex.org/W2085961337","https://openalex.org/W2390500492","https://openalex.org/W180587397","https://openalex.org/W2391951449","https://openalex.org/W2079352224","https://openalex.org/W2085068378","https://openalex.org/W2371928941"],"abstract_inverted_index":{"Robustness":[0],"is":[1,22],"an":[2],"important":[3],"issue":[4],"in":[5,26],"deep":[6],"learning,":[7],"and":[8,45,73,90,102],"Bayesian":[9,29],"neural":[10,39,49,71,77,89],"networks":[11,40],"(BNNs)":[12],"provide":[13],"means":[14],"of":[15],"robustness":[16,105],"analysis,":[17],"while":[18],"the":[19,27,35,42,47,60,84,87,91,95],"minimax":[20,43,61],"method":[21,44],"a":[23,65,69,74],"conservative":[24,57],"choice":[25],"classical":[28],"field.":[30],"Recently,":[31],"researchers":[32],"have":[33],"applied":[34],"closed-loop":[36,48,88],"idea":[37],"to":[38],"via":[41],"proposed":[46],"networks.":[50],"In":[51],"this":[52,80],"paper,":[53],"we":[54,82],"study":[55,103],"more":[56],"BNNs":[58],"with":[59],"method,":[62],"which":[63],"formulates":[64],"two-player":[66],"game":[67],"between":[68,86],"deterministic":[70],"network":[72],"sampling":[75],"stochastic":[76],"network.":[78],"From":[79],"perspective,":[81],"reveal":[83],"connection":[85],"BNNs.":[92],"We":[93],"test":[94],"models":[96],"on":[97],"some":[98],"simple":[99],"data":[100],"sets":[101],"their":[104],"under":[106],"noise":[107],"perturbation,":[108],"etc.":[109]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1}],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2025-10-10T00:00:00"}
