{"id":"https://openalex.org/W3036353678","doi":"https://doi.org/10.1137/21m1445831","title":"GAT\u2013GMM: Generative Adversarial Training for Gaussian Mixture Models","display_name":"GAT\u2013GMM: Generative Adversarial Training for Gaussian Mixture Models","publication_year":2023,"publication_date":"2023-03-10","ids":{"openalex":"https://openalex.org/W3036353678","doi":"https://doi.org/10.1137/21m1445831","mag":"3036353678"},"language":"en","primary_location":{"id":"doi:10.1137/21m1445831","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1137/21m1445831","pdf_url":null,"source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematics of Data Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"http://dx.doi.org/10.1137/21m1445831","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017160178","display_name":"Farzan Farnia","orcid":"https://orcid.org/0000-0002-6049-9232"},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"HK","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Farzan Farnia","raw_affiliation_strings":["The Chinese University of Hong Kong, Shatin, Hong Kong SAR. Research was performed while the author was with Massachusetts Institute of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Chinese University of Hong Kong, Shatin, Hong Kong SAR. Research was performed while the author was with Massachusetts Institute of Technology","institution_ids":["https://openalex.org/I177725633"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065648764","display_name":"W Wang","orcid":"https://orcid.org/0000-0002-7993-5145"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"William W. Wang","raw_affiliation_strings":["Massachusetts Institute of Technology, Cambridge, MA 02139 USA"],"raw_orcid":"https://orcid.org/0000-0002-7993-5145","affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology, Cambridge, MA 02139 USA","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011183160","display_name":"Subhro Das","orcid":"https://orcid.org/0000-0002-7610-2738"},"institutions":[{"id":"https://openalex.org/I1341412227","display_name":"IBM (United States)","ror":"https://ror.org/05hh8d621","country_code":"US","type":"company","lineage":["https://openalex.org/I1341412227"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Subhro Das","raw_affiliation_strings":["MIT-IBM Watson AI Lab, IBM Research, Cambridge, MA 02142 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MIT-IBM Watson AI Lab, IBM Research, Cambridge, MA 02142 USA","institution_ids":["https://openalex.org/I1341412227"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078288116","display_name":"Ali Jadbabaie","orcid":"https://orcid.org/0000-0003-1122-3069"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ali Jadbabaie","raw_affiliation_strings":["Massachusetts Institute of Technology, Cambridge, MA 02139 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology, Cambridge, MA 02139 USA","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9518,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.77886179,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":93,"max":97},"biblio":{"volume":"5","issue":"1","first_page":"122","last_page":"146"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.994700014591217,"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/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.994700014591217,"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.9925000071525574,"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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.9595000147819519,"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/generative-grammar","display_name":"Generative grammar","score":0.7753994464874268},{"id":"https://openalex.org/keywords/mixture-model","display_name":"Mixture model","score":0.7599563598632812},{"id":"https://openalex.org/keywords/adversarial-system","display_name":"Adversarial system","score":0.6876066327095032},{"id":"https://openalex.org/keywords/training","display_name":"Training (meteorology)","score":0.6001988649368286},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.5152907371520996},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4930104911327362},{"id":"https://openalex.org/keywords/training-set","display_name":"Training set","score":0.47428256273269653},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.43845245242118835},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4075482487678528},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.3909485340118408},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.37566038966178894},{"id":"https://openalex.org/keywords/geography","display_name":"Geography","score":0.17036142945289612},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.09324583411216736},{"id":"https://openalex.org/keywords/meteorology","display_name":"Meteorology","score":0.05318361520767212},{"id":"https://openalex.org/keywords/computational-chemistry","display_name":"Computational chemistry","score":0.04528766870498657}],"concepts":[{"id":"https://openalex.org/C39890363","wikidata":"https://www.wikidata.org/wiki/Q36108","display_name":"Generative grammar","level":2,"score":0.7753994464874268},{"id":"https://openalex.org/C61224824","wikidata":"https://www.wikidata.org/wiki/Q2260434","display_name":"Mixture model","level":2,"score":0.7599563598632812},{"id":"https://openalex.org/C37736160","wikidata":"https://www.wikidata.org/wiki/Q1801315","display_name":"Adversarial system","level":2,"score":0.6876066327095032},{"id":"https://openalex.org/C2777211547","wikidata":"https://www.wikidata.org/wiki/Q17141490","display_name":"Training (meteorology)","level":2,"score":0.6001988649368286},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5152907371520996},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4930104911327362},{"id":"https://openalex.org/C51632099","wikidata":"https://www.wikidata.org/wiki/Q3985153","display_name":"Training set","level":2,"score":0.47428256273269653},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.43845245242118835},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4075482487678528},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3909485340118408},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.37566038966178894},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.17036142945289612},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.09324583411216736},{"id":"https://openalex.org/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","level":1,"score":0.05318361520767212},{"id":"https://openalex.org/C147597530","wikidata":"https://www.wikidata.org/wiki/Q369472","display_name":"Computational chemistry","level":1,"score":0.04528766870498657}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/21m1445831","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1137/21m1445831","pdf_url":null,"source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematics of Data Science","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1137/21m1445831","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1137/21m1445831","pdf_url":null,"source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematics of Data Science","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.7200000286102295}],"awards":[{"id":"https://openalex.org/G7758501045","display_name":null,"funder_award_id":"W911NF-19-1-0217","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"}],"funders":[{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"},{"id":"https://openalex.org/F706640890","display_name":"MIT-IBM Watson AI Lab","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":82,"referenced_works":["https://openalex.org/W1522301498","https://openalex.org/W1535281955","https://openalex.org/W1677182931","https://openalex.org/W1956647075","https://openalex.org/W1969015668","https://openalex.org/W2010072035","https://openalex.org/W2014565165","https://openalex.org/W2021422996","https://openalex.org/W2026302946","https://openalex.org/W2047064469","https://openalex.org/W2049633694","https://openalex.org/W2051503552","https://openalex.org/W2062817469","https://openalex.org/W2071513844","https://openalex.org/W2076626169","https://openalex.org/W2094644779","https://openalex.org/W2099471712","https://openalex.org/W2131172946","https://openalex.org/W2146758737","https://openalex.org/W2166944917","https://openalex.org/W2554314924","https://openalex.org/W2577946330","https://openalex.org/W2593729559","https://openalex.org/W2612690371","https://openalex.org/W2617573776","https://openalex.org/W2619503996","https://openalex.org/W2620025707","https://openalex.org/W2632772789","https://openalex.org/W2739748921","https://openalex.org/W2766210095","https://openalex.org/W2769553966","https://openalex.org/W2803117117","https://openalex.org/W2804078698","https://openalex.org/W2808364844","https://openalex.org/W2810203579","https://openalex.org/W2885389089","https://openalex.org/W2889205371","https://openalex.org/W2890708415","https://openalex.org/W2890708902","https://openalex.org/W2891786606","https://openalex.org/W2893749619","https://openalex.org/W2895248218","https://openalex.org/W2911319680","https://openalex.org/W2916041869","https://openalex.org/W2943355826","https://openalex.org/W2949117887","https://openalex.org/W2949186514","https://openalex.org/W2953030256","https://openalex.org/W2959656158","https://openalex.org/W2962677091","https://openalex.org/W2962737134","https://openalex.org/W2962760235","https://openalex.org/W2962790067","https://openalex.org/W2962820675","https://openalex.org/W2962879692","https://openalex.org/W2963006832","https://openalex.org/W2963181447","https://openalex.org/W2963626260","https://openalex.org/W2963658177","https://openalex.org/W2963804063","https://openalex.org/W2963809789","https://openalex.org/W2963836885","https://openalex.org/W2963919714","https://openalex.org/W2963931155","https://openalex.org/W2963981733","https://openalex.org/W2963989027","https://openalex.org/W2964018346","https://openalex.org/W2964073168","https://openalex.org/W2964126461","https://openalex.org/W2964334726","https://openalex.org/W2970971581","https://openalex.org/W2973214398","https://openalex.org/W2980328027","https://openalex.org/W3003692528","https://openalex.org/W3006995042","https://openalex.org/W3022507773","https://openalex.org/W3034862928","https://openalex.org/W3036377857","https://openalex.org/W3037476903","https://openalex.org/W3080934299","https://openalex.org/W3100598174","https://openalex.org/W4255839052"],"related_works":["https://openalex.org/W2502115930","https://openalex.org/W2482350142","https://openalex.org/W4246396837","https://openalex.org/W3126451824","https://openalex.org/W3211393740","https://openalex.org/W3208049411","https://openalex.org/W1578916557","https://openalex.org/W3022908591","https://openalex.org/W4285706568","https://openalex.org/W2142815029"],"abstract_inverted_index":{".Generative":[0],"adversarial":[1,250],"networks":[2],"(GANs)":[3],"learn":[4],"the":[5,30,80,122,127,146,150,155,158,166,172,186,206,243],"distribution":[6,32],"of":[7,33,121,130,133,149,157],"observed":[8],"samples":[9],"through":[10],"a":[11,18,21,66,86,91,99,108,131,194,199],"zero-sum":[12,81],"game":[13,82],"between":[14],"two":[15,134],"machine":[16],"players,":[17],"generator":[19,89],"and":[20,36,90,182,198,236],"discriminator.":[22],"While":[23],"GANs":[24],"achieve":[25],"great":[26,180],"success":[27],"in":[28,42,83,165,232,242],"learning":[29,43,71,163,169,196,234],"complex":[31],"image,":[34],"sound,":[35],"text":[37],"data,":[38],"they":[39],"perform":[40],"suboptimally":[41],"multimodal":[44],"distribution-learning":[45],"benchmarks":[46],"such":[47],"as":[48],"Gaussian":[49,62],"mixture":[50,132,247],"models":[51],"(GMMs).":[52],"In":[53,126],"this":[54,142],"paper,":[55],"we":[56,78,138,189],"propose":[57],"Generative":[58],"Adversarial":[59],"Training":[60],"for":[61,70,162],"Mixture":[63],"Models":[64],"(GAT-GMM),":[65],"minimax":[67,102,119,208,228],"GAN":[68],"framework":[69,161,229],"GMMs.":[72],"Motivated":[73],"by":[74,221],"optimal":[75],"transport":[76],"theory,":[77],"design":[79],"GAT-GMM":[84,123,160,192,207],"using":[85],"random":[87],"linear":[88],"softmax-based":[92],"quadratic":[93],"discriminator":[94],"architecture,":[95],"which":[96,224],"leads":[97],"to":[98,115],"nonconvex":[100],"concave":[101],"optimization":[103,124],"problem.":[104,125],"We":[105,153,215],"show":[106,140,190,225],"that":[107,141,191,226],"gradient":[109],"descent":[110],"ascent":[111],"(GDA)":[112],"method":[113],"converges":[114],"an":[116],"approximate":[117],"stationary":[118,143],"point":[120,144],"benchmark":[128],"case":[129],"symmetric,":[135],"well-separated":[136],"Gaussians,":[137],"further":[139],"recovers":[145],"true":[147],"parameters":[148],"underlying":[151],"GMM.":[152],"discuss":[154],"application":[156],"proposed":[159],"GMMs":[164],"distributed":[167,200],"federated":[168,244],"setting,":[170],"where":[171],"widely":[173],"used":[174],"expectation-maximization":[175],"(EM)":[176],"algorithm":[177,202],"can":[178,203,237],"incur":[179],"computational":[181],"communication":[183],"costs.":[184,214],"On":[185],"other":[187],"hand,":[188],"provides":[193],"scalable":[195],"approach":[197],"GDA":[201],"still":[204],"solve":[205],"problem":[209],"without":[210],"incurring":[211],"extra":[212],"computation":[213],"numerically":[216],"support":[217],"our":[218,227],"theoretical":[219],"results":[220],"performing":[222],"experiments":[223],"is":[230],"successful":[231],"centralized":[233],"tasks":[235],"outperform":[238],"standard":[239],"EM-type":[240],"algorithms":[241],"setting.Keywordsminimax":[245],"learningGaussian":[246],"modelsoptimal":[248],"transportgenerative":[249],"networksfederated":[251],"learningMSC":[252],"codes90C4749Q2262H3068T05":[253]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3}],"updated_date":"2025-12-21T01:58:51.020947","created_date":"2025-10-10T00:00:00"}