{"id":"https://openalex.org/W4411288054","doi":"https://doi.org/10.1137/24m1666628","title":"Statistical Guarantees of Group-Invariant GANs","display_name":"Statistical Guarantees of Group-Invariant GANs","publication_year":2025,"publication_date":"2025-06-13","ids":{"openalex":"https://openalex.org/W4411288054","doi":"https://doi.org/10.1137/24m1666628"},"language":"en","primary_location":{"id":"doi:10.1137/24m1666628","is_oa":false,"landing_page_url":"https://doi.org/10.1137/24m1666628","pdf_url":null,"source":{"id":"https://openalex.org/S2911293512","display_name":"SIAM/ASA Journal on Uncertainty Quantification","issn_l":"2166-2525","issn":["2166-2525"],"is_oa":false,"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/ASA Journal on Uncertainty Quantification","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/A5100373636","display_name":"Ziyu Chen","orcid":"https://orcid.org/0009-0001-4277-1204"},"institutions":[{"id":"https://openalex.org/I177605424","display_name":"Amherst College","ror":"https://ror.org/028vqfs63","country_code":"US","type":"education","lineage":["https://openalex.org/I177605424"]},{"id":"https://openalex.org/I24603500","display_name":"University of Massachusetts Amherst","ror":"https://ror.org/0072zz521","country_code":"US","type":"education","lineage":["https://openalex.org/I24603500"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ziyu Chen","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA, 01003"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA, 01003","institution_ids":["https://openalex.org/I24603500","https://openalex.org/I177605424"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045079747","display_name":"Markos A. Katsoulakis","orcid":"https://orcid.org/0000-0003-4354-1766"},"institutions":[{"id":"https://openalex.org/I177605424","display_name":"Amherst College","ror":"https://ror.org/028vqfs63","country_code":"US","type":"education","lineage":["https://openalex.org/I177605424"]},{"id":"https://openalex.org/I24603500","display_name":"University of Massachusetts Amherst","ror":"https://ror.org/0072zz521","country_code":"US","type":"education","lineage":["https://openalex.org/I24603500"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Markos A. Katsoulakis","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA, 01003"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA, 01003","institution_ids":["https://openalex.org/I24603500","https://openalex.org/I177605424"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066349615","display_name":"Luc Rey-Bellet","orcid":"https://orcid.org/0000-0003-1166-8957"},"institutions":[{"id":"https://openalex.org/I177605424","display_name":"Amherst College","ror":"https://ror.org/028vqfs63","country_code":"US","type":"education","lineage":["https://openalex.org/I177605424"]},{"id":"https://openalex.org/I24603500","display_name":"University of Massachusetts Amherst","ror":"https://ror.org/0072zz521","country_code":"US","type":"education","lineage":["https://openalex.org/I24603500"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Luc Rey-Bellet","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA, 01003"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA, 01003","institution_ids":["https://openalex.org/I24603500","https://openalex.org/I177605424"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101589682","display_name":"Wei Zhu","orcid":"https://orcid.org/0000-0002-9181-5103"},"institutions":[{"id":"https://openalex.org/I177605424","display_name":"Amherst College","ror":"https://ror.org/028vqfs63","country_code":"US","type":"education","lineage":["https://openalex.org/I177605424"]},{"id":"https://openalex.org/I24603500","display_name":"University of Massachusetts Amherst","ror":"https://ror.org/0072zz521","country_code":"US","type":"education","lineage":["https://openalex.org/I24603500"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Wei Zhu","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA, 01003"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA, 01003","institution_ids":["https://openalex.org/I24603500","https://openalex.org/I177605424"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5100373636"],"corresponding_institution_ids":["https://openalex.org/I177605424","https://openalex.org/I24603500"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.06447356,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"13","issue":"2","first_page":"862","last_page":"890"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.8052999973297119,"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/T10320","display_name":"Neural Networks and Applications","score":0.8052999973297119,"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/invariant","display_name":"Invariant (physics)","score":0.5739491581916809},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.5420535206794739},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4399094879627228},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3200606405735016},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1859828531742096},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.12522661685943604},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.044518738985061646}],"concepts":[{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5739491581916809},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5420535206794739},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4399094879627228},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3200606405735016},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1859828531742096},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.12522661685943604},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.044518738985061646}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/24m1666628","is_oa":false,"landing_page_url":"https://doi.org/10.1137/24m1666628","pdf_url":null,"source":{"id":"https://openalex.org/S2911293512","display_name":"SIAM/ASA Journal on Uncertainty Quantification","issn_l":"2166-2525","issn":["2166-2525"],"is_oa":false,"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/ASA Journal on Uncertainty Quantification","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.4399999976158142,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G3897272785","display_name":null,"funder_award_id":"DMS-2052525","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G6518258739","display_name":null,"funder_award_id":"FA9550-21-1-0354","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G6687172693","display_name":null,"funder_award_id":"DMS-2244976","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G7561623003","display_name":null,"funder_award_id":"DMS-2140982","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G8338552064","display_name":null,"funder_award_id":"DMS-2307115","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G8616775632","display_name":null,"funder_award_id":"CISE-1934846","funder_id":"https://openalex.org/F4320332169","funder_display_name":"Directorate for Computer and Information Science and Engineering"}],"funders":[{"id":"https://openalex.org/F4320332169","display_name":"Directorate for Computer and Information Science and Engineering","ror":"https://ror.org/025kzpk63"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1242194915","https://openalex.org/W1582706191","https://openalex.org/W2000992741","https://openalex.org/W2026737855","https://openalex.org/W2328111639","https://openalex.org/W2528305538","https://openalex.org/W2559655401","https://openalex.org/W2612690371","https://openalex.org/W2785331752","https://openalex.org/W2902461580","https://openalex.org/W2953246643","https://openalex.org/W2963626582","https://openalex.org/W2990138404","https://openalex.org/W3006106210","https://openalex.org/W3011784732","https://openalex.org/W3044296827","https://openalex.org/W3048457240","https://openalex.org/W3160447895","https://openalex.org/W3210682132","https://openalex.org/W4239915530","https://openalex.org/W4250954493"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298","https://openalex.org/W2600246793"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}