{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,11]],"date-time":"2025-07-11T10:38:23Z","timestamp":1752230303728,"version":"3.40.5"},"reference-count":29,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","funder":[{"DOI":"10.13039\/100000185","name":"Defense Advanced Research Projects Agency","doi-asserted-by":"publisher","award":["EQUiPS W911NF1520122"],"award-info":[{"award-number":["EQUiPS W911NF1520122"]}],"id":[{"id":"10.13039\/100000185","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000181","name":"Air Force Office of Scientific Research","doi-asserted-by":"publisher","award":["FA-9550-18-1-0214"],"award-info":[{"award-number":["FA-9550-18-1-0214"]}],"id":[{"id":"10.13039\/100000181","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1904992"],"award-info":[{"award-number":["DMS-1904992"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["TRIPODS CISE-1934846"],"award-info":[{"award-number":["TRIPODS CISE-1934846"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-2008970"],"award-info":[{"award-number":["DMS-2008970"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM Journal on Mathematics of Data Science"],"published-print":{"date-parts":[[2021,1]]},"DOI":"10.1137\/20m1368926","type":"journal-article","created":{"date-parts":[[2021,10,6]],"date-time":"2021-10-06T19:18:51Z","timestamp":1633547931000},"page":"1093-1116","source":"Crossref","is-referenced-by-count":14,"title":["Variational Representations and Neural Network Estimation of R\u00e9nyi Divergences"],"prefix":"10.1137","volume":"3","author":[{"given":"Jeremiah","family":"Birrell","sequence":"first","affiliation":[]},{"given":"Paul","family":"Dupuis","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4354-1766","authenticated-orcid":true,"given":"Markos A.","family":"Katsoulakis","sequence":"additional","affiliation":[]},{"given":"Luc","family":"Rey-Bellet","sequence":"additional","affiliation":[]},{"given":"Jie","family":"Wang","sequence":"additional","affiliation":[]}],"member":"351","published-online":{"date-parts":[[2021,10,6]]},"reference":[{"key":"atypb1","first-page":"893","author":"Anantharam V.","year":"2017","journal-title":"Washington, DC"},{"key":"atypb2","first-page":"291","author":"Anil C.","year":"2019","journal-title":"PMLR"},{"key":"atypb3","first-page":"214","author":"Arjovsky M.","year":"2017","journal-title":"PMLR"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1137\/130939730"},{"key":"atypb6","first-page":"435","author":"B\u00e9gin L.","year":"2016","journal-title":"PMLR"},{"key":"atypb7","first-page":"531","author":"Belghazi M. I.","year":"2018","journal-title":"PMLR"},{"key":"atypb8","doi-asserted-by":"crossref","first-page":"2239","DOI":"10.1007\/s11005-017-0990-7","volume":"107","author":"Berta M.","year":"2017","journal-title":"Lett. Math. Phys."},{"key":"atypb12","first-page":"418","author":"Butte A.","year":"2000","journal-title":"NJ"},{"key":"atypb13","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1007\/BF02551274","volume":"2","author":"Cybenko G.","year":"1989","journal-title":"Math. Control Signal Systems"},{"key":"atypb14","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1002\/cpa.3160360204","volume":"36","author":"Donsker M. D.","year":"1983","journal-title":"Comm. Pure Appl. Math."},{"key":"atypb17","doi-asserted-by":"crossref","first-page":"1507","DOI":"10.1214\/19-AAP1468","volume":"30","author":"Dupuis P.","year":"2020","journal-title":"Ann. Appl. Probab."},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1137\/120880811"},{"key":"atypb21","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1007\/s10107-015-0871-8","volume":"156","author":"Ghadimi S.","year":"2016","journal-title":"Math. Program."},{"key":"atypb22","doi-asserted-by":"crossref","first-page":"124","DOI":"10.1016\/j.ins.2013.06.018","volume":"249","author":"Gil M.","year":"2013","journal-title":"Inform. Sci."},{"key":"atypb23","first-page":"2672","author":"Goodfellow I. J.","year":"2014","journal-title":"MA"},{"key":"atypb24","first-page":"5769","author":"Gulrajani I.","year":"2017","journal-title":"NY"},{"key":"atypb26","first-page":"397","author":"Kandasamy K.","year":"2015","journal-title":"Red Hook NY"},{"key":"atypb27","first-page":"2306","author":"Kidger P.","year":"2020","journal-title":"PMLR"},{"key":"atypb29","doi-asserted-by":"crossref","first-page":"3354","DOI":"10.1073\/pnas.1309933111","volume":"111","author":"Kinney J. B.","year":"2014","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"atypb30","doi-asserted-by":"crossref","first-page":"1667","DOI":"10.1109\/TPAMI.2002.1114861","volume":"24","author":"Kwak N.","year":"2002","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"atypb34","doi-asserted-by":"crossref","first-page":"4394","DOI":"10.1109\/TIT.2006.881731","volume":"52","author":"Liese F.","year":"2006","journal-title":"IEEE Trans. Inform. Theory"},{"key":"atypb35","first-page":"6232","author":"Lu Z.","year":"2017","journal-title":"NY"},{"key":"atypb36","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1109\/42.563664","volume":"16","author":"Maes F.","year":"1997","journal-title":"IEEE Trans. Med. Imaging"},{"key":"atypb37","doi-asserted-by":"crossref","first-page":"5847","DOI":"10.1109\/TIT.2010.2068870","volume":"56","author":"Nguyen X.","year":"2010","journal-title":"IEEE Trans. Inform. Theory"},{"key":"atypb38","first-page":"271","author":"Nowozin S.","year":"2016","journal-title":"NY"},{"key":"atypb39","doi-asserted-by":"crossref","first-page":"1191","DOI":"10.1162\/089976603321780272","volume":"15","author":"Paninski L.","year":"2003","journal-title":"Neural Comput."},{"key":"atypb42","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1017\/S0962492900002919","volume":"8","author":"Pinkus A.","year":"1999","journal-title":"Acta Numer."},{"key":"atypb44","doi-asserted-by":"publisher","DOI":"10.1137\/140997774"},{"key":"atypb53","doi-asserted-by":"crossref","first-page":"3797","DOI":"10.1109\/TIT.2014.2320500","volume":"60","author":"Van Erven T.","year":"2014","journal-title":"IEEE Trans. Inform. Theory"}],"container-title":["SIAM Journal on Mathematics of Data Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/20M1368926","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,12,23]],"date-time":"2021-12-23T15:08:30Z","timestamp":1640272110000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/20M1368926"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1]]},"references-count":29,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["10.1137\/20M1368926"],"URL":"https:\/\/doi.org\/10.1137\/20m1368926","relation":{},"ISSN":["2577-0187"],"issn-type":[{"type":"electronic","value":"2577-0187"}],"subject":[],"published":{"date-parts":[[2021,1]]}}}