{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T14:55:35Z","timestamp":1768488935239,"version":"3.49.0"},"reference-count":43,"publisher":"Informa UK Limited","issue":"2","license":[{"start":{"date-parts":[[2023,11,21]],"date-time":"2023-11-21T00:00:00Z","timestamp":1700524800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"funder":[{"name":"ARC Center of Excellence grant","award":["CE140100049"],"award-info":[{"award-number":["CE140100049"]}]}],"content-domain":{"domain":["www.tandfonline.com"],"crossmark-restriction":true},"short-container-title":["Journal of Computational and Graphical Statistics"],"published-print":{"date-parts":[[2024,4,2]]},"DOI":"10.1080\/10618600.2023.2262080","type":"journal-article","created":{"date-parts":[[2023,9,26]],"date-time":"2023-09-26T17:22:27Z","timestamp":1695748947000},"page":"665-680","update-policy":"https:\/\/doi.org\/10.1080\/tandf_crossmark_01","source":"Crossref","is-referenced-by-count":6,"title":["Flexible Variational Bayes Based on a Copula of a Mixture"],"prefix":"10.1080","volume":"33","author":[{"given":"David","family":"Gunawan","sequence":"first","affiliation":[{"name":"School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, Australia"},{"name":"Australian Center of Excellence for Mathematical and Statistical Frontiers, Parkville, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Robert","family":"Kohn","sequence":"additional","affiliation":[{"name":"School of Economics, UNSW Business School, University of New South Wales, Sydney, Australia"},{"name":"Australian Center of Excellence for Mathematical and Statistical Frontiers, Parkville, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"David","family":"Nott","sequence":"additional","affiliation":[{"name":"Department of Statistics and Data Science, National University of Singapore, Singapore"},{"name":"Institute of Operations Research and Analytics, National University of Singapore, Singapore"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"301","published-online":{"date-parts":[[2023,11,21]]},"reference":[{"key":"e_1_3_4_2_1","doi-asserted-by":"publisher","DOI":"10.1162\/089976698300017746"},{"key":"e_1_3_4_3_1","first-page":"171","article-title":"\u201cA Class of Distributions Which Includes the Normal Ones,\u201d","volume":"12","author":"Azzalini A.","year":"1985","unstructured":"Azzalini, A. (1985), \u201cA Class of Distributions Which Includes the Normal Ones,\u201d Scandinavian Journal of Statistics, 12, 171\u2013178.","journal-title":"Scandinavian Journal of Statistics"},{"key":"e_1_3_4_4_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2017.1285773"},{"key":"e_1_3_4_5_1","first-page":"177","volume-title":"Proceedings of the 19th International Conference on Computational Statistics (COMPSTAT2010),","author":"Bottou L.","year":"2010","unstructured":"Bottou, L. (2010), \u201cLarge-Scale Machine Learning with Stochastic Gradient Descent,\u201d in Proceedings of the 19th International Conference on Computational Statistics (COMPSTAT2010), pp. 177\u2013187, Springer."},{"key":"e_1_3_4_6_1","article-title":"\u201cUniversal Boosting Variational Inference,\u201d","volume":"32","author":"Campbell T.","year":"2019","unstructured":"Campbell, T., and Li, X. (2019), \u201cUniversal Boosting Variational Inference,\u201d in Advances in Neural Information Processing Systems (Vol. 32).","journal-title":"Advances in Neural Information Processing Systems"},{"key":"e_1_3_4_7_1","first-page":"2239","article-title":"\u201cGaussian Kullback-Leibler Approximate Inference,\u201d","volume":"14","author":"Challis E.","year":"2013","unstructured":"Challis, E., and Barber, D. (2013), \u201cGaussian Kullback-Leibler Approximate Inference,\u201d Journal of Machine Learning Research, 14, 2239\u20132286.","journal-title":"Journal of Machine Learning Research"},{"key":"e_1_3_4_8_1","volume-title":"Deep Learning","author":"Goodfellow I.","year":"2016","unstructured":"Goodfellow, I., Bengio, Y., and Courville, A. (2016), Deep Learning, Cambridge, MA: MIT Press."},{"key":"e_1_3_4_9_1","unstructured":"Guo F. Wang X. Broderick T. and Dunson D. B. (2017) \u201cBoosting Variational Inference \u201d ArXiv: 1611.05559v2."},{"key":"e_1_3_4_10_1","first-page":"1303","article-title":"\u201cStochastic Variational Inference,\u201d","volume":"14","author":"Hoffman M. D.","year":"2013","unstructured":"Hoffman, M. D., Blei, D. M., Wang, C., and Paisley, J. (2013), \u201cStochastic Variational Inference,\u201d Journal of Machine Learning Research, 14, 1303\u20131347.","journal-title":"Journal of Machine Learning Research"},{"key":"e_1_3_4_11_1","first-page":"1593","article-title":"\u201cThe no-u-turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo,\u201d","volume":"15","author":"Hoffman M. D.","year":"2014","unstructured":"Hoffman, M. D., and Gelman, A. (2014), \u201cThe no-u-turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo,\u201d Journal of Machine Learning Research, 15, 1593\u20131623.","journal-title":"Journal of Machine Learning Research"},{"key":"e_1_3_4_12_1","first-page":"4629","volume-title":"International Conference on Machine Learning","author":"Izmailov P.","year":"2021","unstructured":"Izmailov, P., Vikram, S., Hoffman, M. D., and Wilson, A. G. (2021), \u201cWhat are Bayesian Neural Network Posteriors Really Like?\u201d in International Conference on Machine Learning, pp. 4629\u20134640, PMLR."},{"key":"e_1_3_4_13_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-0716-1418-1"},{"key":"e_1_3_4_14_1","volume-title":"Uncertainty in Artificial Intelligence (UAI), Proceedings of the Thirty-Seventh Conference","author":"Jerfel G.","year":"2021","unstructured":"Jerfel, G., Wang, S. L., Fannjiang, C., Heller, K. A., Ma, Y., and Jordan, M. (2021), \u201cVariational Refinement for Importance Sampling Using the Forward Kullback-Leibler Divergence,\u201d in Uncertainty in Artificial Intelligence (UAI), Proceedings of the Thirty-Seventh Conference, eds. C. de Campos and M. Maathuis."},{"key":"e_1_3_4_15_1","doi-asserted-by":"publisher","DOI":"10.1109\/MCI.2022.3155327"},{"key":"e_1_3_4_16_1","unstructured":"Khaled M. and Kohn R. (2023) \u201cOn Approximating Copulas by Finite Mixtures \u201d https:\/\/arxiv.org\/pdf\/1705.10440.pdf."},{"key":"e_1_3_4_17_1","first-page":"878","volume-title":"Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, AISTATS 2017, 20-22 April 2017, Fort Lauderdale, FL, USA","author":"Khan M. E.","year":"2017","unstructured":"Khan, M. E., and Lin, W. (2017), \u201cConjugate-Computation Variational Inference: Converting Variational Inference in Non-Conjugate Models to Inferences in Conjugate Models,\u201d in Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, AISTATS 2017, 20-22 April 2017, Fort Lauderdale, FL, USA (Vol. 54), eds. A. Singh and X. J. Zhu, pp. 878\u2013887, PMLR."},{"key":"e_1_3_4_18_1","doi-asserted-by":"publisher","DOI":"10.23919\/ISITA.2018.8664326"},{"key":"e_1_3_4_19_1","volume-title":"3rd International Conference on Learning Representations","author":"Kingma D. P.","year":"2015","unstructured":"Kingma, D. P., and Ba, J. (2015), \u201cAdam: A Method for Stochastic Optimization,\u201d in 3rd International Conference on Learning Representations, eds. Y. Bengio and Y. LeCun, ICLR 2015, San Diego, CA, USA, May 7\u20139, 2015, Conference Track Proceedings."},{"key":"e_1_3_4_20_1","volume-title":"2nd International Conference on Learning Representations, ICLR 2014, Banff, AB, Canada, April 14\u201316, 2014, Conference Track Proceedings","author":"Kingma D. P.","year":"2014","unstructured":"Kingma, D. P., and Welling, M. (2014), \u201cAuto-Encoding Variational Bayes,\u201d in 2nd International Conference on Learning Representations, ICLR 2014, Banff, AB, Canada, April 14\u201316, 2014, Conference Track Proceedings."},{"key":"e_1_3_4_21_1","doi-asserted-by":"publisher","DOI":"10.1016\/0377-2217(95)00107-7"},{"key":"e_1_3_4_22_1","first-page":"1","article-title":"\u201cAutomatic Differentiation Variational Inference,\u201d","volume":"18","author":"Kucukelbir A.","year":"2017","unstructured":"Kucukelbir, A., Tran, D., Ranganath, R., Gelman, A., and Blei, D. M. (2017), \u201cAutomatic Differentiation Variational Inference,\u201d Journal of Machine Learning Research, 18, 1\u201345.","journal-title":"Journal of Machine Learning Research"},{"key":"e_1_3_4_23_1","volume-title":"UCI Machine Learning Repository","author":"Lichman M.","year":"2013","unstructured":"Lichman, M. (2013), \u201cUCI Machine Learning Repository,\u201d University of California, Irvine, School of Information and Computer Sciences."},{"key":"e_1_3_4_24_1","first-page":"3992","volume-title":"Proceedings of the 36th International Conference on Machine Learning, Volume 97 of Proceedings of Machine Learning Research","author":"Lin W.","year":"2019","unstructured":"Lin, W., Khan, M. E., and Schmidt, M. (2019), \u201cFast and Simple Natural-Gradient Variational Inference with Mixture of Exponential-Family Approximations,\u201d in Proceedings of the 36th International Conference on Machine Learning, Volume 97 of Proceedings of Machine Learning Research, eds. K. Chaudhuri and R. Salakhutdinov, pp. 3992\u20134002, PMLR."},{"key":"e_1_3_4_25_1","first-page":"464","volume-title":"Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics, Volume 84 of Proceedings of Machine Learning Research","author":"Locatello F.","year":"2018","unstructured":"Locatello, F., Khanna, R., Ghosh, J., and Ratsch, G. (2018), \u201cBoosting Variational Inference: An Optimization Perspective,\u201d in Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics, Volume 84 of Proceedings of Machine Learning Research, eds. A. Storkey and F. Perez-Cruz, pp. 464\u2013472. PMLR."},{"key":"e_1_3_4_26_1","first-page":"2420","volume-title":"Proceedings of the 34th International Conference on Machine Learning, Volume 70 of Proceedings of Machine Learning Research","author":"Miller A. C.","year":"2017","unstructured":"Miller, A. C., Foti, N. J., and Adams, R. P. (2017), \u201cVariational Boosting: Iteratively Refining Posterior Approximations,\u201d in Proceedings of the 34th International Conference on Machine Learning, Volume 70 of Proceedings of Machine Learning Research, pp. 2420\u20132429. PMLR."},{"key":"e_1_3_4_27_1","doi-asserted-by":"publisher","DOI":"10.1080\/10618600.2012.679897"},{"key":"e_1_3_4_28_1","doi-asserted-by":"publisher","DOI":"10.1080\/10618600.2017.1390472"},{"key":"e_1_3_4_29_1","doi-asserted-by":"publisher","DOI":"10.1198\/tast.2010.09058"},{"key":"e_1_3_4_30_1","first-page":"1363","volume-title":"Proceedings of the 29th International Conference on Machine Learning, ICML\u201912","author":"Paisley J.","year":"2012","unstructured":"Paisley, J., Blei, D. M., and Jordan, M. I. (2012), \u201cVariational Bayesian Inference with Stochastic Search,\u201d in Proceedings of the 29th International Conference on Machine Learning, ICML\u201912, pp. 1363\u20131370, Madison, WI, USA. Omnipress."},{"key":"e_1_3_4_31_1","first-page":"2617","article-title":"\u201cNormalizing Flows for Probabilistic Modeling and Inference,\u201d","volume":"22","author":"Papamakarios G.","year":"2021","unstructured":"Papamakarios, G., Nalisnick, E., Rezende, D. J., Mohamed, S., and Lakshminarayanan, B. (2021), \u201cNormalizing Flows for Probabilistic Modeling and Inference,\u201d The Journal of Machine Learning Research, 22, 2617\u20132680.","journal-title":"The Journal of Machine Learning Research"},{"key":"e_1_3_4_32_1","doi-asserted-by":"publisher","DOI":"10.1214\/21-STS840"},{"key":"e_1_3_4_33_1","first-page":"814","volume-title":"Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics, Volume 33 of Proceedings of Machine Learning Research","author":"Ranganath R.","year":"2014","unstructured":"Ranganath, R., Gerrish, S., and Blei, D. M. (2014), \u201cBlack Box Variational Inference,\u201d in Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics, Volume 33 of Proceedings of Machine Learning Research, eds. S. Kaski and J. Corander, pp. 814\u2013822, Reykjavik, Iceland. PMLR."},{"key":"e_1_3_4_34_1","first-page":"1530","volume-title":"International Conference on Machine Learning","author":"Rezende D.","year":"2015","unstructured":"Rezende, D., and Mohamed, S. (2015), \u201cVariational Inference with Normalizing Flows,\u201d in International Conference on Machine Learning, pp. 1530\u20131538. PMLR."},{"key":"e_1_3_4_35_1","first-page":"1278","volume-title":"Proceedings of the 31st International Conference on Machine Learning, Volume 32 of Proceedings of Machine Learning Research","author":"Rezende D. J.","year":"2014","unstructured":"Rezende, D. J., Mohamed, S., and Wierstra, D. (2014), \u201cStochastic Backpropagation and Approximate Inference in Deep Generative Models,\u201d in Proceedings of the 31st International Conference on Machine Learning, Volume 32 of Proceedings of Machine Learning Research, eds. E. P. Xing and T. Jebara, pp. 1278\u20131286, Beijing, China. PMLR."},{"key":"e_1_3_4_36_1","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177729586"},{"key":"e_1_3_4_37_1","doi-asserted-by":"publisher","DOI":"10.1214\/13-BA858"},{"key":"e_1_3_4_38_1","doi-asserted-by":"publisher","DOI":"10.1080\/10618600.2020.1740097"},{"key":"e_1_3_4_39_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11222-020-09944-8"},{"key":"e_1_3_4_40_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11222-017-9729-7"},{"key":"e_1_3_4_41_1","first-page":"1971","volume-title":"Proceedings of the 31st International Conference on Machine Learning, volume 32 of Proceedings of Machine Learning Research","author":"Titsias M.","year":"2014","unstructured":"Titsias, M., and L\u00e1zaro-Gredilla, M. (2014), \u201cDoubly Stochastic Variational Bayes for Non-conjugate Inference,\u201d in Proceedings of the 31st International Conference on Machine Learning, volume 32 of Proceedings of Machine Learning Research, eds. E. P. Xing and T. Jebara, pp. 1971\u20131979, Beijing, China, PMLR."},{"key":"e_1_3_4_42_1","doi-asserted-by":"publisher","DOI":"10.1080\/10618600.2019.1637747"},{"key":"e_1_3_4_43_1","volume-title":"NSP-sponsored Regional Research Conference at Southeastern Massachesetts University","author":"Tukey T. W.","year":"1977","unstructured":"Tukey, T. W. (1977), \u201cModern Techniques in Data Analysis,\u201d NSP-sponsored Regional Research Conference at Southeastern Massachesetts University, North Dartmount, Massachesetts."},{"key":"e_1_3_4_44_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/87.4.954"}],"container-title":["Journal of Computational and Graphical Statistics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.tandfonline.com\/doi\/pdf\/10.1080\/10618600.2023.2262080","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,24]],"date-time":"2024-09-24T22:00:49Z","timestamp":1727215249000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.tandfonline.com\/doi\/full\/10.1080\/10618600.2023.2262080"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,11,21]]},"references-count":43,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2024,4,2]]}},"alternative-id":["10.1080\/10618600.2023.2262080"],"URL":"https:\/\/doi.org\/10.1080\/10618600.2023.2262080","relation":{},"ISSN":["1061-8600","1537-2715"],"issn-type":[{"value":"1061-8600","type":"print"},{"value":"1537-2715","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,11,21]]},"assertion":[{"value":"The publishing and review policy for this title is described in its Aims & Scope.","order":1,"name":"peerreview_statement","label":"Peer Review Statement"},{"value":"http:\/\/www.tandfonline.com\/action\/journalInformation?show=aimsScope&journalCode=ucgs20","URL":"http:\/\/www.tandfonline.com\/action\/journalInformation?show=aimsScope&journalCode=ucgs20","order":2,"name":"aims_and_scope_url","label":"Aim & Scope"},{"value":"2021-06-29","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2023-09-08","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2023-11-21","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}