{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,24]],"date-time":"2026-01-24T01:26:45Z","timestamp":1769218005802,"version":"3.49.0"},"reference-count":32,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2024,6,19]],"date-time":"2024-06-19T00:00:00Z","timestamp":1718755200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,6,19]],"date-time":"2024-06-19T00:00:00Z","timestamp":1718755200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int J Data Sci Anal"],"published-print":{"date-parts":[[2025,9]]},"DOI":"10.1007\/s41060-024-00580-3","type":"journal-article","created":{"date-parts":[[2024,6,19]],"date-time":"2024-06-19T15:02:32Z","timestamp":1718809352000},"page":"2113-2128","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Implicitly adaptive optimal proposal in variational inference for Bayesian learning"],"prefix":"10.1007","volume":"20","author":[{"given":"Mostafa","family":"Bakhouya","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hassan","family":"Ramchoun","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohammed","family":"Hadda","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tawfik","family":"Masrour","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,6,19]]},"reference":[{"key":"580_CR1","first-page":"995","volume":"1","author":"JR Anderson","year":"1987","unstructured":"Anderson, J.R., Peterson, C.: A mean field theory learning algorithm for neural networks. Complex Syst. 1, 995\u20131019 (1987)","journal-title":"Complex Syst."},{"issue":"518","key":"580_CR2","doi-asserted-by":"publisher","first-page":"859","DOI":"10.1080\/01621459.2017.1285773","volume":"112","author":"DM Blei","year":"2017","unstructured":"Blei, D.M., Kucukelbir, A., McAuliffe, J.D.: Variational inference: a review for statisticians. J. Am. Stat. Assoc. 112(518), 859\u2013877 (2017)","journal-title":"J. Am. Stat. Assoc."},{"issue":"4","key":"580_CR3","doi-asserted-by":"publisher","first-page":"60","DOI":"10.1109\/MSP.2017.2699226","volume":"34","author":"MF Bugallo","year":"2017","unstructured":"Bugallo, M.F., Elvira, V., Martino, L., Luengo, D., Miguez, J., Djuric, P.M.: Adaptive importance sampling: the past, the present, and the future. IEEE Signal Process. Mag. 34(4), 60\u201379 (2017)","journal-title":"IEEE Signal Process. Mag."},{"issue":"4","key":"580_CR4","doi-asserted-by":"publisher","first-page":"907","DOI":"10.1198\/106186004X12803","volume":"13","author":"O Capp\u00e9","year":"2004","unstructured":"Capp\u00e9, O., Guillin, A., Marin, J.-M., Robert, C.P.: Population monte carlo. J. Comput. Graph. Stat. 13(4), 907\u2013929 (2004)","journal-title":"J. Comput. Graph. Stat."},{"issue":"1","key":"580_CR5","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1093\/biomet\/83.1.81","volume":"83","author":"G Casella","year":"1996","unstructured":"Casella, G., Robert, C.P.: Rao-blackwellisation of sampling schemes. Biometrika 83(1), 81\u201394 (1996)","journal-title":"Biometrika"},{"key":"580_CR6","unstructured":"Deniz\u00a0Akyildiz, \u00d6., M\u00edguez, J.: Convergence rates for optimised adaptive importance samplers. arXiv e-prints, pages arXiv\u20131903 (2019)"},{"issue":"1","key":"580_CR7","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1214\/18-STS668","volume":"34","author":"V Elvira","year":"2019","unstructured":"Elvira, V., Martino, L., Luengo, D., Bugallo, M.F.: Generalized multiple importance sampling. Stat. Sci. 34(1), 129\u2013155 (2019)","journal-title":"Stat. Sci."},{"key":"580_CR8","doi-asserted-by":"crossref","unstructured":"Feng, M.B., Maggiar, A., Staum, J., W\u00e4chter, A.: Uniform convergence of sample average approximation with adaptive multiple importance sampling. In: 2018 Winter Simulation Conference (WSC), pp. 1646\u20131657. IEEE (2018)","DOI":"10.1109\/WSC.2018.8632370"},{"key":"580_CR9","unstructured":"Figurnov, M., Mohamed, S., Mnih, A.: Implicit reparameterization gradients. Adv. Neural Inf. Process. Syst. 31 (2018)"},{"key":"580_CR10","unstructured":"Jaakkola, T.S., Jordan, M.I.: A variational approach to bayesian logistic regression models and their extensions. In: Sixth International Workshop on Artificial Intelligence and Statistics, pp. 283\u2013294. PMLR (1997)"},{"key":"580_CR11","unstructured":"Jankowiak, M., Obermeyer, F.: Pathwise derivatives beyond the reparameterization trick. In: International Conference on Machine Learning, pp. 2235\u20132244. PMLR (2018)"},{"key":"580_CR12","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1023\/A:1007665907178","volume":"37","author":"MI Jordan","year":"1999","unstructured":"Jordan, M.I., Ghahramani, Z., Jaakkola, T.S., Saul, L.K.: An introduction to variational methods for graphical models. Mach. Learn. 37, 183\u2013233 (1999)","journal-title":"Mach. Learn."},{"issue":"2","key":"580_CR13","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1111\/j.2517-6161.1987.tb01685.x","volume":"49","author":"B J\u00f8rgensen","year":"1987","unstructured":"J\u00f8rgensen, B.: Exponential dispersion models. J. R. Stat. Soc.: Ser. B (Methodol.) 49(2), 127\u2013145 (1987)","journal-title":"J. R. Stat. Soc.: Ser. B (Methodol.)"},{"key":"580_CR14","first-page":"263","volume":"1","author":"H Kahn","year":"1953","unstructured":"Kahn, H., Marshall, A.W.: Methods of reducing sample size in monte carlo computations. Oper. Res. 1, 263\u2013278 (1953)","journal-title":"Oper. Res."},{"key":"580_CR15","unstructured":"Kingma, D.P., Welling, M.: Auto-encoding variational bayes. arXiv preprint arXiv:1312.6114 (2013)"},{"issue":"1","key":"580_CR16","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1214\/aoms\/1177729694","volume":"22","author":"S Kullback","year":"1951","unstructured":"Kullback, S., Leibler, R.A.: On information and sufficiency. Ann. Math. Stat. 22(1), 79\u201386 (1951)","journal-title":"Ann. Math. Stat."},{"key":"580_CR17","doi-asserted-by":"crossref","unstructured":"Li, X., Li, C., Chi, J., Ouyang, J.: Variance reduction in black-box variational inference by adaptive importance sampling. In: IJCAI, pp. 2404\u20132410 (2018)","DOI":"10.24963\/ijcai.2018\/333"},{"key":"580_CR18","doi-asserted-by":"crossref","unstructured":"Mostafa, B., Hassan, R., Mohammed, H., Tawfik, M.: A review of variational inference for bayesian neural network. In: International Conference on Artificial Intelligence & Industrial Applications, pp. 231\u2013243. Springer (2023)","DOI":"10.1007\/978-3-031-43520-1_20"},{"key":"580_CR19","doi-asserted-by":"crossref","unstructured":"Mostafa, B., Hassan, R., Mohammed, H., Tawfik, M.: Gaussian mixture models for training bayesian convolutional neural networks. Evolut. Intell. 1\u201322 (2024)","DOI":"10.1007\/s12065-023-00900-9"},{"issue":"449","key":"580_CR20","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1080\/01621459.2000.10473909","volume":"95","author":"A Owen","year":"2000","unstructured":"Owen, A., Zhou, Y.: Safe and effective importance sampling. J. Am. Stat. Assoc. 95(449), 135\u2013143 (2000)","journal-title":"J. Am. Stat. Assoc."},{"key":"580_CR21","unstructured":"Owen, A.B.: Monte carlo theory, methods and examples (2013)"},{"issue":"2","key":"580_CR22","doi-asserted-by":"publisher","first-page":"16","DOI":"10.1007\/s11222-020-09982-2","volume":"31","author":"T Paananen","year":"2021","unstructured":"Paananen, T., Piironen, J., B\u00fcrkner, P.-C., Vehtari, A.: Implicitly adaptive importance sampling. Stat. Comput. 31(2), 16 (2021)","journal-title":"Stat. Comput."},{"key":"580_CR23","unstructured":"Paisley, J., Blei, D.M., Jordan, M.I.: Variational bayesian inference with stochastic search. In: Proceedings of the 29th International Conference on Machine Learning (2012)"},{"key":"580_CR24","unstructured":"Ranganath, R., Gerrish, S., Blei, D.: Black box variational inference. In: Artificial Intelligence and Statistics, pp. 814\u2013822. PMLR (2014)"},{"key":"580_CR25","unstructured":"Rezende, D.J., Mohamed, S., Wierstra, D.: Stochastic backpropagation and approximate inference in deep generative models. In: International Conference on Machine Learning, pp. 1278\u20131286. PMLR (2014)"},{"key":"580_CR26","doi-asserted-by":"crossref","unstructured":"Robbins, H., Monro, S.: A stochastic approximation method. Ann. Math. Stat. 400\u2013407 (1951)","DOI":"10.1214\/aoms\/1177729586"},{"key":"580_CR27","unstructured":"Ross, S.M.: Simulation (2002)"},{"key":"580_CR28","unstructured":"Ruiz, F.J., Titsias, M.K., Blei, D.M.: Overdispersed black-box variational inference. In: Proceedings of the Thirty-Second Conference on Uncertainty in Artificial Intelligence, pp. 647\u2013656 (2016)"},{"key":"580_CR29","doi-asserted-by":"crossref","unstructured":"Shah, H., Barber, D., Botev, A.: Overdispersed variational autoencoders. In: 2017 International Joint Conference on Neural Networks (IJCNN), pp. 1109\u20131116. IEEE (2017)","DOI":"10.1109\/IJCNN.2017.7965976"},{"key":"580_CR30","doi-asserted-by":"crossref","unstructured":"Veach, E., Guibas, L.J.: Optimally combining sampling techniques for monte carlo rendering. In: Proceedings of the 22nd Annual Conference on Computer Graphics and Interactive Techniques, pp. 419\u2013428 (1995)","DOI":"10.1145\/218380.218498"},{"key":"580_CR31","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1023\/A:1022672621406","volume":"8","author":"RJ Williams","year":"1992","unstructured":"Williams, R.J.: Simple statistical gradient-following algorithms for connectionist reinforcement learning. Mach. Learn. 8, 229\u2013256 (1992)","journal-title":"Mach. Learn."},{"key":"580_CR32","doi-asserted-by":"crossref","unstructured":"Zhang, C., B\u00fctepage, J., Kjellstr\u00f6m, H., Mandt, S.: Advances in variational inference. IEEE Trans. Pattern Anal. Mach. Intell. 41(8), 2008\u20132026 (2018)","DOI":"10.1109\/TPAMI.2018.2889774"}],"container-title":["International Journal of Data Science and Analytics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s41060-024-00580-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s41060-024-00580-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s41060-024-00580-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,5]],"date-time":"2025-09-05T21:18:45Z","timestamp":1757107125000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s41060-024-00580-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,6,19]]},"references-count":32,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2025,9]]}},"alternative-id":["580"],"URL":"https:\/\/doi.org\/10.1007\/s41060-024-00580-3","relation":{},"ISSN":["2364-415X","2364-4168"],"issn-type":[{"value":"2364-415X","type":"print"},{"value":"2364-4168","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,6,19]]},"assertion":[{"value":"22 December 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 May 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 June 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no Conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"This article does not contain any studies with human participants or animals performed by any of the authors.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}}]}}