{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,5]],"date-time":"2024-09-05T18:24:11Z","timestamp":1725560651970},"publisher-location":"Berlin, Heidelberg","reference-count":18,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540290735"},{"type":"electronic","value":"9783540317289"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2005]]},"DOI":"10.1007\/11559887_17","type":"book-chapter","created":{"date-parts":[[2005,10,13]],"date-time":"2005-10-13T13:21:18Z","timestamp":1129209678000},"page":"281-295","source":"Crossref","is-referenced-by-count":5,"title":["Variational Bayes Estimation of Mixing Coefficients"],"prefix":"10.1007","author":[{"given":"Bo","family":"Wang","sequence":"first","affiliation":[]},{"given":"D. M.","family":"Titterington","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"17_CR1","first-page":"21","volume-title":"Proc. 15th Conference on Uncertainty in Artificial Intelligence","author":"H. Attias","year":"1999","unstructured":"Attias, H.: Inferring parameters and structure of latent variable models by variational Bayes. In: Prade, H., Laskey, K. (eds.) Proc. 15th Conference on Uncertainty in Artificial Intelligence, Stockholm, Sweden, pp. 21\u201330. Morgan Kaufmann Publishers, San Francisco (1999)"},{"key":"17_CR2","first-page":"209","volume-title":"Advances in Neural Information Processing Systems","author":"H. Attias","year":"2000","unstructured":"Attias, H.: A variational Bayesian framework for graphical models. In: Solla, S., Leen, T., Muller, K.R. (eds.) Advances in Neural Information Processing Systems, vol.\u00a012, pp. 209\u2013215. MIT Press, Cambridge (2000)"},{"key":"17_CR3","unstructured":"Beal, M.J.: Variational Algorithms for Approximate Bayesian Inference. PhD thesis, University College London (2003)"},{"key":"17_CR4","first-page":"27","volume-title":"Proceedings Eighth International Conference on Artificial Intelligence and Statistics","author":"A. Corduneanu","year":"2001","unstructured":"Corduneanu, A., Bishop, C.M.: Variational Bayesian model selection for mixture distributions. In: Richardson, T., Jaakkola, T. (eds.) Proceedings Eighth International Conference on Artificial Intelligence and Statistics, pp. 27\u201334. Morgan Kaufmann, San Francisco (2001)"},{"key":"17_CR5","first-page":"507","volume-title":"Advances in Neural Information Processing Systems","author":"Z. Ghahramani","year":"2001","unstructured":"Ghahramani, Z., Beal, M.J.: Propagation algorithms for variational Bayesian learning. In: Leen, T., Dietterich, T., Tresp, V. (eds.) Advances in Neural Information Processing Systems, vol.\u00a013, pp. 507\u2013513. MIT Press, Cambridge (2001)"},{"key":"17_CR6","first-page":"331","volume-title":"COMPSTAT 2000","author":"K. Humphreys","year":"2000","unstructured":"Humphreys, K., Titterington, D.M.: Approximate Bayesian inference for simple mixtures. In: Bethlehem, J.G., van der Heijden, P.G.M. (eds.) COMPSTAT 2000, pp. 331\u2013336. Physica-Verlag, Heidelberg (2000)"},{"key":"17_CR7","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1023\/A:1008932416310","volume":"10","author":"T.S. Jaakkola","year":"2000","unstructured":"Jaakkola, T.S., Jordan, M.I.: Bayesian logistic regression: a variational approach. Statistics and Computing\u00a010, 25\u201337 (2000)","journal-title":"Statistics and Computing"},{"key":"17_CR8","first-page":"105","volume-title":"Learning in Graphical Models","author":"M.I. Jordan","year":"1999","unstructured":"Jordan, M.I., Ghahramani, Z., Jaakkola, T.S., Saul, L.K.: An introduction to variational methods for graphical models. In: Jordan, M.I. (ed.) Learning in Graphical Models, pp. 105\u2013162. MIT Press, Cambridge (1999)"},{"key":"17_CR9","unstructured":"MacKay, D.J.C.: Ensemble learning for hidden Markov models. Technical report, Cavendish Laboratory, University of Cambridge (1997)"},{"key":"17_CR10","unstructured":"Penny, W.D., Roberts, S.J.: Variational Bayes for 1-dimensional mixture models. Technical Report PARG-2000-01, Oxford University (2000)"},{"key":"17_CR11","doi-asserted-by":"publisher","first-page":"362","DOI":"10.1137\/0135032","volume":"35","author":"B.C. Peters","year":"1978","unstructured":"Peters, B.C., Walker, H.F.: An iterative procedure for obtaining maximum-likelihood estimates of the parameters for a mixture of normal distributions. SIAM J. Appl. Math.\u00a035, 362\u2013378 (1978)","journal-title":"SIAM J. Appl. Math."},{"key":"17_CR12","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1137\/1026034","volume":"26","author":"R.A. Redner","year":"1984","unstructured":"Redner, R.A., Walker, H.F.: Mixture densities, maximum likelihood and the EM algorithm. SIAM Review\u00a026, 195\u2013239 (1984)","journal-title":"SIAM Review"},{"key":"17_CR13","unstructured":"Wang, B., Titterington, D.M.: Convergence and asymptotic normality of variational Bayesian approximations for exponential family models with missing values. In: Chickering, M., Halpern, J. (eds.) Proceedings of the twentieth conference on Uncertainty in Artificial Intelligence, Banff, Canada, pp. 577\u2013584. AUAI Press (2004)"},{"key":"17_CR14","first-page":"80","volume":"31","author":"A.M. Walker","year":"1969","unstructured":"Walker, A.M.: On the asymptotic behaviour of posterior distributions. J. R. Statist. Soc. B\u00a031, 80\u201388 (1969)","journal-title":"J. R. Statist. Soc. B"},{"key":"17_CR15","first-page":"184","volume":"41","author":"C.C. Heyde","year":"1979","unstructured":"Heyde, C.C., Johnstone, I.M.: On asymptotic posterior normality for stochastic processes. J. R. Statist. Soc. B\u00a041, 184\u2013189 (1979)","journal-title":"J. R. Statist. Soc. B"},{"key":"17_CR16","first-page":"540","volume":"47","author":"C.F. Chen","year":"1985","unstructured":"Chen, C.F.: On asymptotic normality of limiting density functions with Bayesian implications. J. R. Statist. Soc. B\u00a047, 540\u2013546 (1985)","journal-title":"J. R. Statist. Soc. B"},{"key":"17_CR17","doi-asserted-by":"publisher","DOI":"10.1002\/9780470316870","volume-title":"Bayesian Theory","author":"J.M. Bernardo","year":"1994","unstructured":"Bernardo, J.M., Smith, A.F.M.: Bayesian Theory. John Wiley & Sons, Inc., New York (1994)"},{"key":"17_CR18","doi-asserted-by":"publisher","first-page":"2145","DOI":"10.1214\/aos\/1034713651","volume":"23","author":"S. Ghosal","year":"1995","unstructured":"Ghosal, S., Ghosh, J.K., Samanta, T.: On convergence of posterior distributions. The Annals of Statistics\u00a023, 2145\u20132152 (1995)","journal-title":"The Annals of Statistics"}],"container-title":["Lecture Notes in Computer Science","Deterministic and Statistical Methods in Machine Learning"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/11559887_17.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,27]],"date-time":"2021-04-27T07:12:36Z","timestamp":1619507556000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/11559887_17"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005]]},"ISBN":["9783540290735","9783540317289"],"references-count":18,"URL":"https:\/\/doi.org\/10.1007\/11559887_17","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2005]]}}}