{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:57:09Z","timestamp":1760245029030,"version":"3.32.0"},"publisher-location":"Berlin, Heidelberg","reference-count":16,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540292425"},{"type":"electronic","value":"9783540316961"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2005]]},"DOI":"10.1007\/11564089_10","type":"book-chapter","created":{"date-parts":[[2005,10,10]],"date-time":"2005-10-10T13:51:09Z","timestamp":1128952269000},"page":"107-121","source":"Crossref","is-referenced-by-count":2,"title":["Stochastic Complexity for Mixture of Exponential Families in Variational Bayes"],"prefix":"10.1007","author":[{"given":"Kazuho","family":"Watanabe","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sumio","family":"Watanabe","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"10_CR1","first-page":"143","volume-title":"Bayesian Statistics","author":"H. Akaike","year":"1980","unstructured":"Akaike, H.: Likelihood and Bayes procedure. In: Bernald, J.M. (ed.) Bayesian Statistics, pp. 143\u2013166. University Press, Valencia (1980)"},{"issue":"217","key":"10_CR2","doi-asserted-by":"publisher","first-page":"373","DOI":"10.1090\/S0025-5718-97-00807-7","volume":"66","author":"H. Alzer","year":"1997","unstructured":"Alzer, H.: On some inequalities for the Gamma and Psi functions. Mathematics of computation\u00a066(217), 373\u2013389 (1997)","journal-title":"Mathematics of computation"},{"key":"10_CR3","unstructured":"Attias, H.: Inferring parameters and structure of latent variable models by variational bayes. In: Proc. of Uncertainty in Artificial Intelligence(UAI 1999) (1999)"},{"key":"10_CR4","unstructured":"Beal, M.J.: Variational algorithms for approximate bayesian inference. Ph.D. Thesis, University College London (2003)"},{"key":"10_CR5","unstructured":"Brown, L.D.: Fundamentals of statistical exponential families. IMS Lecture Notes-Monograph Series, vol.\u00a09 (1986)"},{"key":"10_CR6","doi-asserted-by":"crossref","unstructured":"Ghahramani, Z., Beal, M.J.: Graphical models and variational methods. In: Saad, D., Opper, M. (eds.) Advanced Mean Field Methods \u2013 Theory and Practice. MIT Press, Cambridge (2000)","DOI":"10.7551\/mitpress\/1100.003.0015"},{"key":"10_CR7","unstructured":"Hartigan, J.A.: A Failure of likelihood asymptotics for normal mixtures. In: Proceedings of the Berkeley Conference in Honor of J.Neyman and J. Kiefer, vol.\u00a02, pp. 807\u2013810 (1985)"},{"issue":"2","key":"10_CR8","doi-asserted-by":"publisher","first-page":"415","DOI":"10.1162\/neco.1992.4.3.415","volume":"4","author":"D.J. Mackay","year":"1992","unstructured":"Mackay, D.J.: Bayesian interpolation. Neural Computation\u00a04(2), 415\u2013447 (1992)","journal-title":"Neural Computation"},{"issue":"3","key":"10_CR9","doi-asserted-by":"publisher","first-page":"1080","DOI":"10.1214\/aos\/1176350051","volume":"14","author":"J. Rissanen","year":"1986","unstructured":"Rissanen, J.: Stochastic complexity and modeling. Annals of Statistics\u00a014(3), 1080\u20131100 (1986)","journal-title":"Annals of Statistics"},{"issue":"7","key":"10_CR10","doi-asserted-by":"publisher","first-page":"1649","DOI":"10.1162\/089976601750265045","volume":"13","author":"M. Sato","year":"2004","unstructured":"Sato, M.: Online model selection based on the variational bayes. Neural Computation\u00a013(7), 1649\u20131681 (2004)","journal-title":"Neural Computation"},{"issue":"2","key":"10_CR11","doi-asserted-by":"publisher","first-page":"461","DOI":"10.1214\/aos\/1176344136","volume":"6","author":"G. Schwarz","year":"1978","unstructured":"Schwarz, G.: Estimating the dimension of a model. Annals of Statistics\u00a06(2), 461\u2013464 (1978)","journal-title":"Annals of Statistics"},{"key":"10_CR12","doi-asserted-by":"crossref","unstructured":"Watanabe, K., Watanabe, S.: Lower bounds of stochastic complexities in variational bayes learning of gaussian mixture models. In: Proceedings of IEEE conference on Cybernetics and Intelligent Systems (CIS 2004), pp. 99\u2013104 (2004)","DOI":"10.1109\/ICCIS.2004.1460394"},{"issue":"4","key":"10_CR13","doi-asserted-by":"publisher","first-page":"899","DOI":"10.1162\/089976601300014402","volume":"13","author":"S. Watanabe","year":"2001","unstructured":"Watanabe, S.: Algebraic analysis for non-identifiable learning machines. Neural Computation\u00a013(4), 899\u2013933 (2001)","journal-title":"Neural Computation"},{"key":"10_CR14","doi-asserted-by":"publisher","first-page":"1029","DOI":"10.1016\/S0893-6080(03)00005-4","volume":"16","author":"K. Yamazaki","year":"2003","unstructured":"Yamazaki, K., Watanabe, S.: Singularities in mixture models and upper bounds of stochastic complexity. International Journal of Neural Networks\u00a016, 1029\u20131038 (2003)","journal-title":"International Journal of Neural Networks"},{"key":"10_CR15","unstructured":"Yamazaki, K., Watanabe, S.: Stochastic complexity of bayesian networks. In: Proc. of Uncertainty in Artificial Intelligence (UAI 2003) (2003)"},{"key":"10_CR16","doi-asserted-by":"crossref","unstructured":"Yamazaki, K., Watanabe, S.: Newton diagram and stochastic complexity in mixture of binomial distributions. In: Proc. of Algorithmic Learning Theory (ALT 2004), pp. 350\u2013364 (2004)","DOI":"10.1007\/978-3-540-30215-5_27"}],"container-title":["Lecture Notes in Computer Science","Algorithmic Learning Theory"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/11564089_10.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,4]],"date-time":"2025-01-04T21:43:18Z","timestamp":1736026998000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/11564089_10"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005]]},"ISBN":["9783540292425","9783540316961"],"references-count":16,"URL":"https:\/\/doi.org\/10.1007\/11564089_10","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2005]]}}}