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Statistics and Computing
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Inferring parameters and structure of latent variable models by variational bayes
UAI'99 Proceedings of the Fifteenth conference on Uncertainty in artificial intelligence
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SLSFS'05 Proceedings of the 2005 international conference on Subspace, Latent Structure and Feature Selection
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We investigate theoretically some properties of variational Bayes approximations based on estimating the mixing coefficients of known densities. We show that, with probability 1 as the sample size n grows large, the iterative algorithm for the variational Bayes approximation converges locally to the maximum likelihood estimator at the rate of O(1/n). Moreover, the variational posterior distribution for the parameters is shown to be asymptotically normal with the same mean but a different covariance matrix compared with those for the maximum likelihood estimator. Furthermore we prove that the covariance matrix from the variational Bayes approximation is ‘too small' compared with that for the MLE, so that resulting interval estimates for the parameters will be unrealistically narrow.