Asymptotic analysis of approximate Bayesian inference methods

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We developed an approximate inference method for the constrained exponential-family mixture models that are used for the simultaneous dimensionality reduction and clustering of high-dimensional data. It was applied to the hand-written digit recognition task and its effectiveness was demonstrated. We also derived an approximate inference method for the varying binomial process that efficiently estimates the varying probabilities of some event. Furthermore, we demonstrated the general framework and the information-theoretic view of the local variational approximation.