Algebraic Analysis for Nonidentifiable Learning Machines
Neural Computation
Inferring parameters and structure of latent variable models by variational bayes
UAI'99 Proceedings of the Fifteenth conference on Uncertainty in artificial intelligence
Optimal error exponents in hidden Markov models order estimation
IEEE Transactions on Information Theory
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Variational Bayesian learning is proposed for approximation method of Bayesian learning. In spite of efficiency and experimental good performance, their mathematical property has not yet been clarified. In this paper we analyze variational Bayesian Stochastic Context Free Grammar which includes the true distribution thus the model is non-identifiable. We derive their asymptotic free energy. It is shown that in some prior conditions, the free energy is much smaller than identifiable models and satisfies eliminating redundant non-terminals.