Fundamentals of statistical exponential families: with applications in statistical decision theory
Fundamentals of statistical exponential families: with applications in statistical decision theory
Neural Computation
On some inequalities for the gamma and psi functions
Mathematics of Computation
Online Model Selection Based on the Variational Bayes
Neural Computation
Algebraic Analysis for Nonidentifiable Learning Machines
Neural Computation
Nonmonotonic Generalization Bias of Gaussian Mixture Models
Neural Computation
Stochastic Complexities of Gaussian Mixtures in Variational Bayesian Approximation
The Journal of Machine Learning Research
Inferring parameters and structure of latent variable models by variational bayes
UAI'99 Proceedings of the Fifteenth conference on Uncertainty in artificial intelligence
Stochastic complexity of bayesian networks
UAI'03 Proceedings of the Nineteenth conference on Uncertainty in Artificial Intelligence
Stochastic complexity for mixture of exponential families in variational bayes
ALT'05 Proceedings of the 16th international conference on Algorithmic Learning Theory
Stochastic complexity for mixture of exponential families in generalized variational Bayes
Theoretical Computer Science
Variational Bayesian mixture model on a subspace of exponential family distributions
IEEE Transactions on Neural Networks
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In this paper, we focus on variational Bayesian learning of general mixture models. Variational Bayesian learning was proposed as an approximation of Bayesian learning. While it has provided computational tractability and good generalization in many applications, little has been done to investigate its theoretical properties. The asymptotic form was obtained for the stochastic complexity, or the free energy in the variational Bayesian learning of a mixture of exponential-family distributions, which is the main contribution this paper makes. We reveal that the stochastic complexities become smaller than those of regular statistical models, which implies that the advantages of Bayesian learning are still retained in variational Bayesian learning. Moreover, the derived bounds indicate what influence the hyperparameters have on the learning process, and the accuracy of the variational Bayesian approach as an approximation of true Bayesian learning.