Neural Computation
Keeping the neural networks simple by minimizing the description length of the weights
COLT '93 Proceedings of the sixth annual conference on Computational learning theory
Learning in graphical models
Bayesian Networks and Decision Graphs
Bayesian Networks and Decision Graphs
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
Stochastic complexity of bayesian networks
UAI'03 Proceedings of the Nineteenth conference on Uncertainty in Artificial Intelligence
Upper bound for variational free energy of Bayesian networks
Machine Learning
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In recent years, variational Bayesian learning has been used as an approximation of Bayesian learning. In spite of the computational tractability and good generalization performance in many applications, its statistical properties have yet to be clarified. In this paper, we analyze the statistical property in variational Bayesian learning of Bayesian networks which are widely used in information processing and uncertain artificial intelligence. We derive upper bounds for asymptotic variational stochastic complexities of Bayesian networks. Our result theoretically supports the effectiveness of variational Bayesian learning as an approximation of Bayesian learning.