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
Model Selection Criteria for Learning Belief Nets: An Empirical Comparison
ICML '00 Proceedings of the Seventeenth International Conference on Machine Learning
Lack of Consistency of Mean Field and Variational break Bayes Approximations for State Space Models
Neural Processing Letters
Asymptotic Model Selection for Naive Bayesian Networks
The Journal of Machine Learning Research
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1 - Volume 01
Algebraic Analysis for Nonidentifiable Learning Machines
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
Upper bounds for variational stochastic complexities of bayesian networks
IDEAL'06 Proceedings of the 7th international conference on Intelligent Data Engineering and Automated Learning
Review: learning bayesian networks: Approaches and issues
The Knowledge Engineering Review
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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 in many applications, its statistical properties have yet to be clarified. In this paper, we focus on variational Bayesian learning of Bayesian networks which are widely used in information processing and uncertain artificial intelligence. We derive upper bounds for asymptotic variational free energy or stochastic complexities of bipartite Bayesian networks with discrete hidden variables. Our result theoretically supports the effectiveness of variational Bayesian learning as an approximation of Bayesian learning.