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
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 generalized variational Bayes
Theoretical Computer Science
Upper bound for variational free energy of Bayesian networks
Machine Learning
Accuracy of Loopy belief propagation in Gaussian models
Neural Networks
Generalization error of automatic relevance determination
ICANN'07 Proceedings of the 17th international conference on Artificial neural networks
Theoretical Analysis of Bayesian Matrix Factorization
The Journal of Machine Learning Research
Hi-index | 0.00 |
Bayesian learning has been widely used and proved to be effective in many data modeling problems. However, computations involved in it require huge costs and generally cannot be performed exactly. The variational Bayesian approach, proposed as an approximation of Bayesian learning, has provided computational tractability and good generalization performance in many applications. The properties and capabilities of variational Bayesian learning itself have not been clarified yet. It is still unknown how good approximation the variational Bayesian approach can achieve. In this paper, we discuss variational Bayesian learning of Gaussian mixture models and derive upper and lower bounds of variational stochastic complexities. The variational stochastic complexity, which corresponds to the minimum variational free energy and a lower bound of the Bayesian evidence, not only becomes important in addressing the model selection problem, but also enables us to discuss the accuracy of the variational Bayesian approach as an approximation of true Bayesian learning.