Upper bounds for variational stochastic complexities of Bayesian networks

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.