Upper bound for variational free energy 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 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.