Stochastic Variational Inference for Structured Bayesian Hierarchical Models

In this paper we consider stochastic variational inference for finite mixtures of Dirichlet-Multinomial distributions. By exploiting simple hypotheses concerning the full conditional distributions of the hierarchical model and the distributions of the variational parameters, a gradient ascent algorithm can be derived that under the Robbins-Monro conditions converges to a local maximum of the surface approximating the posterior distribution.