Variational Inference for Hierarchical Dirichlet Process Based Nonparametric Models

We examine two popular statistical models, the hidden Markov model and mixed membership stochastic blockmodel. Using the hierarchical Dirichlet process, we define nonparametric variants of these models. We develop a memoized online variational inference algorithm that uses a new objective function to properly penalize the addition of unneeded states in either model. Finally, we demonstrate that our models outperform competing methods in a wide array of tasks, including speaker diarization, academic co-authorship network analysis, and motion capture comprehension.