Combined Belief Propagation-Mean Field Message Passing Algorithm for Dirichlet Process Mixtures

This letter deals with variational inference for Dirichlet process mixtures (DPM) models. We propose a combined message-passing algorithm introducing belief propagation (BP) into the original mean field (MF) rules, which leads to a more precise approximate posterior in DPM. To compute the BP message, we change an exponential distribution to a non-exponential utilizing a flexible expression of Dirac delta function. Therefore, BP rules can be used to handle such functions, resulting to a local exact expectation instead of approximate expectation from the original MF method. Simulation results show that the proposed combined BP- MF algorithm results in a significant performance improvement compared to the state-of-the-art inference methods.