Improving on Deterministic Approximate Bayesian Inferences for Mixture Distributions

This paper presents the branching approach, which can improve deterministic implementation methods (such as variational Bayesian inference and expectation propagation method) for Bayesian mixture distributions. This proposed approach utilizes a set of artificial conditions defined by using the latent variables of the mixture distribution. This condition set is updated iteratively by branching based on a condition selected from the previous condition set. The target approximate Bayesian inference is obtained by merging the approximate conditional inferences under each condition in the condition set. The proposed approach is compared with several standard implementation methods by using a numerical example and a real-world example.