Density-Preserving Hierarchical EM Algorithm: Simplifying Gaussian Mixture Models for Approximate Inference

We propose an algorithm for simplifying a finite mixture model into a reduced mixture model with fewer mixture components. The reduced model is obtained by maximizing a variational lower bound of the expected log-likelihood of a set of virtual samples. We develop three applications for our mixture simplification algorithm: recursive Bayesian filtering using Gaussian mixture model posteriors, KDE mixture reduction, and belief propagation without sampling. For recursive Bayesian filtering, we propose an efficient algorithm for approximating an arbitrary likelihood function as a sum of scaled Gaussian. Experiments on synthetic data, human location modeling, visual tracking, and vehicle self-localization show that our algorithm can be widely used for probabilistic data analysis, and is more accurate than other mixture simplification methods.