Approximate Inference for Generic Likelihoods via Density-Preserving GMM Simplification

We consider recursive Bayesian filtering where the posterior is represented as a Gaussian mixture model (GMM), and the likelihood function as a sum of scaled Gaussians (SSG). In each iteration of filtering, the number of components increases. We propose an algorithm for simplifying a GMM into a reduced mixture model with fewer components, which is based on maximizing a variational lower bound of the expected log-likelihood of a set of virtual samples. We also propose an efficient algorithm for approximating an arbitrary likelihood function as an SSG. Experiments on synthetic 2D GMMs, simulated belief propagation and visual tracking show that our algorithm can be widely used for approximate inference.