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

Lei Yu, Tianyu Yang, Antoni B. Chan
2018 IEEE Transactions on Pattern Analysis and Machine Intelligence  
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
more » ... ose 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. Index Terms-density simplification, likelihood approximation, Gaussian mixture model, recursive Bayesian filtering. ! This is the author's version of an article that has been published in this journal. Changes were made to this version by the publisher prior to publication. The final version of record is available at http://dx. 3. In contrast, [21] defines localization as having a single primary mode in 10 frames and this mode is within 20m of the ground-truth. Here we use an evaluation criteria based on a more realistic scenario where the primary modes are used to propose possible locations while driving, without knowledge of the ground-truth. This is the author's version of an article that has been published in this journal. Changes were made to this version by the publisher prior to publication. The final version of record is available at http://dx.
doi:10.1109/tpami.2018.2845371 pmid:29994194 fatcat:5qm3jc4j7fesrg7j4wjixvtqne