Simplifying Mixture Models with the Hierarchical EM Algorithm
By Dr. Antoni B. CHAN
Department of Computer Science
City University of Hong Kong
We propose a hierarchical EM 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 four applications for our mixture simplification algorithm: recursive Bayesian filtering using Gaussian mixture model posteriors, KDE mixture reduction, belief propagation without sampling, and clustering hidden Markov models. 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, vehicle self-localization, and eye gaze analysis show that our algorithm can be widely used for probabilistic data analysis, and is more accurate than other mixture simplification methods.
Dr. Antoni B. Chan received the B.S. and M.Eng. degrees in electrical engineering from Cornell University, Ithaca, NY, USA, in 2000 and 2001, respectively, and the Ph.D. degree in electrical and computer engineering from University of California at San Diego (UCSD), La Jolla, CA, USA, in 2008. He was a Visiting Scientist with the Vision and Image Analysis Laboratory, Cornell University, from 2001 to 2003, and a Post-Doctoral Researcher with the Statistical Visual Computing Laboratory, UCSD, in 2009. In 2009 he joined the Department of Computer Science, City University of Hong Kong, Hong Kong, and is currently an Associate Professor. His research interests include computer vision, machine learning, pattern recognition, eye-gaze analysis, and music analysis. Dr. Chan received the National Science Foundation Integrative Graduate Education and Research Training Fellowship from 2006 to 2008, and an Early Career Award from the Research Grants Council of the Hong Kong Special Administrative Region, China, in 2012. He is currently a senior area editor for IEEE Signal Processing Letters, and was an area chair for ICCV 2015 and 2017.
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