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CANSSI Saskatchewan HSCC Webinar Series January-April 2022: Jiahua Chen

Wednesday, February 23, 2022 - 13:00 to 14:00
Jiahua Chen, UBC Statistics Professor
Statistics Seminar
Zoom (to register, see CANSSI website)

Registration & talk details

This talk has been organized by the Canadian Statistical Sciences Institute (CANSSI) Saskatchewan Health Science Collaborating Centre (HSCC). Learn more and register for this talk here.

Talk Title: Gaussian Mixture Reduction based on Composite Transportation Divergence

Abstract: In many applications, researchers wish to approximate a finite Gaussian mixture distribution with a high order by one with a lower order. Examples include density estimation, recursive tracking in hidden Markov model, and belief propagation. A direct solution to such a Gaussian Mixture Reduction problem is computationally challenging due to the non-convexity of commonly employed optimality targets.

One popular line of approach is to employ some clustering-based iterative algorithms. Neither their convergence nor destination, however, are thoroughly discussed. In this paper, we propose a new GMR method by minimizing some novel composite transportation divergence (CTD). This divergence permits an easy to implement Majorization-Minimization (MM) algorithm. We prove that the MM algorithms converge under general conditions, and many existing clustering-based algorithms are special cases of our approach. We further investigate the property of this approach with various choices of cost functions and demonstrate its effectiveness and computational costs.