Department of Mathematics

Applied Mathematics

  •  Hyenkyun Woo, Korea University of Technology & Education
  •  Bregman-divergence for Legendre exponential families and data analysis
  •  08/24/2018
  •  4:10 PM - 5:00 PM
  •  C517 Wells Hall

Bregman-divergence is a well-known generalized distance framework in various applications, such as machine learning and image processing. In this talk, by using dual structure of the Bregman-divergence associated with the subclass of convex function of Legendre function, we analyze the structure of the Legendre exponential families whose cumulant function corresponds to the conjugate convex function of Legendre type. Actually, Legendre exponential families are the extended version of the regular exponential families to include non-regular exponential families, such as the inverse Gaussian distribution. The main advantage of the proposed Bregman-divergence-based approach is that it offers systematic successive approximation tools to handle closed domain issues arising in non-regular exponential families and the statistical distribution having discrete random variables, such as Bernoulli distribution and Poisson distribution. In addition, we also introduce the generalized center-based clustering algorithm based on the Tweedie distribution. 

 

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Department of Mathematics
Michigan State University
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