Globally Convergent Algorithms for Learning Multivariate Generalized Gaussian Distributions

Bin Wang, Huanyu Zhang, Ziping Zhao, Ying Sun

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The multivariate generalized Gaussian distribution has been used intensively in various data analytics fields. Due to its flexibility in modeling different distributions, developing efficient methods to learn the model parameters has attracted lots of attentions. Existing algorithms including the popular fixed-point algorithms focus on learning the shape parameters and scatter matrices, but convergence is only established when the shape parameters are taken as given. When coupled with the shape parameters, convergence properties of the existing alternating algorithms remain unknown. In this paper, globally convergent algorithms based on the block majorization minimization method are proposed to jointly learn all the model parameters in the maximum likelihood estimation setting. The negative log-likelihood function w.r.t. the shape parameter is proved to be strictly convex, which to our best knowledge is the first result of this kind in the literature. Superior performance of the proposed algorithms are validated numerically based on synthetic data with comparisons to existing methods.

Original languageEnglish (US)
Title of host publication2021 IEEE Statistical Signal Processing Workshop, SSP 2021
PublisherIEEE Computer Society
Pages336-340
Number of pages5
ISBN (Electronic)9781728157672
DOIs
StatePublished - Jul 11 2021
Event21st IEEE Statistical Signal Processing Workshop, SSP 2021 - Virtual, Rio de Janeiro, Brazil
Duration: Jul 11 2021Jul 14 2021

Publication series

NameIEEE Workshop on Statistical Signal Processing Proceedings
Volume2021-July

Conference

Conference21st IEEE Statistical Signal Processing Workshop, SSP 2021
Country/TerritoryBrazil
CityVirtual, Rio de Janeiro
Period7/11/217/14/21

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering
  • Applied Mathematics
  • Signal Processing
  • Computer Science Applications

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