A GPM-based algorithm for solving regularized Wasserstein barycenter problems in some spaces of probability measures

S. Kum, Manh Hong Duong, Y. Lim, S. Yun

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Abstract

In this paper, we focus on the analysis of the regularized Wasserstein barycenter problem. We provide uniqueness and a characterization of the barycenter for two important classes of probability measures, each regularized by a particular entropy functional: (i) Gaussian distributions and (ii) q-Gaussian distributions. We propose an algorithm based on gradient projection method (GPM) in the space of matrices in order to compute these regularized barycenters. Finally, we numerically show the influence of parameters and stability of the algorithm under small perturbation of data and compare the gradient projection method with Riemannian gradient method.
Original languageEnglish
Article number114588
JournalJournal of Computational and Applied Mathematics
Volume416
Early online date12 Jul 2022
DOIs
Publication statusPublished - 21 Jul 2022

Bibliographical note

Funding Information:
The work of M. H. Duong was supported by EPSRC, UK Grants EP/W008041/1 and EP/V038516/1 . The work of S. Yun was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2016R1A5A1008055 and No. 2022R1A2C1011503 ). The work of Y. Lim was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) No. 2015R1A3A2031159 .

Publisher Copyright:
© 2022 The Author(s)

Keywords

  • Wasserstein barycenter
  • q-Gaussian measures
  • Gradient projection method
  • Optimization

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