A note on the relations between mixture models, maximum-likelihood and entropic optimal transport

Titouan Vayer, Etienne Lasalle
1/21/2025
stat.MLcs.LG

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Abstract

This note aims to demonstrate that performing maximum-likelihood estimation for a mixture model is equivalent to minimizing over the parameters an optimal transport problem with entropic regularization. The objective is pedagogical: we seek to present this already known result in a concise and hopefully simple manner. We give an illustration with Gaussian mixture models by showing that the standard EM algorithm is a specific block-coordinate descent on an optimal transport loss.

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Cite this paper

@article{vayer2025note,
  title  = {A note on the relations between mixture models, maximum-likelihood and entropic optimal transport},
  author = {Titouan Vayer and Etienne Lasalle},
  year   = {2025},
  eprint = {2501.12005},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2501.12005v2}
}

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