A note on the relations between mixture models, maximum-likelihood and entropic optimal transport
Machine Learning
2025-01-24 v2 Machine Learning
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.
Cite
@article{arxiv.2501.12005,
title = {A note on the relations between mixture models, maximum-likelihood and entropic optimal transport},
author = {Titouan Vayer and Etienne Lasalle},
journal= {arXiv preprint arXiv:2501.12005},
year = {2025}
}