Pré-Publication, Document De Travail Année : 2025

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

Résumé

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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Dates et versions

hal-04901607 , version 1 (20-01-2025)
hal-04901607 , version 2 (22-01-2025)

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Titouan Vayer, Etienne Lasalle. A note on the relations between mixture models, maximum-likelihood and entropic optimal transport. 2025. ⟨hal-04901607v2⟩
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